High-power and high-beam-quality photonic-crystal surface-emitting lasers: a tutorial

Susumu Noda; Susumu Noda; Takuya Inoue; Takuya Inoue; Masahiro Yoshida; Masahiro Yoshida; John Gelleta; Menaka De Zoysa; Kenji Ishizaki

doi:10.1364/AOP.502863

1. Introduction

Semiconductor lasers have contributed to modern society over a wide range of fields, particularly data- and telecommunications and optical storage. To date, much interest has been devoted toward expanding the utility of semiconductor lasers for these fields, such as by widening their range of accessible wavelengths and improving their modulation speed. On the other hand, with regard to high-power applications, semiconductor lasers have had difficulty simultaneously achieving high output powers and high beam qualities. The brightness, defined as the optical power per unit area per unit solid angle, is a figure of merit which encapsulates both the output power and the beam quality and expresses how intensely a laser beam can be focused, or how narrowly an emitted laser beam diverges. The brightness of semiconductor lasers is much less than that (1 GW cm^–2 sr^–1) of bulky lasers such as gas and solid-state lasers. The low brightness of semiconductor lasers is due to the fact that the maximum emission area that can support operation in a single lateral mode is limited; namely, widening the emission area to increase the output power of semiconductor lasers leads to the onset of many lateral-mode oscillations, which seriously degrade the beam quality [1,2]. Even worse, under continuous-wave (CW) operation, the beam quality is prone to degrade further due to a thermally induced refractive index distribution inside the resonator, which is one of the critical factors responsible for unstable oscillation [3,4].

Realization of single-mode and high-brightness operation of semiconductor lasers, therefore, remains an ultimate, yet elusive goal in photonics and laser physics. Such high-brightness semiconductor lasers are required for a wide range of emerging applications, including next-generation remote sensing for smart mobility, high-precision laser processing for smart manufacturing, long-distance free-space (including inter-satellite) communications for beyond 5G communications, and even light propulsion for spaceflight [5–8]. The photonic-crystal surface-emitting laser (PCSEL) [9–22] shows potential for such directions. In 1999, we and another group independently and almost coincidentally proposed [9,10,23] the concept of using a singularity point of a band structure of two-dimensional (2D) photonic crystals (PCs) for a laser cavity of a semiconductor laser. In the other group, Meier et al. reported lasing at the X point of a triangular-lattice PC with an organic gain medium [23]. This laser, however, did not exhibit coherent, 2D resonance, an essential property to realize high-brightness operation. Because the resonance was based on the X point of the triangular-lattice PC, the fundamental Bloch waves propagating forward and backward along three different directions couple one dimensionally into each other, but not two-dimensionally among different directions, within the cavity [13]. On the other hand, we proposed the use of the Γ point of a triangular-lattice, semiconductor-based PC [9,10], whose fundamental Bloch waves propagate along three different directions and couple both one- and two-dimensionally to create truly coherent 2D resonance [9,10,13]. In addition, due to the nature of the Γ point, which is above the air light line, emission can be obtained from the surface of the PC; we named this laser a PCSEL to reflect this property.

Initial research on PCSELs [9,10,13] started with 2D triangular-lattice PCs [9,13] and were focused on investigating the basic laser physics and operation. In this research, unique beams including so-called vector beams were successfully observed. Then, PCSELs with 2D square-lattice PCs, especially those with transverse-electric- (TE-) polarized modes, became the main target of research, because these PCSELs were found to be more suitable for high-power single-mode lasing oscillation as well as for realizing various functionalities [15,18,20,21]. The key to realize 2D broad-area coherent oscillation in a 2D square-lattice PC with TE-polarized modes is to construct the PC with a large refractive index contrast such as air/semiconductor. In this high-contrast square-lattice PC, all four fundamental Bloch waves propagating in the PC can be coupled with each other through higher-order Bloch waves to form a stable 2D resonant mode. Note that PCSELs are different from 2D distributed feedback (DFB) lasers, whose periodic structures have a smaller refractive index contrast such as semiconductor/semiconductor (namely, all semiconductor), where the coupling among the fundamental Bloch waves cannot be facilitated because higher-order Bloch waves are not involved, which prevents the realization of 2D coherent oscillation.

Based on the PCSELs with a high-contrast 2D square-lattice PC, the output powers of PCSELs were continuously increased while their high beam qualities were maintained. Using a unit cell with asymmetric features such as triangular air holes, watt-class, single-mode, single-lobed operation was successfully realized in 2014 [20]. In 2018, even newer types of PCs called “double-lattice PCs” were introduced, where one lattice point group is shifted from a second in the x and y directions by approximately one quarter of the wavelength in the material [22]. Owing to this shift, the strength of optical coupling between fundamental Bloch waves through 180° diffraction is weakened because the optical path difference of 180° diffractions between the two lattice groups becomes π, leading to destructive interference for 180° diffractions. Consequently, the mode profile of each cavity mode spatially expands, and the optical losses of higher-order cavity modes from the periphery of the resonator increase relative to that of the fundamental cavity mode, resulting in a wider threshold gain margin between these modes and thus more stable oscillation in the fundamental mode. As a result, 10-W-class (and even higher-power) single-mode high-beam-quality operation was successfully realized under pulsed conditions using PCSELs with a circular diameter of 500 µm. These developed PCSELs had a very narrow beam divergence angle of 0.2° (at 1/e²), indicating the possibility of lens-free collimated operation, and they were successfully applied to lens-free light-detection and ranging (LiDAR) sensors with the smallest size of their class for smart mobility of robots [24]. Then, fine tuning of the distance between the two lattices and the balance between the sizes of the air holes of the two lattices of the double-lattice PC was investigated theoretically to control not only 180° but also 90° diffractions in the crystal [22]. Through such fine tuning, the optical couplings among fundamental Bloch waves were further optimized, and the device size which can support single- (fundamental-)mode operation was theoretically predicted to be able to be increased to up to 1–2.5 mm in diameter. Based on this concept, an output power of 7 W and a brightness of 180 MW cm^–2 sr^–1 were experimentally demonstrated using PCSELs with resonant diameters of 800 µm [22] under CW conditions.

Following these developments, a design guideline to realize single-mode high-brightness operation over areas of even larger (≥3 mm) diameters was established [25], which was based on the control of not only optical couplings among fundamental waves through in-plane 180° and 90° diffractions described above, but also the couplings through radiative waves, where the former and latter were referred to as Hermitian and non-Hermitian couplings because they are not and are accompanied by radiation loss, respectively. According to this guideline, the threshold gain difference between the fundamental mode and higher-order mode can be increased by increasing their difference of radiation loss, instead of their difference of in-plane loss. It was theoretically shown that 50-to-100-W single-mode operation can be realized using PCSELs with 3-mm-diameter areas, and 500-to-1000-W single-mode operation can be achieved using PCSELs with 10-mm-diameter areas. Based on this strategy, 50-W CW operation in a single mode (with a single wavelength) and with a nearly-diffraction-limited beam divergence angle of ∼0.05° was very recently achieved using a 3-mm-diameter PCSEL [26]. The brightness of this laser reached 1 GW cm^-2 sr^-1 even under CW conditions, which was more than one order of magnitude greater than those of conventional semiconductor lasers and even rivalled those of existing bulky gas and solid-state lasers.

In this tutorial paper, we first describe the theory of PCSELs including their basic structure and lasing principle, simulation methods, and strategies to realize single-mode, high-power and high-beam-quality operation (up to 1 kW). We then present experimental demonstrations, from pioneering works to the state of the art, including both pulsed and CW single-mode and high-brightness (1 GW cm^–2 sr^–1) operations. We also discuss applications toward smart mobility and smart manufacturing as well as the extension of wavelengths of PCSELs to the telecommunications band and the mid-infrared regime. Note that this tutorial paper does not deal with the high functionalities of PCSELs, such as beam steering [21,27], the emission of arbitrary beam patterns [21,27–29], high-peak-power short-pulse generation [30–32], and short-wavelength operation [33]; these developments will be reported elsewhere [34].

2. Theory

2.1 Basic Structure and Lasing Principle of PCSELs

In this subsection, we describe the basic structure of PCSELs and the lasing principle. Figure 1(a) shows a schematic cross section of typical PCSELs operating under current injection. A PC layer is located near an active layer so that the light generated in the active layer can couple evanescently to the PC layer. The active layer is typically composed of quantum wells (QWs) and has a gain with a TE polarization based on the band-to-band transition. As an exception, an active layer based on intersubband transition in QWs has a gain with a transverse magnetic (TM) polarization [35]. The active layer is sandwiched by upper and lower cladding layers for current injection. The lateral cavity size is defined by the size of the current injection region (=gain region), which is almost equal to the diameter of the bottom electrode. Unlike vertical-cavity surface-emitting lasers (VCSELs), in which light is confined with a pair of distributed Bragg reflectors (DBRs) in the vertical direction, PCSELs realize the confinement of light in the vertical direction using the refractive-index contrast akin to edge-emitting semiconductor lasers. Figure 1(b) shows an example of vertical electric field distribution of in-plane guided modes inside these multi-layered structures, where the refractive index of the PC layer is approximated with its average index. Here, light is distributed around the active layer, which generally has the highest refractive index among all the layers. When the electric field distribution in the vertical direction is defined as ${\varTheta _0}(z)$, the light confinement factors in the active layer and the PC layer (Γ_act and Γ_pc) are respectively determined as follows:

(1)$${\Gamma _{\textrm{act}}} = \frac{{\int_{\textrm{active layer}}^{} {{{|{{\Theta_0}(z)} |}^2}dz} }}{{\int_{\textrm{all layers}}^{} {{{|{{\Theta_0}(z)} |}^2}dz} }}, $$

(2)$${\Gamma _{\textrm{pc}}} = \frac{{\int_{\textrm{PC layer}}^{} {{{|{{\Theta_0}(z)} |}^2}dz} }}{{\int_{\textrm{all layers}}^{} {{{|{{\Theta_0}(z)} |}^2}dz} }}. $$

Here Γ_act determines the gain of the lasing mode, which typically takes a value of 2–3% per well. This value is larger than those of VCSELs (typically Γ_act =1–1.5% per well) because PCSELs can tightly confine the light near the active layer by adjusting the refractive-index contrast between the active layer and the cladding layers. The confinement factor Γ_pc determines the overall magnitude of optical couplings in the PC layer. When Γ_pc is increased, the strength of coupling among fundamental Bloch waves and that between each fundamental Bloch wave and a radiation wave are increased.

Figure 1. (a) Schematic cross section of a typical square-lattice PCSEL operating with current injection. (b) Vertical electric field distribution of in-plane guided modes inside the PCSEL. (c),(d) Schematic top views of square-lattice and triangular-lattice PCs with circular lattice points. (e),(f) Photonic band structures of the square-lattice and triangular-lattice PC for TE-like polarization. The electromagnetic field distribution of the lowest-frequency resonant mode at the Γ⁽²⁾ point is shown in each inset. (g) Bloch wave states in square-lattice PCs, represented by wave vectors (arrows) in reciprocal space including four basic waves (red arrows), high-order waves (gray arrows), and a radiative wave (blue dot).

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Figures 1(c) and 1(d) illustrate schematic top views of PC layers with square-lattice and triangular-lattice PCs, respectively, with circular lattice points, where the lattice constant (or period) is set as a. The refractive index distributions of the PC layer $\varepsilon ({x,y} )$ for these structures can be expressed with a Fourier expansion using their fundamental reciprocal lattice vectors ${\mathbf{G}_1},{\mathbf{G}_2}$ as

(3)$$\varepsilon ({x,y} )= \sum\limits_{m,n} {{\xi _{m,n}}} \exp [{i({m{\mathbf{G}_1} + n{\mathbf{G}_2}} )\cdot \mathbf{r}} ]\quad ({\mathbf{r} = (x,y),\;m,n:\textrm{integers}} ), $$

where ${\mathbf{G}_1},{\mathbf{G}_2}$ are given by

(4)$${\mathbf{G}_1} = \left( {\frac{{2\pi }}{a},0} \right),{\mathbf{G}_2} = \left( {0,\frac{{2\pi }}{a}} \right) \textrm{(for square-lattice PCs)},$$

(5)$${\mathbf{G}_1} = \left( {\frac{{2\pi }}{a}, - \frac{{2\pi }}{{\sqrt 3 a}}} \right),{\mathbf{G}_2} = \left( {0,\frac{{4\pi }}{{\sqrt 3 a}}} \right) \textrm {(for triangular-lattice PCs)}.$$

The corresponding photonic band structures for individual PC structures with a TE-like polarization are shown in Figs. 1(e) and 1(f), respectively. For typical PCSELs, lasing oscillation occurs at the second-order Γ (= Γ⁽²⁾) point [9,21], where the group velocity of light becomes zero and 2D broad-area resonant modes are formed by optical couplings among fundamental Bloch waves. Examples of the electromagnetic field distributions of the 2D resonant modes with the lowest frequencies at the Γ⁽²⁾ point are shown in the insets of these figures; those of the other band-edge modes are described in Section 2.3 [see Figs. 3(b) and 3(c)]. Note that other singularity points in the photonic band can be also utilized for 2D lasing oscillation; for example, so-called “modulated PCSELs” [21,27,29] utilize band-edge modes at the M point of the band structure of a square-lattice PC.

Here, let us focus on the Γ⁽²⁾ point of the square-lattice PC shown in Fig. 1(e), where four band-edge modes exist, and lasing oscillation occurs at one of these modes, in which the total loss becomes minimal. According to the Bloch’s theorem [36,37], the electric fields of these band-edge modes for an infinite-size PCSEL can be expressed as follows

(6)$${E_j}(\boldsymbol{r}) = \sum\limits_{m,n} {{E_{j,m,n}}(z)} \exp [{{{ - i2\pi ({mx + ny} )} / a}} ]\quad (j = x,y,z), $$

where ${E_{j,m,n}}(z)$ is the z-dependent amplitude of each Bloch wave, a is the lattice constant, and m and n are integers. Figure 1(g) shows a schematic of individual Bloch waves in reciprocal space. Red arrows show four fundamental Bloch waves propagating in the +x, –x, +y, and –y directions, which correspond to the terms with (m, n) = (1, 0), (–1, 0), (0, 1), (0, –1) in Eq. (6), respectively. Gray arrows in Fig. 1(g) represent high-order Bloch waves with m²+ n²> 1. A blue dot represents a radiative wave with m = n = 0, which corresponds to the propagating wave in the vertical direction. At the Γ⁽²⁾ point, mutual couplings among the four fundamental Bloch waves are induced directly or indirectly (through high-order Bloch waves) by the periodicity of the PC layer [or mG₁ + nG₂ vectors shown in Eq. (3)], which gives rise to the formation of 2D broad-area resonant modes. The surface emission occurs through the coupling between each fundamental Bloch wave and a radiative wave by G₁ or G₂ vectors in Eq. (3). A more detailed description of these optical couplings is given in Section 2.2d and Fig. 2.

Figure 2. Schematic of mutual couplings among fundamental Bloch waves inside of a square-lattice PCSEL with TE polarization: (a) direct 180° (1D) couplings; (b) indirect ±90° (2D) and 180° (1D) couplings; (c) indirect 180° (1D) couplings via radiative waves.

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As shown in the insets of Figs. 1(e) and 1(f) (and also as detailed in Section 2.3), some of the above 2D resonant modes at the Γ⁽²⁾ point have rotationally symmetric electromagnetic-field distributions, leading to very small radiation constants due to the cancellation of radiative waves in the far field, even though the resonant modes are located above the light line. Although this kind of cancellation effect of symmetric resonant modes has long since been pointed out in Ref. [13], such phenomena have recently attracted renewed interest in the context of bound states in continuum (BIC) [38], involving various mechanisms including symmetry protection and multiple-mode interference. Note that the BIC effect makes the radiation constant very small (ideally zero) as described above, leading to very-low-brightness operation of PCSELs. We therefore would like to emphasize that it is not appropriate to call PCSELs BIC lasers. To achieve single-mode high-brightness oscillation in PCSELs, it is important to understand the basic physics behind the formation of the 2D resonant modes from the viewpoint of coupling among various Bloch waves in the PC layer. These physics are detailed in the following subsections.

2.2 Simulation Method of PCSELs

In this subsection, we describe several representative simulation methods to analyze the lasing characteristics of PCSELs. Since each method has pros and cons, it is important to choose the most appropriate method according to the purpose of analysis.

2.2a Plane-Wave Expansion Method

The plane-wave expansion method (PWEM) [39,40] is a method for the calculation of photonic band structures with infinite periodic structures. In this method, frequencies and electromagnetic-field distributions of resonant modes can be calculated by expanding the Maxwell equations with a large number of plane waves. Although 2D PCSELs contain a PC layer with a finite thickness, its band structure can be calculated by using 2D PWEM by assuming a 2D PC with an infinite thickness whose refractive index contrast is properly modified according to Γ_pc [9]. The entire band structures shown in Figs. 1(e) and 1(f) were calculated by this method. To calculate the radiation constant of each resonant mode at the Γ⁽²⁾ point, 3D PWEM with perfect-matching layers in the vertical direction [40] can be used, although this technique requires large computational resources. In addition, PWEM is in general difficult to use for the analysis of the lasing modes of finite-sized PCSELs, although a super-cell method is employed.

2.2b Rigorous Coupled-Wave Analysis

Rigorous coupled-wave analysis (RCWA) [41] has been developed as a method to calculate transmission/reflection/absorption spectra for multi-layered structures with one-dimensional (1D) or 2D periodic structures in the layer plane. In typical RCWA simulations, scattering matrices of multilayered structures are considered and calculated by changing only the (real-valued) frequency of input light. For infinite-sized PCSELs, one can calculate both the frequencies and the radiation constants of band-edge resonant modes by instead considering a complex-valued frequency of light [42]. RCWA can accurately take into account the mixing (or crossing) of TE- and TM-like modes around the Γ⁽²⁾ point, as well as different values of Γ_pc for different band-edge modes with different vertical electromagnetic field distributions. Such features of RCWA enable the extraction of various design parameters of PCSELs such as coupling coefficients at angles of 180° (or in one dimension) and 90° (or in two dimensions); see Section 2.2d. It should be noted, however, that RCWA is also difficult to apply to the analysis of finite-sized PCSELs.

2.2c Finite-Difference Time-Domain Method

The finite-difference time-domain (FDTD) method [43] is a general method to analyze the spatial and temporal evolution of electromagnetic fields inside any structure in the time domain. FDTD can also deal with both infinite and finite structures by employing appropriate boundary conditions. For example, photonic band structures and radiation constants of the band-edge modes in an infinite-sized PCSEL can be analyzed using three-dimensional (3D)-FDTD with a periodic boundary condition within the plane of the PC, and this analysis can be performed using relatively few computational resources. On the other hand, the analysis of a finite-sized device consumes many more computational resources, which limits the maximum device size of PCSELs for simulation. In the early studies of triangular-lattice PCSELs (detailed in Section 3.1), 3D-FDTD was used to calculate the electromagnetic field distributions inside and outside the PCSELs [9,13]. In general, 3D-FDTD is useful in evaluating resonant frequencies, in-plane and vertical losses, and mode profiles of small-sized PCSELs with fewer than around 100 × 100 lattice points [44–46]. However, for the analysis of larger-sized PCSELs (for example, those with 1000 × 1000 lattice points), FDTD is not feasible in terms of computation time.

2.2d Coupled-Wave Theory

Unlike the above three numerical methods, coupled-wave theory (CWT) is a more analytical method used to predict the lasing characteristics of PCSELs, in which the amplitudes of the fundamental Bloch waves shown in Fig. 1(g) and their mutual couplings are considered. Investigations using CWT were initially carried out for 2D DFB lasers (namely, lasers with a low refractive-index-contrast square-lattice structure and TE-polarized modes) [47] by extending the CWT developed for conventional 1D DFB lasers [48]. These investigations did not consider 90° (or 2D) couplings among the four fundamental Bloch waves, and they concluded that 2D DFB structures with TE-polarized modes cannot oscillate coherently, as described in Section 1. A separate investigation using CWT was also carried out for both square- and triangular-lattice PCSELs [49], but this investigation too did not consider 90° (or 2D) couplings among the fundamental Bloch waves of the square-lattice PCSEL with TE polarization.

In 2006, a new CWT for square-lattice PCSELs with a high-refractive-index contrast was developed based on an eight-wave model [50,51] that considered optical couplings through four higher-order Bloch waves, and this new theory revealed that 2D coherent oscillation is indeed possible. Then, a more comprehensive CWT that considered optical couplings through many more high-order Bloch waves and also radiative waves [52–55] was developed; this more comprehensive theory was named 3D-CWT. 3D-CWT enables accurate predictions of lasing characteristics of finite-sized PCSELs, such as their lasing frequencies, in-plane and vertical radiation losses, mode profiles, and far-field beam patterns, using relatively few computational resources. A time-dependent 3D-CWT that considers even carrier–photon interactions as well as thermal effects was also developed [56,57] to enable the comprehensive analysis of both below- and above-threshold lasing characteristics, including current-light-output (I–L) characteristics, lasing spectra, and transient waveforms.

In the following, the formulation of 3D-CWT for large-refractive-index-contrast square-lattice PCSELs with TE polarization is provided. As stated before, this structure is most suitable for high-brightness operation. For a 3D-CWT-based analysis of other PC structures and polarizations, please refer to Refs. [54,55]. The mutual couplings among the four fundamental Bloch waves (R_x, S_x, R_y, S_y) at the Γ⁽²⁾ point, which are shown with red arrows in Fig. 1(g), can be expressed as follows:

(7)$$\left( {\delta + i\frac{\alpha }{2}} \right)\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right) = ({{\mathbf{C}_{\textrm{direct - 1D}}} + {\mathbf{C}_{\textrm{indirect - 2D\& 1D}}} + {\mathbf{C}_{\textrm{rad - 1D}}}} )\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right) + i\left( {\begin{array}{@{}c@{}} {{{\partial {R_x}} / {\partial x}}}\\ { - {{\partial {S_x}} / {\partial x}}}\\ {{{\partial {R_y}} / {\partial y}}}\\ { - {{\partial {S_y}} / {\partial y}}} \end{array}} \right), $$

(8)$${\mathbf{C}_{\textrm{direct - 1D}}} = \left( {\begin{array}{@{}cccc@{}} 0&{ - {\kappa_{2,0}}}&0&0\\ { - {\kappa_{ - 2,0}}}&0&0&0\\ 0&0&0&{ - {\kappa_{0,2}}}\\ 0&0&{ - {\kappa_{0, - 2}}}&0 \end{array}} \right), $$

(9)$${\mathbf{C}_{\textrm{indirect - 2D\& 1D}}} = \left( {\begin{array}{@{}cccc@{}} {\chi_{y,1,0}^{(1,0)}}&{ - \chi_{y,1,0}^{( - 1,0)}}&{ - \chi_{y,1,0}^{(0,1)}}&{\chi_{y,1,0}^{(0, - 1)}}\\ { - \chi_{y, - 1,0}^{(1,0)}}&{\chi_{y, - 1,0}^{( - 1,0)}}&{\chi_{y, - 1,0}^{(0,1)}}&{ - \chi_{y, - 1,0}^{(0, - 1)}}\\ { - \chi_{x,0,1}^{(1,0)}}&{\chi_{x,0,1}^{( - 1,0)}}&{\chi_{x,0,1}^{(0,1)}}&{ - \chi_{x,0,1}^{(0, - 1)}}\\ {\chi_{x,0, - 1}^{(1,0)}}&{ - \chi_{x,0, - 1}^{( - 1,0)}}&{ - \chi_{x,0, - 1}^{(0,1)}}&{\chi_{x,0, - 1}^{(0, - 1)}} \end{array}} \right), $$

(10)$${\mathbf{C}_{\textrm{rad - 1D}}} = \left( {\begin{array}{@{}cccc@{}} {\zeta_{1,0}^{(1,0)}}&{ - \zeta_{1,0}^{( - 1,0)}}&0&0\\ { - \zeta_{ - 1,0}^{(1,0)}}&{\zeta_{ - 1,0}^{( - 1,0)}}&0&0\\ 0&0&{\zeta_{0,1}^{(0,1)}}&{ - \zeta_{0,1}^{(0, - 1)}}\\ 0&0&{ - \zeta_{0, - 1}^{(0,1)}}&{\zeta_{0, - 1}^{(0, - 1)}} \end{array}} \right). $$

Here, δ denotes detuning from a wavenumber of 2π/λ₀, where λ₀ is the Bragg wavelength which is equal to the product of the effective refractive index and the lattice constant a. The terms C_direct-1D, C_{indirect-2D&1D}, and C_rad-1D correspond to direct 180° couplings (= 1D couplings), indirect 90° and 180°/0° couplings (= 2D couplings and 1D couplings including self-coupling) via high-order waves, and indirect 180°/0° couplings (= 1D couplings including self-coupling) via radiative waves, respectively. Schematics of these couplings are shown in Fig. 2. It should be noted that 90° couplings (= 2D couplings) are only induced via higher-order Bloch waves [see Fig. 2(b)] as described in Section 1. This is because the polarizations of the fundamental waves propagating in x and y directions are orthogonal to each other. Note that 2D couplings can occur directly [54,55] for the cases of square-lattice PCSELs with TM polarization and triangular-lattice PCSELs with either TE or TM polarization. The magnitudes of the 2D couplings for square-lattice PCSELs with TE polarization are inherently smaller than those of their 1D couplings, and thus it is desirable to increase the refractive index contrast of the PC layer as well as the optical confinement factor (Γ_pc) in the PC layer so that the PC can induce sufficient 2D couplings as already described in Section 1. The calculation of each coupling coefficient in these matrices can be performed using the Fourier coefficients of the PC layer [${\xi _{m,n}}$ in Eq. (3)] and vertical electric field distribution of each Bloch wave (detailed expressions are provided in Refs. [52,53]). For example, the direct 1D coupling coefficient ${\kappa _{2,0}}$ in Eq. (8) can be expressed as follows:

(11)$${\kappa _{\textrm{2,0}}} ={-} \frac{{\omega _0^2a}}{{4\pi {c^2}}}\int_{\textrm{pc}}^{} {{\xi _{2,0}}{{|{{\Theta _0}(z)} |}^2}dz}. $$

The last term of Eq. (7) denotes the spatial change of the envelope function of the electric field in a finite-sized cavity.

One of the most important advantages of 3D-CWT over the other simulation methods described in Sections 2.2a–2.2c is that it can provide analytical insight into improving the performance of the PCSELs while requiring very little computation time. This allows one to determine an appropriate design of PCSELs for high-brightness operation in terms of coupling coefficients of the PC without repeating the time-consuming simulations. Moreover, 3D-CWT can accommodate a finite-sized device with a large number of periods (such as 1000 × 1000 or more), unlike the other simulation methods.

The above framework of 3D-CWT is restricted to steady-state analysis. However, transient photon and carrier distributions inside PCSELs can be analyzed by using time-dependent 3D-CWT [56]. In this theory, the rate equations for the complex amplitudes of the fundamental Bloch waves inside the PC and the carrier density (N) are expressed as follows:

(12)$$\scalebox{0.9}{$\displaystyle\frac{\partial }{{\partial t}}\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right) = \frac{c}{{{n_\textrm{g}}}}\left[ { - i\frac{{2\pi }}{\lambda }{\Gamma _{\textrm{act}}}\Delta n(N) + \frac{{{\Gamma _{\textrm{act}}}g(N) - {\alpha_0}}}{2}} \right]\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right) + \frac{{ic}}{{{n_\textrm{g}}}}\mathbf{C}\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right) - \frac{c}{{{n_\textrm{g}}}}\left( {\begin{array}{@{}c@{}} {{{\partial {R_x}} / {\partial x}}}\\ { - {{\partial {S_x}} / {\partial x}}}\\ {{{\partial {R_y}} / {\partial y}}}\\ { - {{\partial {S_y}} / {\partial y}}} \end{array}} \right) + \left( {\begin{array}{@{}c@{}} {{f_1}}\\ {{f_2}}\\ {{f_3}}\\ {{f_4}} \end{array}} \right),$}$$

(13)$$\frac{{\partial N}}{{\partial t}} = \frac{J}{{e{d_{\textrm{QW}}}}} - \frac{N}{{{\tau _\textrm{c}}}} - \frac{c}{{{n_\textrm{g}}}}g(N)U + D{\nabla ^2}N.$$

Here C = C_direct-1D+ C_{indirect-2D&1D}+ C_rad-1D is the same coupling matrix as written in Eq. (7), n_g is the group refractive index of the multi-layered structure, Δn(N) and g(N) are the carrier-dependent refractive-index change and optical gain, respectively, α₀ is the intrinsic loss, f_i (i = 1–4) are the spontaneous emission terms, J is the injected current density, d_QW is the thickness of the active layer, τ_c is the carrier lifetime, and D is the carrier diffusion coefficient. U, which is the photon density inside the active layer, is given by the following equation:

(14)$$U = {\Gamma _{\textrm{act}}}\frac{{2{\varepsilon _0}{n_{\textrm{eff}}}{n_\textrm{g}}}}{{\hbar \omega {d_{\textrm{QW}}}}}[{|{R_x}{|^2} + |{S_x}{|^2} + |{R_y}{|^2} + |{S_y}{|^2}} ].$$

In Eqs. (12)–(14), both the electric field amplitudes and the carrier density (and the other related parameters) depend on the position r. The first to fourth terms on the right-hand side of Eq. (12) denote carrier-induced frequency and gain changes, mutual couplings among the fundamental waves, spatial propagation, and spontaneous emission terms, respectively. The first to fourth terms on the right-hand side of Eq. (13) denote carrier injection, carrier recombination, stimulated emission, and carrier diffusion, respectively.

By solving Eqs. (12) and (13) simultaneously, the temporal and spatial evolution of both photon and carrier distributions in finite-sized PCSELs can be obtained, enabling transient analyses including high-peak-power and short-pulse operation [30–32]. Solving Eq. (12) also clarifies the evolution of all possible lasing modes simultaneously in a finite-sized PCSEL. When the mode with the lowest threshold gain starts lasing, the carrier density inside the active layer is generally fixed owing to the stimulated emission term in Eq. (13), which suppresses the lasing of the other modes. However, as the spatial distribution of each mode is different, lasing in multiple modes sometimes occurs nevertheless. Such phenomena can be well reproduced by this method. In addition, time-dependent 3D-CWT enables direct calculation of lasing spectra and spectral linewidths [58] by performing a Fourier transform of the transient response of electric fields.

It should be noted that Eqs. (12) and (13) do not consider the change in optical gain and refractive index caused by an in-plane temperature distribution, which is caused by heat generation during CW operation. During CW operation, a temperature distribution inside the PCSEL affects the mode profile through a change in the band-edge frequency distribution inside the device, which in turn affects the temperature distribution of the device itself due to the non-uniform device cooling due to the stimulated emission. In 2021, the above-mentioned time-dependent 3D-CWT was further updated to consider such multi-physics among photons, carriers, and heat [57], which enabled self-consistent analysis of PCSELs even under CW operation.

2.3 Basic Design Guideline of PCSELs

In this section, the basic design guideline of PCSELs for the purpose of increasing their slope efficiencies is described. The slope efficiency, defined as optical power per unit injection current, is one of the most important parameters of a PCSEL because it is directly related to the realization of high-brightness operation. The slope efficiency is given by the following equation:

(15)$${\eta _{SE}} = \frac{{\hbar \omega }}{e}({1 - A} ){\eta _\textrm{i}}\frac{{{\alpha _{\textrm{v,up}}}}}{{{\alpha _{\textrm{v,up}}} + {\alpha _{\textrm{v,down}}} + {\alpha _{\textrm{/{/}}}} + {\alpha _0}}}. $$

Here $\hbar \omega$ is the photon energy, e is the elementary charge, A is the one-pass optical absorptivity of the laser substrate, η_i is the carrier injection efficiency of the active layer, α_v,up and α_v,down are the upward and downward radiation constants of the lasing mode, α_// is the in-plane loss of the lasing mode into the area surrounding the current injection area of a finite-sized PCSEL, and α₀ is the intrinsic loss consisting of material absorption and scattering losses. A schematic visualization of α_v,up, α_v,down, α_//, and α₀ in a finite-sized PCSEL is shown in Fig. 3(a). To increase the slope efficiency, one should increase α_v,up while reducing the other losses α_v,down, α_//, and α₀.

First, we consider how to increase α_v,up, starting with a discussion of the total radiation constant α_v, which is the sum of α_v,up and α_v,down. One of the most important factors to determine the value of α_v is the degree of cancellation of radiation wave in the far field, which are emitted into the far field from 2D resonant modes formed in the PC layer by optical couplings among the fundamental Bloch waves. The degree of cancellation depends on the symmetry of the 2D resonant modes, which are determined predominantly by the lattice type and the shape of the lattice points in the unit cell [12,13,15,21,52]. Here, we consider two lattice types; a square-lattice PC with C_4v symmetry and a triangular-lattice PC with C_6v symmetry. Figures 3(b) and 3(c) show the calculated electric field (E_x, E_y) and magnetic field (H_z) distributions of each resonant mode at the Γ⁽²⁾ point in the square-lattice and the triangular-lattice PCs with symmetric circular lattice points, respectively. Individual resonant modes can be categorized in the theory of group representations as A₁, B₁, E, B₂, E₁, and E₂ [59]. As shown in the figures, the square-lattice PC with C_4v symmetry has two symmetric modes A₁, B₁, which are canceled out in the far field when they are coupled to radiative waves. Thus, these two modes can be regarded as non-radiative modes for which α_v is zero-valued. (Note that in a finite-sized PCSEL, this cancellation is imperfect at the periphery of the device, and therefore these modes are not completely non-radiative.) On the other hand, the triangular-lattice PC with C_6v symmetry has four non-radiative modes A₁, B₂, and E₂, where E₂ is doubly degenerate. Since the lasing oscillation occurs at the resonant mode with the lowest loss, the slope efficiency becomes very small when non-radiative modes are present. Thus, it is important to break the rotational symmetry (particularly C₂ symmetry) of the lattice points, so that non-radiative modes disappear and that α_v of the mode with lowest loss is reasonably larger than its α_// and α₀, as required to obtain a sufficiently high slope efficiency. Because the number of non-radiative modes in a square-lattice PC is smaller than that of the triangular-lattice PC, it is easier to increase α_v for the square-lattice structure, which indicates that square-lattice PCs are more suited to high-brightness operation as already described. Figure 3(d) shows the radiation constants calculated using 3D-CWT for square-lattice PCSELs with three different unit-cell structures: (i) circular, (ii) equilateral triangular, and (iii) right-angled isosceles-triangular [52]; note that, in this figure, modes A₁ and B₁ are rewritten simply as A and B, respectively. These calculations indicate that, among the three considered lattice-point shapes, the highest radiation constants can be obtained by using right-angled isosceles-triangular unit-cell structures, for which mirror symmetry is simultaneously broken along the x and y axes [20,60].

Figure 3. (a) Schematic of radiation constant α_v (consisting of upward and downward radiation constants α_v,up and α_v,down, respectively), in-plane loss α_// and material loss α₀ in PCSELs. (b),(c) Calculated electromagnetic field distributions of band-edge modes in square-lattice and triangular-lattice PCSELs with TE polarization. The calculations were performed using 3D-CWT. Arrows show the in-plane electric field vectors, and the colormap shows the amplitude of the magnetic field H_z. (d) Calculated radiation constants of a square-lattice PCSEL with three different (circular, equilateral-triangular, and right-angled isosceles-triangular) unit-cell structures [52]. (e),(f) Calculated upward radiation constant and slope efficiency of a GaAs-based PCSEL with a backside DBR as functions of the interference phase between the reflected and upward-radiated light, where A = 0.1, η_i= 1.0, α_v= 16.0 cm^–1, α_// = 3.0 cm^–1, and α₀= 6.0 cm^–1 were assumed [24].

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As stated above, it should be noted that even for non-radiative modes supported by rotationally symmetric PCs, complete cancellation of radiation does not occur when the cavity size is finite. This is because both the amplitude and phase of the electric field distribution near the edge of the cavity becomes different from those at the center of the cavity, which leads to the imperfect cancellation of radiation [13,53]. The radiation from such finite-sized PCSELs enables the generation of various vector beams such as doughnut-shape beams, radially polarized beams, higher-order vector beams, and even more intricate beam patterns [13,15,19], the detail of which is given in Section 3.1.

Next, we discuss how to increase α_v,up while suppressing α_v,down. In general, radiative waves couple equally into both upward and downward directions (i.e. α_v,up= α_v,down) from the PC of the PCSEL. To increase α_v,up while suppressing α_v,down, it is important to reflect the downward radiation upward by using a highly reflective backside mirror such as a DBR [24]. The resultant value of α_v,up is dependent on the power reflectivity R of the backside mirror and the interference phase θ_B of the reflected and upward-radiated light as follows:

(16)$${\alpha _{\textrm{v,up}}} = \frac{{\alpha _\textrm{v}^0}}{2}\left( {1 + 2\sqrt R \cos {\theta_B} + R} \right), $$

where $\alpha _\textrm{v}^0$ is the total radiation constant without the backside mirror. It is shown in Eq. (16) that α_v,up becomes $2\alpha _\textrm{v}^0$ when the interference is completely constructive (θ_B= 0°), and the reflectivity R of the mirror is unity. Figures 3(e) and 3(f) show an example of the calculated α_v,up and the associated slope efficiency of a PCSEL as a function of θ_B. In these calculations, the following parameters were used: ħω/e = 1.32 eV, A = 0.1, η_i= 1.0, $\alpha _\textrm{v}^0$=16.0 cm^-1, α_//=3.0 cm^-1, α₀= 6.0 cm^-1. Although these parameters have not been optimized, it is seen in the figures that a slope efficiency higher than 0.8 W/A can be obtained nevertheless. It should be noted that constructive interference is not always the best solution because a large value of α_v,up leads to an increase of the threshold currents of the PCSEL. Thus, it is also important to reduce α_// and α₀ sufficiently to realize a high slope efficiency and a low threshold current simultaneously.

We next discuss how to reduce the in-plane loss α_//, which depends on the strengths of in-plane optical couplings among the fundamental Bloch waves and on the device size [53]. When the device size is sufficiently small (less than a few tens of micrometers in diameter), an introduction of in-plane heterostructures is considered to be effective for reducing α_//; such heterostructures can be formed by surrounding the active area of the PCSEL, through which current is injected, by an outer area whose lattice constant is modified so that a mode gap at the resonant frequency is formed at the periphery of the active area, which sufficiently confines the resonant light within the active area [45,46,61]. When the PCSEL is moderate in size (several tens to hundreds of micrometers in diameter), α_// can be reduced appropriately by controlling in-plane optical couplings among fundamental Bloch waves by adjusting the optical confinement factor [see Eq. (2)] as well as the filling factor of a low-refractive-index portion in unit cells. When the PCSEL is sufficiently large in size (several hundreds of micrometers in diameter), α_// becomes small automatically. In this case, however, multiple lateral-mode oscillations start to occur because not only the fundamental resonant mode but also higher-order resonant modes are confined strongly, and a sufficiently wide threshold margin for single-mode oscillation can no longer be obtained. In addition, carrier-induced refractive-index difference between inside and outside the current injection section may further decrease α_// [62]. In Sections 2.4 and 2.5, we discuss how to realize single-mode oscillation even when the device size becomes very large, which is a key to realize high-brightness operation of PCSELs, leading to the realization of PCSELs which can rival (or even replace) bulky lasers such as gas, solid-state, and fiber lasers. In such ultimate cases, Eq. (16) is no longer valid, as discussed in Section 2.5.

Finally, we discuss briefly how to reduce α₀. In any laser, a fixed amount of intrinsic loss α₀ exists, which consists of material absorption loss and scattering loss. In III-V semiconductor lasers, material absorption loss is based mainly on free-carrier absorption in cladding layers. The free-carrier absorption loss in the p-cladding layer is much larger than that in the n-cladding layer, and thus the employment of an asymmetric vertical structure that reduces the light distribution inside the p-cladding layer [63] is effective to reduce material absorption loss.

2.4 Introduction of Double-Lattice PCs for 10-W-Class High-Brightness Single-Mode Operation

In this subsection, the concept of double-lattice PCs [22], which enable high-power single-mode operation of broad-area PCSELs, is explained. Figure 4(a) show schematics of the mode profiles of the fundamental mode and the first and second higher-order modes in a finite-sized PCSEL with a lasing diameter of L. Here, the fundamental mode has a mode profile whose intensity is highest at the center, while the first and second higher-order modes have nodes in their electric fields at the center and antinodes near the edge of the device. Owing to this difference of the electric field distributions, the higher-order modes generally have higher in-plane losses α_// than the fundamental mode, which ensures single-lateral-mode lasing in PCSELs. However, when the lasing diameter L becomes larger (several hundred micrometers in diameter), single-mode lasing is difficult to maintain because the higher-order modes also become strongly laterally confined, which reduces their in-plane losses to a similar value as that of the fundamental mode and results in a small threshold gain margin between them. To address this issue, the coupling coefficients among fundamental Bloch waves should be appropriately weakened while maintaining 2D coherent oscillation so that the mode profiles spatially expand and the in-plane losses of the higher-order modes become sufficiently larger than that of the fundamental mode [64].

Figure 4. (a) Schematics of mode profiles of the fundamental modes and the first and second higher-order modes inside the finite-size cavities. (b) Schematic and basic principle of double-lattice PCs. (c) Calculated threshold gain margin Δα between the fundamental mode and the first higher-order mode for a single-lattice PC with right-angled isosceles-triangular holes and several double-lattice PCs (structures I, II, and III) as functions of the cavity diameter. (d) Schematic of double-lattice PCs that realize the cancellation of the 1D and 2D coupling coefficients. (e) Calculated threshold gain margin Δα between the fundamental mode and the first higher-order mode for a double-lattice PC based on the cancellation of the 1D and 2D coupling coefficients.

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To realize this effect, the concept of double-lattice PCs was proposed [22]. Figure 4(b) shows the schematic and basic principle of a double-lattice PC. Here, the PC is composed of two single-lattice PCs, where one single-lattice PC is shifted in the x and y directions by d ∼ 0.25a (where a is the lattice constant, which is approximately equal to the wavelength λ inside the medium) from the other. In this case, the refractive-index distribution of the double-lattice PC can be expressed by using that of the single-lattice PC [Eq. (3)] as follows:

(17)$$\begin{aligned} \varepsilon ({x,y} )+ \varepsilon ({x - d,y - d} )&= \sum\limits_{m,n} {{\xi _{m,n}}\exp [{{{i2\pi ({mx + ny} )} / a}} ]} \\ &+ \sum\limits_{m,n} {{\xi _{m,n}}\exp [{{{i2\pi ({m(x - d) + n(y - d)} )} / a}} ]} \\ &= \sum\limits_{m,n} {{\xi _{m,n}}[{1 + {e^{{{ - i2\pi ({m + n} )d} / a}}}} ]\exp [{{{i2\pi ({mx + ny} )} / a}} ]}. \end{aligned} $$

In Eq. (17), the Fourier coefficient of the double-lattice PC is modified from that of the original single-lattice PC ${\xi _{m,n}}$ by the following term:

(18)$$[{1 + {e^{{{ - i2\pi ({m + n} )d} / a}}}} ].$$

This term describes the optical interference between the two single-lattice PCs, which highlights the difference between the double-lattice and the single-lattice PC. The amplitude of the Fourier coefficient of the double-lattice PC varies from 0 to 2 times that of the single-lattice ${\xi _{m,n}}$, depending on the values of m, n, and d. Based on Eqs. (11) and (18), the direct 1D coupling coefficient of the double-lattice PC $\kappa _{\textrm{2,0}}^{\textrm{double - lattice}}$ is also modified from that of the single-lattice PC $\kappa _{\textrm{2,0}}^{}$ as follows:

(19)$$\kappa _{\textrm{2,0}}^{\textrm{double - lattice}} = \kappa _{\textrm{2,0}}^{}({1 + {e^{{{ - i4\pi d} / a}}}} ). $$

According to Eq. (19), one can easily understand that the magnitude of the direct 1D coupling coefficient of the double-lattice PC can be weakened when the separation between the two lattice points d is nearly equal to a/4, which physically represents the destructive interference between the two lattices. Note that the magnitude of the indirect 2D coupling is maintained even though the double-lattice PC is employed [22]. As a consequence of such a small 1D coupling coefficient, the mode profiles of both the fundamental mode and the higher-order modes spread in a large area, and the difference of α_// between the fundamental mode and the higher-order modes become much larger as explained in the previous paragraph. It should be also noted that when the separation between the two lattice points d is nearly equal to a/2, the magnitude of the direct 1D coupling coefficient becomes larger than that of a single lattice, which can be used for devices with a relatively small diameter [46].

Figure 4(c) shows the calculated threshold gain margin Δα between the fundamental mode and the first higher-order mode for a single-lattice PC with right-angled isosceles-triangular air holes and several double-lattice PCs (structures I, II, and III) as functions of the cavity diameter [22]. The magnitude of the 1D coupling coefficients of the single-lattice and the three double-lattice PCs are as follows: single-lattice, ∼2000 cm^–1; I, 470 cm^–1; II, 250 cm^–1; and III, 100 cm^–1. As shown in this figure, the double-lattice PCs have much larger Δα than the single-lattice PC, and the value of Δα monotonically increases as the magnitude of the 1D coupling coefficient becomes smaller. This result clearly demonstrates the effectiveness of the concept of the double-lattice PC. Based on this concept, high-power (>10 W) single-mode oscillation of 500-µm-to-1-mm-diameter PCSELs were demonstrated experimentally, the details of which are discussed in Section 3.3.

To further increase the threshold margin Δα for even larger lasing diameters, not only the canceling of the 1D coupling coefficients, but also the canceling of both the 1D and 2D coupling coefficients is necessary [22]. In the double-lattice PC, the canceling of the 1D and 2D coupling coefficients can be realized by adjusting the hole distance d and the shape (size and ellipticity) of each hole, as shown in Fig. 4(d). Figure 4(e) shows the calculated threshold gain margin Δα of the double-lattice PC as a function of the hole distance, where relatively large Δα (>3 cm^–1) is obtained even when the lasing diameter is increased to 2–3 mm. More rigorous theoretical analyses that also consider radiative loss were established in 2022 [25]. Importantly, the latter theoretical analyses consider not only Hermitian couplings which do not accompany loss but also non-Hermitian couplings which accompany radiation loss, and they focus on the difference in the radiation constants between the fundamental mode and high-order modes to realize ultra-large-area single-mode lasing in PCSELs. In the next subsection, the theoretical analyses for 100-W-to-1-kW single-mode operation in ultra-large-area PCSELs (3∼10 mm) are reviewed.

2.5 Hermitian and Non-Hermitian Control in Double-Lattice Structures for 100-W-to-1-kW High-Brightness Single-Mode Operation

In this subsection, we analytically derive the general conditions for ultra-large-area (3–10 mm) single-mode operation in PCSELs [25]. As discussed in Sections 2.3 and 2.4, to realize single-mode lasing in ultra-large-area devices, one should increase (1) the threshold gain difference between different band-edge modes and (2) the threshold gain difference between the fundamental and higher-order band-edge modes within the same band. In the following, we discuss the general recipe to increase both differences in the framework of 3D-CWT considering both Hermitian and non-Hermitian couplings, and we explain the advantage of the double-lattice PC for increasing the threshold gain differences between resonant modes of different band edges and within the same band.

2.5a Hermitian and Non-Hermitian Optical Couplings Inside PCSELs

Figures 5(a) and 5(b) show a schematic of the mutual couplings among the basic waves in a double-lattice PC. Here, the mutual couplings among the basic waves shown in Fig. 2 are reclassified into (a) Hermitian couplings and (b) non-Hermitian couplings. The Hermitian couplings [Fig. 5(a)] express the optical couplings without accompanying vertical radiation loss, while the non-Hermitian couplings [Fig. 5(b)] express the optical couplings accompanying vertical radiation loss. Considering the reflection symmetry along y = x in the double-lattice PC as shown in Fig. 5(a), these mutual couplings between these fundamental waves in the vicinity of the second-order Γ point of the photonic band can be expressed with the following matrix equations in the framework of 3D-CWT [25]:

(20)$$\left( {\delta + i\frac{\alpha }{2}} \right)\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right) = ({{\mathbf{C}_{\textrm{Hermitian}}} + {\mathbf{C}_{\textrm{non - Hermitian}}} + {\mathbf{C}_{\textrm{non - Gamma}}}} )\left( {\begin{array}{@{}c@{}} {{R_x}}\\ {{S_x}}\\ {{R_y}}\\ {{S_y}} \end{array}} \right), $$

(21)$$\scalebox{0.9}{$\displaystyle{\mathbf{C}_{\textrm{Hermitian}}} = {\mathbf{C}_{\textrm{direct - 1D}}} + {\mathbf{C}_{\textrm{indirect - 2D\& 1D}}} + \frac{1}{2}({{\mathbf{C}_{\textrm{rad - 1D}}} + \mathbf{C}_{\textrm{rad - 1D}}^{\dagger} } )= \left( {\begin{array}{@{}cccc@{}} {{\kappa_{11}}}&{{\kappa_{1\textrm{D}}}}&{{\kappa_{2\textrm{D} + }}}&{{\kappa_{2\textrm{D} - }}}\\ {\kappa_{1\textrm{D}}^\ast }&{{\kappa_{11}}}&{\kappa_{2\textrm{D} - }^\ast }&{\kappa_{2\textrm{D} + }^{}}\\ {\kappa_{2\textrm{D} + }^{}}&{{\kappa_{2\textrm{D} - }}}&{{\kappa_{11}}}&{{\kappa_{1\textrm{D}}}}\\ {\kappa_{2\textrm{D} - }^\ast }&{\kappa_{2\textrm{D} + }^{}}&{\kappa_{1\textrm{D}}^\ast }&{{\kappa_{11}}} \end{array}} \right),$}$$

(22)$${\mathbf{C}_{\textrm{non - Hermitian}}} = \frac{1}{2}({{\mathbf{C}_{\textrm{rad - 1D}}} - \mathbf{C}_{\textrm{rad - 1D}}^{\dagger} } )= \left( {\begin{array}{@{}cccc@{}} {i\mu }&{i\mu {e^{i{\theta_{\textrm{pc}}}}}}&0&0\\ {i\mu {e^{ - i{\theta_{\textrm{pc}}}}}}&{i\mu }&0&0\\ 0&0&{i\mu }&{i\mu {e^{i{\theta_{\textrm{pc}}}}}}\\ 0&0&{i\mu {e^{ - i{\theta_{\textrm{pc}}}}}}&{i\mu } \end{array}} \right), $$

(23)$${\mathbf{C}_{\textrm{non - Gamma}}} = \left( {\begin{array}{@{}cccc@{}} {{k_x}}&0&0&0\\ 0&{ - {k_x}}&0&0\\ 0&0&{{k_y}}&0\\ 0&0&0&{ - {k_y}} \end{array}} \right). $$

Figure 5. (a) Schematic of Hermitian couplings between the four fundamental waves inside a double-lattice PCSEL. (b) Schematic of non-Hermitian couplings via radiated waves, where a backside reflector is used for the control of the non-Hermitian coupling coefficient iµ.

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Here ${\mathbf{C}_{\textrm{Hermitian}}}$ is a Hermitian matrix that satisfies ${\mathbf{C}_{\textrm{Hermitian}}} = \mathbf{C}_{\textrm{Hermitian}}^{\dagger}$, ${\mathbf{C}_{\textrm{non - Hermitian}}}$ is an anti-Hermitian matrix that satisfies ${\mathbf{C}_{\textrm{non - Hermitian}}} ={-} \mathbf{C}_{\textrm{non - Hermitian}}^{\dagger}$, and ${\mathbf{C}_{\textrm{non - Gamma}}}$ is a matrix that denotes the deviation of the wave vector (k_x, k_y) from the Γ point. It should be noted that direct 1D couplings (C_direct-1D) and indirect 2D and 1D couplings via higher-order waves (C_{indirect-2D&1D}) are classified into the Hermitian matrix because they do not accompany any loss, while 1D couplings via radiative waves (C_rad-1D) involve both Hermitian and non-Hermitian components, which physically mean that the radiative waves are partially confined inside the PC layer in the vertical direction while accompanying energy loss. In Eq. (21), κ_1D denotes the total 1D coupling coefficient that involves both direct and indirect components, κ_2D+ and κ_2D- denote the 2D coupling coefficients, and κ₁₁ denotes the self-coupling coefficient for fundamental waves without accompanying vertical emission loss. It should be noted that κ_2D+ and κ_2D- are different in a double-lattice PC because it does not have C₄ symmetry unlike a single-lattice PC with circular lattice points. It should be also noted that κ_1D and κ_2D- are complex numbers while κ_2D+ is a real number owing to the reflection symmetry about the line of y = x. In Eq. (22), iµ is a purely imaginary number, which expresses self-coupling of four fundamental waves through radiative waves with accompanying vertical emission loss. The magnitude of µ can be continuously controlled by adjusting the phase difference between the upward-radiated wave and the downward-radiated wave that is reflected at the bottom reflector as shown in Fig. 5(b). The term $i\mu {e^{ {\pm} i{\theta _{\textrm{pc}}}}}$ expresses ±180° coupling through radiative waves with accompanying vertical emission loss, where θ_pc stands for the phase shift during the cross coupling of counterpropagating fundamental waves via radiative waves. We determine θ_pc by the position at which non-Hermitian couplings occur relative to the origin of the coordinate system [25]. It should be noted that in the previous 3D-CWT expressed with Eq. (7), mutual couplings via radiative waves were expressed with ${\mathbf{C}_{\textrm{rad}}}$ [Eq. (10)]. The difference between ${\mathbf{C}_{\textrm{rad}}}$ and ${\mathbf{C}_{\textrm{non - Hermitian}}}$ is that the former contains both non-Hermitian and Hermitian couplings, while the latter contains only non-Hermitian couplings. By isolating iµ and θ_pc, succinct analytical expressions for the complex eigenfrequencies of each band-edge mode can be derived as discussed in the next subsection.

2.5b Conditions for Increasing the Threshold Gain Difference Between Different Band-Edge Modes

By using the above-mentioned coupled-wave matrices, we can analytically derive the resonant frequencies δ_i (relative shift from the Bragg frequency) and radiation constants α_i of the four band-edge modes (i = A, B, C, D) around the Γ point. When we consider the photonic band along the axis of symmetry of double-lattice PCs (y = x), for which ${k_x} = {k_y} = {{\Delta k} / {\sqrt 2 }}$, the complex eigenfrequencies of the four modes are derived as follows.

For modes A and C (anti-symmetric modes about the axis of y = x)

(24)$$\scalebox{0.82}{$\begin{aligned} {\delta _{\textrm{A,C}}} + i{{{\alpha _{\textrm{A,C}}}} / 2}& = {\kappa _{11}} + {\kappa _{\textrm{2D} + }} + i\mu \mp \sqrt {[{({{\kappa_{\textrm{1D}}} + {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}} + i\mu } ][{{{\{{({{\kappa_{\textrm{1D}}} + {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}}} \}}^ \ast } + i\mu } ]+ {{\left( {{{\Delta k} / {\sqrt 2 }}} \right)}^2}} \\ &\equiv {\kappa _{11}} + {\kappa _{\textrm{2D} + }} + i\mu \mp \sqrt {({R + iI + i\mu } )({R - iI + i\mu } )+ {{\left( {{{\Delta k} / {\sqrt 2 }}} \right)}^2}} \end{aligned},$}$$

and for modes B and D (symmetric modes about the axis of y = x)

(25)$$\scalebox{0.83}{$\begin{aligned} {\delta _{\textrm{B,D}}} + i{{{\alpha _{\textrm{B,D}}}} / 2} &= {\kappa _{11}} - {\kappa _{\textrm{2D} + }} + i\mu \mp \sqrt {[{({{\kappa_{\textrm{1D}}} - {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}} + i\mu } ][{{{\{{({{\kappa_{\textrm{1D}}} - {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}}} \}}^ \ast } + i\mu } ]+ {{\left( {{{\Delta k} / {\sqrt 2 }}} \right)}^2}} \\ &= {\kappa _{11}} - {\kappa _{\textrm{2D} + }} + i\mu \mp \sqrt {({R^{\prime} + iI^{\prime} + i\mu } )({R^{\prime} - iI^{\prime} + i\mu } )+ {{\left( {{{\Delta k} / {\sqrt 2 }}} \right)}^2}}. \end{aligned}$}$$

In Eq. (24), R and I are Hermitian coupling coefficients defined as $R \equiv \textrm{Re} [{({{\kappa_{\textrm{1D}}} + {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}}} ]$ and $I \equiv {\mathop{\rm Im}\nolimits} [{({{\kappa_{\textrm{1D}}} + {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}}} ]$, which express the degree of cancellation between 1D and 2D diffractions for the modes with anti-symmetric electric field about the axis of y = x (modes A and C). More specifically, R denotes the overall strength of in-plane feedback of combined 180° and 90° diffractions at the Γ point, which determines the size of the frequency gap between modes A and C at the Γ point, and I determines the phase of the in-plane electric fields, which consequently determines the degree of cancellation of the vertical radiation in mode A at the Γ point. In the case of the double-lattice PC, R and I can be almost independently controlled by changing the hole distance and the size balance of the two holes as shown in Section 2.5d. Similarly, R’ and I’ are defined as $R^{\prime} \equiv \textrm{Re} [{({{\kappa_{\textrm{1D}}} - {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}}} ]$ and $I^{\prime} \equiv {\mathop{\rm Im}\nolimits} [{({{\kappa_{\textrm{1D}}} - {\kappa_{\textrm{2D} - }}} ){e^{ - i{\theta_{\textrm{pc}}}}}} ]$, which are the Hermitian coupling coefficients for the modes with symmetric electric field about the axis of y = x (modes B and D). It should be noted that the band structures along the perpendicular axis (y = −x) is almost equal to those along y = x when the amplitudes of κ_2D+ and κ_2D- are similar.

Using Eqs. (24) and (25), we can discuss the strategy to increase the threshold gain difference, which is based on the radiation constant difference, between the four band-edge modes. When the condition of $|{{\kappa_{\textrm{1D}}} + {\kappa_{\textrm{2D} - }}} |\sim 0$ and ${\kappa _{\textrm{1D}}} - {\kappa _{\textrm{2D} - }}\sim{\pm} iK{e^{i{\theta _{\textrm{pc}}}}}({K > > \mu } )$ are satisfied, which corresponds to the case in which the destructive interference of 1D and 2D diffractions is achieved only for the anti-symmetric band-edge modes (A and C), the radiation constants of the four modes can be calculated as follows [25]:

(26)$$\begin{aligned} {\alpha _\textrm{A}}&\sim \frac{\mu }{{{\mu ^2} + {R^2}}}{I^2}_{}({\textrm{arbitrarily controllable}} )\\ {\alpha _\textrm{C}} &= 4\mu - {\alpha _\textrm{A}} > > 0\\ {\alpha _\textrm{B}}&\sim 2\mu > > 0\\ {\alpha _\textrm{D}}&\sim 2\mu > > 0. \end{aligned}$$

In this case, the radiation constant of mode A (α_A) can be much smaller than those of the other modes (B, C, D), ensuring a single-band-edge-mode lasing in mode A. In addition, the value of α_A can be continuously controlled to moderate values (α_A= 10–20 cm^-1) by changing the value of I or the size balance of the double holes, which enables us to realize a high slope efficiency while maintaining a relatively low threshold current as discussed in Section 2.3.

These characteristics of double-lattice PCs are attributed to the complete breaking of the 180° rotational symmetry in the structure and to the precise adjustments of the Hermitian and non-Hermitian coupling coefficients. They are striking differences from those of conventional PCs with circular holes shown in Figs. 3(b) and 3(c). In the latter case, more than two band-edge modes have zero-valued radiation constants, which not only inhibits the realization of a high slope efficiency but also induces lasing in multiple band-edge modes. Even when a small structural perturbation is added to the PC to enable vertical emission, the radiation constant difference between these two non-radiative modes remains small, leading to multiple-mode lasing. It should be also noted that the use of accidental Dirac cones or exceptional rings in square-lattice or triangular-lattice PCs have been recently proposed to realize single-mode oscillation in large-area PCSELs [65–68], but these structures also involve the above-mentioned fundamental issues of low slope efficiencies and small threshold gain differences between different band-edge modes.

2.5c Conditions for Increasing the Threshold Gain Difference Between Band-Edge Modes within the Same Band in an Ultra-Large-Area Device

In this subsection, we consider the conditions for increasing the threshold gain difference between the fundamental mode and higher-order modes originating from the same band-edge mode in a finite-sized PCSEL with a large (e.g. 3 mm) lasing diameter. In Section 2.4, the threshold gain difference between these modes is enhanced by weakening the in-plane feedback (κ_1D) of the PC, which increases the difference of the in-plane losses of these modes. However, when the lasing diameter is larger than 3 mm, this strategy is not sufficient because the existence of the non-Hermitian coupling [shown in Fig. 5(b)] inhibits the complete cancellation of the in-plane feedback and, therefore, the in-plane losses of both the fundamental mode and higher-order modes become zero in such a large-scale device. Therefore, to increase the threshold gain difference between the fundamental mode and higher-order modes, the radiation constant difference of the two modes should be increased by controlling both Hermitian and non-Hermitian couplings. Figures 6(a) and 6(b) show this concept, where the electric field distributions and far-field radiation of the fundamental mode and the first higher-order mode inside a finite-sized device are shown schematically. Here, the in-plane wavenumbers of the envelop functions of the two modes are approximately π/L and 2π/L, respectively, and the corresponding far-field radiation angles are slightly different from each other. Therefore, by increasing the sensitivity of change of the radiation constant with respect to the in-plane wavenumbers (or radiation angle), the threshold gain difference between the fundamental and higher-order modes can be increased even when their in-plane losses are very small. In the following, the general conditions to maximize the threshold gain difference for single-mode lasing are derived.

Figure 6. (a),(b) Electric-field intensity distribution (left) and schematic of radiation (right) of the fundamental mode and the first higher-order mode in a PCSEL with a diameter of L. (c),(d) Calculated radiation constant and frequency change of mode A in the vicinity of the Γ point when the values of the real part of the Hermitian coupling coefficient R and the magnitude of the non-Hermitian coupling coefficient µ are simultaneously changed.

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Under the condition of $\left( {\sqrt {{I^2} + {{\left( {{{\Delta k} / {\sqrt 2 }}} \right)}^2}} < \sqrt {{R^2} + {\mu^2}} } \right)$, which corresponds to the condition to obtain a moderate radiation constant of mode A, the change in the eigenfrequency of mode A in the vicinity of the Γ point [Eq. (24)] can be approximated as follows:

(27)$${\alpha _\textrm{A}}({\Delta k} )- {\alpha _\textrm{A}}(0 )\sim \frac{\mu }{{{\mu ^2} + {R^2}}}{\left( {{{\Delta k} / {\sqrt 2 }}} \right)^2}, $$

(28)$${\delta _\textrm{A}}({\Delta k} )- {\delta _\textrm{A}}(0 )\sim{-} \frac{R}{{2({{\mu^2} + {R^2}} )}}{\left( {{{\Delta k} / {\sqrt 2 }}} \right)^2}. $$

Here both the frequency and radiation constant changes are proportional to the square of the in-plane wavenumber Δk, and their curvatures are determined by the real part of the Hermitian coupling coefficient R and the amplitude of the non-Hermitian coupling coefficient µ. From these equations, the radiation constant difference and frequency difference between the fundamental mode and the next higher-order mode are derived as follows:

(29)$$\Delta {\alpha _\textrm{v}} = {\alpha _\textrm{A}}({{{2\pi } / L}} )- {\alpha _\textrm{A}}({{\pi / L}} )\sim \frac{\mu }{{{\mu ^2} + {R^2}}}\frac{{3{\pi ^2}}}{{2{L^2}}}, $$

(30)$$|{\Delta \delta } |= |{{\delta_\textrm{A}}({{{2\pi } / L}} )- {\delta_\textrm{A}}({{\pi / L}} )} |\sim \frac{R}{{2({{\mu^2} + {R^2}} )}}\frac{{3{\pi ^2}}}{{2{L^2}}}. $$

Figures 6(c) and 6(d) show the calculated radiation constant and frequency change of mode A in the vicinity of the Γ point when the values of R and µ are simultaneously changed. In this calculation, the value of I is adjusted in each case so that a moderate radiation constant α_A of ∼10 cm^–1 is obtained at the Γ point. As shown in Fig. 6(c), the curvature of the radiation constant change is drastically increased when both R and µ decrease, which implies that the radiation constant difference between the fundamental mode (Δk = π/L) and the first higher-order mode (Δk = 2π/L) is also increased. The physical explanations behind this result can be given as follows: when the amplitudes of the Hermitian and non-Hermitian coupling coefficients are very small, even a slight deviation of the in-plane wavenumber Δk from the Γ point can break the mutual couplings among the fundamental Bloch waves. As a result, the cancellation of the far-field radiation at the Γ point, where the radiation constant has a moderate value, is no longer maintained at a point deviating from the Γ point, leading to a drastic increase of the radiation constant as shown in Fig. 6(c). It should be noted that it is difficult to specify a value of the threshold gain difference Δα_v (or dimensionless threshold gain difference Δα_vL) that is sufficient for single-mode oscillation in actual devices because this value depends on various physical parameters that determine the magnitude of the spatial hole burning effect such as the current injection level and refractive-index change coefficient of the active layer [56]. Nevertheless, increasing Δα_v by simultaneously reducing R and µ contributes to the preservation of single-mode oscillation even at high current injection levels or in the presence of a non-uniform in-plane refractive index distribution borne by various physical phenomena.

In addition, the frequency difference between these two modes also increases as R and µ decrease as shown in Fig. 6(d). This is also a consequence of weaker mutual couplings between the fundamental Bloch waves, by which the photonic band structure effectively approaches that of an empty lattice without a refractive-index contrast and changes from a parabolic dispersion to a linear dispersion. Such a large frequency difference between the two modes is also beneficial to maintain single-mode lasing, because this difference inhibits the unwanted coupling of the two modes (and multi-mode lasing) due to the carrier-induced or thermally induced refractive-index change during lasing operation (the details will be reported elsewhere).

It should be noted that the value of µ should be chosen to ensure a sufficient radiation constant difference among the four different band-edge modes (A–D) shown in Eq. (26). It should be also noted that the radiation constant difference shown in Eq. (29) takes a maximum value at R = 0 cm^–1, where both the frequencies and the radiation constants of modes A and C are degenerate at $\Delta k ={\pm} \sqrt {2({{\mu^2} - {I^2}} )}$, forming an exceptional point [67,69]. However, at R = 0 cm^–1, the frequency difference shown in Eq. (30) becomes zero, which leads to unstable multi-mode oscillation as shown in the next subsection.

2.5d Concrete Design of Single-Mode Ultra-Large-Area PCSELs and Lasing Stability Analysis Considering Carrier–Photon Interactions

In this subsection, concrete designs of single-mode ultra-large-area PCSELs are provided and their lasing stability is analyzed by considering carrier–photon interactions inside the device. Figures 7(a) and 7(b) show illustrated top and cross-sectional views of the designed double-lattice PCSELs for single-mode ultra-large-area lasing [25]. As described in Section 2.4, the double-lattice PC enables the precise control of the magnitude of κ_1D (or the real part of κ_1D) by changing the hole distance d, while it also enables the control of the phase of κ_1D (or the imaginary part of κ_1D) by the size balance of the two holes (x) [Fig. 7(a)]. On the other hand, the magnitude of the non-Hermitian coupling coefficient µ can be continuously changed by adjusting the phase difference between the upward and downward emission, which can be controlled by adjusting the thickness of the p-cladding layer t_pclad [Fig. 7(b)]. Figures 7(c) and 7(d) show examples of the calculated Hermitian and non-Hermitian coupling coefficients for double-lattice PCSELs with various d, x, and t_pclad. As shown in these figures, the double-lattice PC resonators with backside reflectors enable the arbitrary control of the Hermitian and non-Hermitian coupling coefficients, by which the general conditions discussed in the previous subsections can be satisfied.

Figure 7. (a),(b) Illustrated top view of the double-lattice PC composed of an elliptical and circular hole. Here d is the lattice separation and x is the tuning parameter for the hole sizes. (b) Illustrated cross-sectional view of a double-lattice PCSEL with a DBR. (c) Calculated Hermitian coupling coefficient in the complex plane, when d and x are varied. (d) Calculated magnitude of non-Hermitian coupling coefficient µ as a function of the p-clad thickness t_pclad. Reprinted from with permission from Springer Nature: Inoue et al., Nature Commu. 13, 3262, © 2022.

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Figures 8(a) and 8(b) show the current–output-power (I–L) characteristics and lasing spectra for 3-mm-diameter double-lattice PCSELs with three different values of the real part of the Hermitian coupling coefficients (R), which were calculated by time-dependent 3D-CWT considering carrier–photon interactions [25]. In this simulation, the magnitude of the non-Hermitian coupling coefficient is fixed to µ = 87 cm^–1, and the imaginary part of Hermitian coefficients (I) are adjusted in each structure so that a moderate radiation constant (∼20 cm^–1) is obtained for mode A while much higher radiation constants (>40 cm^–1) are obtained for the other band-edge modes. In Fig. 8(a), the threshold current and slope efficiency are almost the same for the devices with R = 178 cm^–1 and R = 86 cm^–1, while the device with R ∼ 0 cm^–1 shows saturation of the emission power at high injection currents. As for the lasing spectra and the far-field beam patterns shown in Fig. 8(b), single-mode lasing with a nearly diffraction-limited divergence angle (θ_1/e² ∼ 0.03°) is obtained at an injection current of 140 A when R almost equals µ (middle panel). On the other hand, the lasing spectra broadens and the beam divergence angle increases due to multi-mode lasing when R is much larger than µ (left panel), and the divergence angle increases even further when R is nearly zero (right panel). Such an unstable lasing oscillation at R ∼ 0 cm^–1 is caused by the carrier-induced refractive index change and the resultant frequency change inside the device; a device with R ∼ 0 cm^-1 is especially susceptible to such refractive-index (frequency) change because the resonant frequency difference between the fundamental mode and the higher-order mode is zero as shown in Eq. (30) and they are easily coupled with each other via the perturbation of the refractive index distribution. Therefore, for realizing stable single-mode lasing in an ultra-large-area device, it is important to decrease R and µ while maintaining a balance between the two coefficients in order to ensure stable lasing.

Figure 8. (a) Calculated I–L characteristics of 3-mm-diameter PCSELs with three different values of the real part of Hermitian coupling coefficient R. (b) Calculated lasing spectra and far-field beam patterns for the three devices. (c) Calculated I–L characteristics, lasing spectra, and far-field beam patterns for the designed 10-mm-diameter PCSEL. Reprinted from with permission from Springer Nature: Inoue et al., Nature Comm. 13, 3262, © 2022.

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Based on the prior discussion, an even larger-sized PCSEL with a lasing diameter of L = 10 mm was designed [25]. Figure 8(c) show the calculated I–L characteristics, lasing spectrum, and a far-field beam pattern of the designed structure with R = 45 cm^–1, µ = 44 cm^–1, and I = 32 cm^-1. As shown in this figure, kilowatt-class single-mode lasing with a divergence angle of less than θ_1/e²< 0.01° is expected in this 10-mm-diameter PCSEL.

3. Experiments

3.1 Initial Demonstration and Vector Beam Generations

In this subsection, we first describe the initial demonstration of PCSELs. Figure 9(a) shows a schematic of the first PCSEL demonstrated in 1999 [9], followed by the detailed analysis [13]: The PCSEL had a triangular-lattice PC with C_6v symmetry [see also Figs. 1(d) and 1(f)]. The PC layer was integrated with an active (or gain) layer by bonding two wafers A and B. The PC was constructed on top of the wafer B over a 480-µm-diameter area by forming air holes in an InP matrix by electron-beam lithography and reactive ion etching (see the scanning electron microscope image of Fig. 9(a)). An InGaAsP multiple-quantum-well (MQW) active layer with a TE gain and an emission wavelength of ∼1.3 µm was formed in the wafer A. After bonding two wafers A and B in hydrogen atmosphere and removing the substrate of the wafer A, a circular shape p-electrode with 350 µm in diameter was deposited on the wafer A, while a flat n-electrode was formed on the wafer B, and the surface-emission was obtained from the area around the periphery of the p-electrode.

Figure 9. (a) Schematic of the first PCSEL demonstrated in 1999. The inset shows the SEM image of triangular-lattice PC with C_6v symmetry. (b) I–L characteristics and far-field pattern of the PCSEL measured under RT (room temperature) pulsed operation. (c) Lasing spectra of several PCSELs (devices 1–7). The lasing oscillations of the PCSELs occurred at three groups of lasing frequencies (or wavelengths), which agree with the three groups of the symmetric modes (A₁, B₂, and E₂) of the triangular-lattice PC with C_6v symmetry. (d) One example of the polarization state measured for device 4 of Fig. 9(c), which oscillated at the lowest frequency corresponding to that of mode B₂. (e) Polarization state calculated by 3D FDTD for the B₂ mode. (f) Electric-field distribution on (left) and above (right) the plane of the PC calculated by 3D FDTD. (a),(b) Reprinted with permission from Imada et al., Appl. Phys. Lett. 75, 316–318 (1999) [9]. Copyright 1999, AIP Publishing LLC. (c)–(f) Figures 7 and 8 reprinted with permission from Imada et al., Phys. Rev. B 65, 195306 (2002) Ref. [13]. Copyright 2002 by the American Physical Society.

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The developed PCSELs successfully oscillated at RT as shown in the current–light-output power (I–L) characteristics of Fig. 9(b), and a narrow-beam divergence angle of 1.8° was observed [9,13]. As described in Section 2.3 [Fig. 3(c)], the triangular-lattice PC with C_6v symmetry has symmetric modes categorized into three groups A₁, B₂, and E₂, where E₂ is degenerate, and the lasing oscillation is considered to occur at either of these symmetric modes with three different frequencies due to their low radiation constants. The lasing spectra of several PCSELs were measured and the results are summarized in Fig. 9(c) [13]. It is seen in this figure that lasing oscillations of the PCSELs indeed occurred at three different groups of frequencies (or wavelengths), which agrees with the theoretical prediction. We also measured the polarization state of the lasing mode to make a more detailed comparison between the experimental and the theoretical results [13]. One example of the measurement result, which was measured for device 4 of Fig. 9(c), is shown in Fig. 9(d), where device 4 oscillated at the lowest frequency corresponding to that of the mode B₂ of Fig. 3(c). The polarization state calculated by 3D FDTD for the B₂ mode is also shown in Fig. 9(e). The experimental result and theoretical calculation are well coincident, indicating that the developed PCSEL successfully oscillated with a band-edge resonant mode at second-order Γ point of the triangular-lattice PC.

It is physically interesting that the polarization state on the scale of the lattice constant shown in Fig. 3(c), when emitted through the surface, leads to a similar polarization state on the much larger length scale of the electrode as shown in Figs. 9(d) and 9(e). This can be examined in terms of the electric-field distribution. Figure 9(f) shows the electric-field distribution on and above the plane of the PC calculated by 3D FDTD method. Note that the right part of Fig. 9(f) is the same as Fig. 9(e) without the electrode shown. The large broken circle in the left figure indicates the electrode area. It can be seen in the left part of Fig. 9(f) that the field pattern resembles that of the Bloch wave shown in the mode B₂ of Fig. 3(c) for the area under electrode. However, the fields weaken or vanish when the pattern is observed above the PC plane especially for the center area as shown in the right part of Fig. 9(f). The underlying physics of this phenomenon is due to the interference of radiation wave coupled out from the cavity mode (B₂), which was already discussed in Section 2.3. For example, the amplitude of electric field in six equivalent directions is equal in the center area (small circle), as a result, corresponding interference pattern above the crystal becomes zero due to the destructive interference. On the other hand, the amplitude of electric field in six equivalent directions is not equal at the boundary of the electrode (square), resulting in the generation of a non-zero interference pattern with a unique polarization state.

The above series of results indicate that by using symmetric resonant modes at Γ⁽²⁾ point of PCs, one can produce a laser beam with a doughnut-like shape having a unique polarization state, which is so-called vector beam. Note that in the initial device [Fig. 9(a)], because the surface-emission area was limited to only a very small area around the periphery of the p-electrode (in contrast to the total size of the electrode), the cancellation effect of the electric field could not occur sufficiently and a doughnut-like beam pattern was not clearly observed [Fig. 9(b)]. The first clear observation of vector beams was reported in 2004 as shown in Fig. 10 [14], where a square-lattice PC with a symmetric circular unit-cell structure was employed and a sufficient surface-emitting area (in contrast to the total electrode size) was prepared to allow the realization of sufficient cancellation effect. Single-mode CW oscillation with a unique vector beam with tangential polarization were successfully obtained. Then, the band structure of this PCSEL was measured as shown in Fig. 11(a) in 2005 [70], and lasing oscillation was confirmed to occur with a band edge mode having the lowest frequency corresponding to the A₁ mode in Fig. 3(b). In 2006 and 2011, a range of unique vector beams were successfully generated [15,19], where the device configuration was changed from Fig. 9(a) to Fig. 1(a) so that the output beam can be emitted from a substrate side having a ring-shaped n-electrode with a transparency window, by which the emission of laser beam is not disturbed any more by the electrode itself. The PC structures involved both triangular- and square-lattice structures with a symmetric circular unit cell. Figure 12 shows examples of experimentally obtained vector beams emitted from PCSELs with differently designed three PCs: the first two PCs, namely (a) and (b), were square- and triangular-lattice structures which were designed to oscillate at lowest-frequency band-edge modes at the Γ⁽²⁾ point, and the last PC, namely (c), was again square lattice but designed to oscillate at the lowest-frequency band edge of fifth-order Γ (Γ⁽⁵⁾) point [19]. It is clearly seen that various vector beams are successfully emitted: the beam patterns recorded through the polarizer showed different numbers of multiple lobes: two lobes for (a), four lobes for (b), and six lobes for (c). This implies that the polarization direction along the circumference of the doughnut beam rotates once for (a), twice for (b), and three times for (c).

Figure 10. (a) Schematic of PCSEL having a square-lattice PC with a circular unit-cell. (b) I–L characteristics. (c) Lasing spectrum. (d) (Left) Near-field pattern and polarization characteristics. The blue open circles indicate the measurement points with a diameter of about 10 µm, and red double-headed arrows show the direction of polarization at each point. (Right) Far-field pattern of the device. Reprinted with permission from [14]. © The Optical Society.

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Figure 11. (a) Band structure of the device shown in Fig. 10, which was obtained by angle-dependent spectra taken well below the lasing threshold, (b) band structure taken just above the lasing threshold, and (c) detailed structure in the region of the of the Γ point. © 2005 IEEE. Reprinted, with permission, from Sakai et al., IEEE J. Sel. Areas Commun. 23, 1335–1340 (2005) [70].

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Figure 12. Vector beams (lower panels) emitted from PCSELs with differently designed three PCs (upper panels). (a), (b) Beam patterns obtained from the PCSELs with square- and triangular-lattice structures that were designed to oscillate at band-edge modes at the second-order Γ point. (c) Beam pattern from the PCSEL with square lattice but designed to oscillate at the band edge of the fifth-order Γ point. Yellow arrows indicate the electric field direction. For each device, the two panels on the lower-right side show the beam patterns recorded through the polarizer, which have different numbers of multiple lobes: two lobes for (a), four lobes for (b), and six lobes for (c). This implies that the polarization direction along the circumference of the doughnut beam rotates once for (a), twice for (b), and three times for (c). Reprinted with permission from [19]. © The Optical Society.

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3.2 Introduction of Asymmetric Unit-Cell Structure and Watt-Class Operation

Although very unique vector beams can be obtained from symmetric resonant modes at the Γ point of PCs as described previously, we should emphasize here that the symmetric resonant modes are, in principle, unsuitable for high-brightness operations, because their radiation constants are small due to the cancellation effect at the far field. As discussed in Section 2.3 [Fig. 3(d)], the utilization of a square-lattice structure with an asymmetry unit-cell structure is most effective to reduce the cancellation effect. The first trial to introduce an asymmetric unit cell structure for the square lattice was performed in 2006 [15], where the equilateral triangular unit cell structure shown in the center panel of Fig. 3(d) was employed as shown in Fig. 13(a). The device emitted a single lobe beam with a linear polarization as shown in Fig. 13(b).

Figure 13. (a) Scanning electron microscope image and (b) beam pattern for the PCSEL, where the square-lattice PC with the equilateral triangular unit cell structure was employed. The single lobed beam with the linear polarization was emitted as indicated by the yellow arrow, which shows the electric field direction. Reprinted with permission from Springer Nature: Miyai et al., Nature 441, 946–946, © 2006.

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Following the above initial trial to introduce an asymmetric unit-cell structure, the unit-cell structure was further devised. In 2014, a right-angled isosceles-triangular unit-cell structure [20] as discussed in Section 2.3 [Fig. 3(d)] was introduced. Moreover, the wafer-bonding method was replaced by an air-hole-retained epitaxial regrowth method to form PC layer inside the device, which is more suitable for high-brightness operation of the PCSELs: The employment of epitaxial regrowth is important to avoid the formation of undesired interface defects between regions of discontinuous crystallinity, which was unavoidable when we used the wafer-bonding method. Epitaxial growth techniques such as metal–organic vapor-phase epitaxy (MOVPE) [71–73] and molecular beam epitaxy (MBE) [74] were performed, and the regrowth mechanism to retain air holes to form high refractive-index contrast PC layers and also the control of shape of the air hole were investigated [71–74]. Then, watt-class high-power and high-beam-quality operation was demonstrated by a PCSEL developed by a method based on the MOVPE [20].

Figures 14(a)–14(c) show a schematic diagram of the device and SEM images of fabricated PC air holes employed in the demonstration of watt-class operation of a PCSEL. As illustrated in Fig. 14(a), an n-AlGaAs cladding layer, an InGaAs/AlGaAs MQW layer, and a p-GaAs layer for preparing the PC were grown on a n-GaAs substrate. Then, a square-lattice PC with right-angled isosceles-triangular air holes shown in Fig. 14(b) was fabricated by electron beam lithography and dry etching of this wafer. Here, the lattice constant was set to 287 nm to align the resonant wavelength at the Γ-point band edge to the emission wavelength of the MQW. Subsequently, a p-AlGaAs cladding layer and a p-GaAs contact layer were grown atop the PC pattern. As a result, as shown in Fig. 14(c), the air holes were formed near the active layer. Finally, a p-electrode and a window-shaped n-electrode were deposited on the bottom and top sides of the device, respectively. The current injection area was determined by the shape of the p-electrode, which had a square area of a 200 µm × 200 µm, and the laser beam was efficiently emitted through the window-shaped electrode on the side of the n-GaAs substrate.

Figure 14. (a) Schematic of the device fabricated by using the MOVPE regrowth method. (b) Top-view SEM image after dry etching and (c) cross-sectional-view SEM image after regrowth of the PC with right-angled isosceles-triangular air holes. Reprinted with permission from Springer Nature: Hirose et al., Nat. Photonics 8, 406–411, © 2014.

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Lasing characteristics of the developed PCSEL under pulsed conditions are shown in Figs. 15(a)–15(c). In order to suppress thermal broadening of the spectrum during current injection, the pulse width and duty cycle were set to 1 µs and 1%, respectively, for the measurement of the I–L characteristics and the far-field pattern (FFP), and to 50 ns and 5%, respectively, for the measurement of the lasing spectrum. A high slope efficiency of 0.73 W/A and a maximum output power of 3.4 W at a current of 5 A were obtained as shown in the I–L characteristics of Fig. 15(a), where the maximum output power was limited by the laser diode driver. Figure 15(c) shows the FFPs at several injection currents. The device emitted a single-lobed beam with a narrow beam divergence of less than 1° up to 5 A. Such high-power, single-lobed operation is attributed to the asymmetric unit-cell structure as discussed previously. The lasing spectrum shown in Fig. 15(b), which was measured at 280 mA through a single-mode fiber using an optical spectrum analyzer, indicates that single-mode operation was achieved. The measured peak wavelength (λ_peak), full-width at half-maximum (FWHM) of the spectrum, and side-mode suppression ratio (SMSR) were 941.15 nm, 0.02 nm (limited by the instrument resolution), and >60 dB, respectively.

Figure 15. (a) Output power versus current under pulsed operation at 20℃. (b) Lasing spectrum measured through a single-mode fiber with a pulsed injection current of 280 mA. A rather short pulse width of 50 ns was used to suppress thermal broadening of the spectrum during current injection. (c) FFPs at several pulsed injection currents. A narrow beam divergence with FWHM < 1° is maintained up to 5 A. Reprinted with permission from Springer Nature: Hirose et al., Nat. Photonics 8, 406–411, © 2014.

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Next, we show the lasing characteristics of the PCSEL under CW conditions. Figure 16(a) shows the I–L characteristics under CW conditions, which indicate that a high slope efficiency of 0.66 W/A and a high output power of 1.5 W were realized. Figure 16(c) shows the FFPs at several CW injection currents. At an output power of 0.5 W (∼1 A), the divergence angle was less than 0.5°, suggesting that operation with a very high beam quality was achieved. The divergence angle broadened at higher CW injection currents, which was considered to be caused by the emergence of a spatial refractive-index distribution resulting from spatially non-uniform temperature distribution within the lasing area due to heat accumulation during CW current injection. The lasing spectrum measured at a CW injection current of 300 mA indicated that single-mode operation was achieved as shown in Fig. 16(b). The measured λ_peak, FWHM of the spectrum, and SMSR were 941.51 nm, 0.02 nm (limited by the instrument resolution), and >60 dB, respectively. The beam quality factor M² can be evaluated based on measurements of beam propagation properties. The beam radii measured under room-temperature CW conditions at different points along the axis of propagation (z axis) are shown in Fig. 16(d). From these measurements, M² was found to be nearly 1 in both the x and y directions up to a CW current injection of 1.0 A (or output power of up to 0.5 W), indicating that oscillation in a single, fundamental transverse mode was achieved at these currents. In addition, lasers with such a narrow beam divergence do not require any lens for their operation, and thus they are expected to enable unique applications. Such potential was demonstrated by direct irradiation of a sheet of paper placed 8.5 cm from the PCSEL driven at a CW injection current of 1.7 A at 25°C, which yielded a CW output power of 0.86 W. This irradiation immediately ignited the paper, forming a small hole as shown in Fig. 16(e).

Figure 16. (a) Light–current–voltage characteristics under CW operation at 20°C. (b) Lasing spectrum measured through a single-mode fiber at a CW injection current of 300 mA. (c) FFPs at several CW injection currents. The beam had a FWHM < 3° up to 2.5 A. An increase of beam divergence was observed above 1.0 A. (d) Beam radius versus position of focus along the z axis under CW operation at 0.9 A and 1.0 A at 25°C. M² is evaluated by fitting (black and red lines) the experimental data (black circles and red squares). Black and red colors represent the beam radius along the x- and y-directions, respectively. (e) Photograph taken immediately after direct radiation of the PCSEL on a sheet of black paper placed 8.5 cm from the PCSEL. The PCSEL was driven at a CW injection current of 1.7 A at 25°C, which yielded an output power of 0.86 W. Reprinted with permission from Springer Nature: Hirose et al., Nat. Photonics 8, 406–411, © 2014.

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Next, we present the calculated and experimentally obtained lasing band edges and polarization properties of the aforementioned watt-class PCSEL. The band structure was measured near the Γ point by injecting current below threshold and is shown in Fig. 17(a). Four photonic bands are visible, which are labeled A, B, C, and D in order of increasing frequency. Here, the right-angled isosceles-triangular unit cell does not have C_4v symmetry, so the modes of the radiative band edge E, which are shown in Fig. 3(b), were split into modes C and D. Above the threshold current, single-mode lasing was observed in the mode of band edge B, as indicated by the lasing spectrum shown in Fig. 17(a). To understand the mechanism of this single-mode operation, the threshold gain and mode frequencies of all four band-edge modes [A–D; Fig. 17(b)] were calculated while considering the embedded air-hole structure shown in Fig. 14(c). As shown in Fig. 17(b), the mode of band edge B has the smallest radiation constant, which corresponds to the calculated results shown in Fig. 3(d), and thus oscillation occurs on this band edge, in agreement with the experimentally obtained lasing spectrum shown in Fig. 17(a). In addition, the threshold gain margin Δα between the fundamental and higher-order modes within band edge B were sufficiently large when the device size L = 200 µm, as already shown in Fig. 4(c) of Section 2.4, resulting in operation in the single fundamental mode of this band edge. Furthermore, the radiation constant of the lasing mode is large (36 cm^–1) to provide high slope efficiency and high output power because the cancellation in the far field is suppressed due to the asymmetry in the unit-cell structure as discussed already. Note that, in this device, the p-side gold electrode acted as a partial reflector, which improved the slope efficiency by reflecting some of the downward-emitted light toward the n-side, where it was included in the total measured output power [20]. However, this reflection-mediated recycling of downward-emitted light was limited by the absorption by the metal layers used for ohmic contact to the p-GaAs layer and by the roughness of the metal surface. Such limitations can be avoided by using a high-reflectivity DBR reflector, as theoretically shown in Figs. 3(e) and 3(f) and demonstrated experimentally later. The measured FFP and polarization profiles of the output beam are shown in Fig. 17(c). The polarization profiles were obtained by inserting a polarizing plate between the sample and a charge-coupled device (CCD) camera [where polarization angle θ is defined in the upper inset of Fig. 17(c)]. The FFP exhibited a linearly polarized, single-lobed pattern, with a maximum intensity observed at a polarization angle of θ = 45°, corresponding to the asymmetry of the unit-cell structure. The calculated FFP and polarization profiles showed similar features [Fig. 17(d)]. A detailed comparison of the calculated and measured beam profiles, which are in excellent agreement, is presented in Fig. 17(e).

Figure 17. (a) Band structure measured well below the threshold current. The lasing spectrum (right-hand panel) was measured in the surface-normal direction above the threshold current, indicating that single-mode lasing occurs on band edge B. (b) Calculated mode frequencies and threshold gains of band-edge modes A–D. The high thresholds of band-edge modes C and D are scaled for clarity. (c) Measured FFP and polarization profiles in four typical directions (polarization direction is indicated by angle θ, as defined in the upper inset). (d) Calculated FFPs and polarization profiles. (e) Comparison of measured and calculated peak intensities of polarized components. Reprinted with permission from Springer Nature: Hirose et al., Nat. Photonics 8, 406–411, © 2014.

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3.3 Introduction of Double-Lattice Structure and 10-Watt-Class Operation

Following the above progress of the PCSEL, further studies were carried out toward 10-watt-class high-power, high-beam-quality operation using “double-lattice” PCs [22], which were described in Section 2.4. A double-lattice PC consists of two lattice groups shifted from each other in the x and y directions by approximately one quarter of the wavelength in the material. This shift reduces the magnitude of 1D coupling via destructive interference of waves diffracted by 180° at each of the two lattice points while maintaining the magnitude of the indirect 2D coupling as described in Section 2.4. Consequently, optical losses of higher-order modes from the periphery of the resonator increase relative to that of the fundamental mode, resulting in a wider threshold gain margin Δα between these modes and thus single, fundamental mode oscillation in a large lasing diameter of well over several hundred micrometers. Figure 18(a) shows a fabricated double-lattice PC before the MOVPE regrowth technique using an organic-arsenic source. Here, structure II in Fig. 4(c) of Section 2.4 was employed for the device with lasing diameter of 500 µm, in which two elliptical air holes of the same size were combined to obtain a large Δα in a 500-µm-diameter circular area as described in Fig. 4(c). Note that in this design, structural asymmetry was introduced in the vertical rather than the in-plane directions by creating a difference in the height of these two elliptical holes as shown in the cross-sectional scanning electron microscopy (SEM) images of Fig. 18(b) in order to obtain a sufficiently high radiation constant (∼20 cm^–1). To experimentally realize a double-lattice structure with such a height difference, a two-step etching process was performed, in which one hole was masked while the other was etched to a depth commensurate with the desired height difference, and then both were etched simultaneously [22]. Following this etching process, MOVPE regrowth was performed. An adequate difference of air-hole height was maintained following this regrowth as shown in Fig. 18(b).

Figure 18. Demonstration of 10-W-class high-power, high-beam-quality operation of a PCSEL employing a double-lattice PC under pulsed conditions. (a) SEM image of the double-lattice PC after dry etching. (b) Cross-sectional SEM images of the deeper and shallower air holes after MOVPE regrowth. (c) I–L characteristics of a double-lattice PCSEL with 500-µm-diameter circular lasing area under pulsed operation. (d) Near-field and (e) far-field patterns. Reprinted with permission from Springer Nature: Yoshida et al., Nat. Mater. 18, 121–128, © 2019.

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Figures 18(c)–18(e) show the measured lasing characteristics of a device with a circular p-electrode of 500 µm diameter under pulsed conditions with a pulse width of 200 ns. As shown in Fig. 18(c), an output power exceeding 10 W was successfully obtained. In this device, the slope efficiency was about 0.4 W/A and was restricted by undesired emission into the p-side toward the p-electrode, which scattered and absorbed some of the light. This undesired loss can be mitigated by efficiently redirecting the p-side-emitted light toward the n-side by introducing a reflector, such as a DBR, between the PC layer and the p-electrode, upon which the slope efficiency is expected to improve to more than 0.8 W/A, as described later. The measured near-field patterns (NFPs) and FFPs at various injection currents [Figs. 18(d) and 18(e)] show that a single-spot beam with a very narrow divergence angle of less than 0.3° estimated from the 1/e² width was emitted over the entire 500-µm-diameter area. These results indicate that broad-area (500-µm-diameter) coherent lasing was realized. The brightness of this laser reached 300 MW cm^–2 sr^–1, which is three times higher than the brightness of conventional semiconductor lasers (≤100 MW cm^–2 sr^–1).

In the 500-µm-diameter device described above, a backside DBR mirror was not introduced, so the p-side-radiated (i.e., downward) radiation was not efficiently converted into output power [22]. To improve the slope efficiency of the PCSEL, the introduction and optimization of a DBR mirror on the backside of the device were carried out as discussed in Section 2.3 [Figs. 3(e) and 3(f)]. Figures 19(a) and 19(b) show top- and cross-sectional-view SEM images of the fabricated device with the DBR mirror [24]. Here, the DBR mirror was composed of 18 pairs of Al_0.1Ga_0.9As/Al_0.9Ga_0.1As grown next to the p-cladding layer. The reflectivity R of this DBR was measured to be ∼0.9 at the lasing wavelength of ∼940 nm. In addition, the device employed a double-lattice PC, whose in-plane asymmetry was introduced by combining circular and elliptical air holes instead of air holes with different heights as done before; in this way, the PC could be fabricated by a simpler, one-step etching process [24]. Figure 19(c) shows the dependence of the slope efficiency on the p-cladding layer thickness, evaluated from I–L characteristics. The slope efficiency and threshold current density were periodic over a change of ∼140 nm of the p-cladding layer thickness, corresponding to a change of one wavelength in the p-cladding layer. Constructive interference of the reflected and upward radiated light was considered to occur at a p-cladding layer thickness of ∼1130 nm, resulting in a high slope efficiency exceeding 0.8 W/A. These experimental results showed good agreement with the theoretical analysis based on Eq. (15) in Section 2.3 [dotted line in Fig. 19(c)]. The I–L characteristics of a PCSEL whose p-cladding layer thickness was set to obtain a high slope efficiency based on the results of Fig. 19(c), is shown in Fig. 19(d). Owing to the high slope efficiency, a peak output power exceeding 20 W was obtained. In addition, the FFP was observed to have a narrow beam divergence angle of 0.2° (measured at the 1/e² width). Such high-power, high-beam-quality operation resulted in a laser brightness of 1.5 GW cm^–2 sr^–1 under pulsed conditions. With this performance, the application of PCSELs to lens-free LiDAR system with the smallest size of their class for smart mobility of robots [24], which are described in Section 4.1, has become possible.

Figure 19. Demonstration of improvement of slope efficiency by introducing a backside DBR reflector. (a) Top- and (b) cross-sectional-view SEM images after regrowth. (c) Slope efficiencies evaluated for devices with various p-cladding layer thicknesses. (d) I–L characteristics for a fabricated PCSEL with an optimized p-cladding layer thickness. A high peak output power exceeding 20 W and a high beam quality (M² ∼ 1.1 and M² ∼ 1.6 in the x and y directions, respectively), as indicated by a FFP with the very narrow beam divergence, resulted in a laser brightness of 1.5 GW cm^–2 sr^–1. Reprinted from [24] under a Creative Commons license.

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Next, we explain the progress of high-power PCSELs under CW operation. Compared with PCSELs used for pulsed operation, it is important to increase the device size to suppress heat accumulation under CW operation [22,75]. First, we show 10-W-class operation of a PCSEL under CW conditions by increasing the area from 500 µm in diameter, where 10-W-class (and even higher power) pulsed operation was achieved as described above, to 800 µm [22,75] to 1 mm in diameter. To maintain high-beam-quality, single-mode operation in the larger area, the double-lattice structure was optimized to have a sufficiently high Δα. To further increase Δα for larger lasing diameters, it is necessary to achieve not only the cancellation of 1D coupled waves, but also the canceling of 1D and 2D coupled waves [22] as discussed in Fig. 4(d) of Section 2.4. To do this, the distance between the two lattice-point groups and the balance between the sizes of the air holes of the two lattice-point groups were finely tuned. Here, we show the results of 1-mm-diameter PCSELs. The fabricated 1-mm-diameter PCSEL was mounted on a heat sink via a submount with high thermal conductivity in the p-side down configuration as shown in Fig. 20(a). Figures 20(b)–20(d) show the measured lasing characteristics of the device under CW operation. As shown in Fig. 20(b), an output power of 10 W was successfully obtained even under CW operation. The measured FFPs at various injection currents [Fig. 20(b)] show that a single-spot beam with a very narrow divergence angle of ∼0.1° (at 1/e²) was obtained. Such high-power, high-beam-quality CW operation enables the application of PCSELs to laser marking, as described in Section 4.2. Figure 20(d) shows the measured lasing spectra at various injection currents. Single-peak spectra were observed at all tested injected currents, indicating that purely single-mode oscillation was realized even in the 1-mm-diameter PCSEL. Although the linewidths of these spectral measurements were limited by the resolution of the spectrometer, an example of a more detailed result of the linewidth for a 1-mm-diameter PCSEL is shown in Fig. 20(e). Figure 20(e) shows the frequency noise spectrum of another 1-mm-diameter PCSEL with a similar PC design to the PCSEL shown in Figs. 20(a)–20(d), which was measured with a linewidth analyzer. As shown in the figure, the intensity of the frequency noise increased as its frequency decreased; the origin of such low-frequency noise was mainly attributed to the external noise of the current source. On the other hand, the noise intensity became almost constant in a frequency range above 1 MHz, which indicates the regime where white noise induced by spontaneous emission is dominant. Therefore, the intrinsic spectral linewidth could be evaluated using the frequency noise level at frequencies in this region, and a linewidth of less than 1.23 kHz (which reaches the lower limit of the measurement) was observed [76]. This extremely narrow linewidth is due to the PCSEL's high-power (i.e., high-photon-density), yet purely single-mode operation. This result suggests that PCSELs are promising for applications requiring laser souses with high coherence.

Figure 20. Demonstration of 10-W-class single-mode CW operation of a 1-mm-diameter PCSEL. (a) Photograph of the 1-mm-diameter PCSEL, which was mounted on a heat sink via a submount in the p-side-down configuration. Au wires were bonded to the n-side electrode of the PCSEL and to the submount surface (p-side). (b) I–L characteristics under CW operation. (c) FFPs at injection currents of 10 A, 14 A, and 18 A. (d) Lasing spectra measured at various injection currents. A narrow spectral width was observed. Single-mode oscillation was realized. (e) Frequency noise spectra measured by the linewidth analyzer for a different 1-mm-diameter device with a similar PC design. A linewidth of less than 1.23 kHz (which reaches the lower limit of the measurement) was observed.

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3.4 Hermitian/Non-Hermitian Control and Realization of CW 50-W-Class Output Power with CW Brightness of 1 GW cm^–2 sr^–1

Next, we describe the very recent result of CW high-brightness operation of PCSELs with an even larger area (3 mm in diameter). In Section 2.5, we described the design guideline to realize single-mode oscillation over areas of 3–10 mm in diameter, wherein both the Hermitian coupling (i.e., coupling without energy loss) and the non-Hermitian coupling (i.e., coupling with energy loss through radiation) are controlled (or reduced) while maintaining their balance. Based on this guideline, a 3 mm PCSEL was developed [26], where the Hermitian coupling was controlled by adjusting structural parameters of the double-lattice structure (specifically, the lattice separation d and the balance of air-hole sizes x [see Figs. 7(a) and 7(c)], while the non-Hermitian coupling was controlled by changing the degree of interference of radiative waves [see Figs. 7(b) and 7(d)]. Furthermore, to compensate for a refractive index change caused by the temperature rise under the CW current injection, a pre-installed lattice-constant distribution was introduced to maintain the Hermitian and non-Hermitian optical couplings.

Based on this strategy, we developed the 3-mm-diameter PCSEL as shown in Fig. 21(a) [26]. Figure 21(b) shows I–L characteristics of the 3 mm PCSEL under CW conditions. The threshold current was 25 A and the slope efficiency was ∼0.72 W/A. A CW output power exceeding 50 W was obtained from the single-chip PCSEL at injection currents of 100–110 A. Figure 21(c) shows the FFPs at 50W, and it is seen that the divergence angle is extremely narrow ∼0.05°. Note that the value of M² is 2.36 in spite of single-mode oscillation, which is due to the super-Gaussian electromagnetic-field intensity profile caused predominantly by the uniform current injection. The CW brightness, evaluated using the measured output power and FFP widths at 110 A, reached 1 GW cm^–2 sr^–1. The lasing spectrum at ∼50 W is also shown in Fig. 21(c). The spectral width was measured to be 3 pm, which was limited by the spectral resolution of our spectrometer, and was finer than the predicted spectral spacing between the fundamental and next-higher-order modes, indicating that single-mode oscillation was successfully achieved.

Figure 21. (a) Photograph of the fabricated 3-mm-diameter PCSEL chips. (b) I–L characteristics under CW conditions. (c) Lasing spectrum and far-field pattern at 110 A (50 W). Reprinted from [26] under a Creative Commons license.

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The results show that the pre-installed lattice-constant distribution together with the control of Hermitian and non-Hermitian couplings have contributed to the realization of single-mode (single-wavelength), high brightness operation of 1 GW cm^–2 sr^–1. This obtained brightness rivals those of bulky lasers such as gas and solid-state lasers. Controlling the Hermitian and non-Hermitian coupling coefficients and introducing a lattice-constant distribution suitable for devices of even larger scales (for example, 10 mm diameters) are expected to contribute to the realization of 1-kW-class, high-beam-quality operation of PCSELs. This result is an important milestone toward the replacement of conventional, bulkier solutions and toward innovation in a wide variety of industrial applications, from smart material processing to aerospace applications. The details on this topic will be reported separately more in detail [34].

3.5 Extension of Emission Wavelength Range of High-Power PCSELs

In this subsection, we describe further developments of optical-communication-band InP-based PCSELs after its initial demonstration, and also quantum cascade PCSELs operating at far- and mid-infrared wavelength ranges.

3.5a InP-Based PCSELs Operating in the Optical Communication Band

As described in Section 3.1, an InP-based PCSEL was demonstrated in 1999 [9,10] as the first PCSEL. This PCSEL consisted of a triangular-lattice PC and a detailed discussion of its basic characteristics were provided in Section 3.1. As explained in Section 3.1, PCSELs at this early stage were fabricated by bonding of two wafers to form the PC air holes near the active layer. To realize high-power operation of InP-based PCSELs, it is important to achieve a reasonably low threshold current density as well as to develop a fabrication method that avoids unwanted defects which can be formed at the bonding interface in the wafer bonding process. To achieve a low threshold, it is worthwhile enhancing the PC resonance effect by reducing the distance between the active layer and the PC layer, such that optical coupling between the PC layer and the active layer is strengthened. In addition, it is important to make the PC layer as thick as possible while confining only a single mode in the vertical direction. Next, to avoid the formation of the aforementioned defects, it is essential to employ a crystal regrowth method to embed the air holes in semiconductor [77–79], which eliminates the need for wafer bonding.

The fabrication of 1.3-μm-wavelength InP-based PCSELs by the above-mentioned crystal regrowth were reported in Refs. [77,78]. In these works, an n-InGaAsP layer was first grown on an n-type InP substrate by the MOVPE method. Then, a square-lattice 2D PC structure with circular air holes was formed in the n-InGaAsP PC layer and the InP substrate using electron-beam lithography and dry etching processes. The lattice constant of the PC was set to 404 nm in order to operate at a wavelength of 1.3 µm. After the PC formation, the InP layer was regrown to seal the air holes. Figures 22(a) and 22(b) show cross-sectional SEM images of the air holes before and after the regrowth of the InP layer, respectively. It is shown in Fig. 22(a) that the diameter and depth of the air holes before the regrowth were 181 nm and 650 nm, respectively. After the regrowth, vertically uniform air-hole shapes with a thin and flat overgrown InP layer of less than 100 nm were obtained, as shown in Fig. 22(b). The diameter and depth of the air holes after the regrowth were found to be 190 nm and 505 nm, respectively. It is seen that, even following regrowth, the diameter of the air holes was almost unchanged and an air-hole depth of more than 500 nm was still obtained. Then, on the flat InP space layer, an InGaAsP MQW active layer and a separated confinement heterostructure (SCH) layer were grown. This kind of structure, with its narrow spacing between the PC layer and the active layer, strengthened the optical coupling between these two layers. After the regrowth, p- and n-electrodes were formed. The current injection area was determined by the diameter of the p-electrode, which was 150 µm. The emission of this laser was observed from the region of the PC surrounding the p-electrode.

Figure 22. Cross-sectional SEM images of air holes (a) before and (b) after regrowth of the InP spacer on the PC layer and the InP substrate. Reprinted from [77] © The Optical Society.

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The lasing characteristics of the fabricated InP-based PCSEL were evaluated under CW conditions at a temperature of 15°C. Figure 23(a) shows the optical power (L)–current (I)–voltage (V) characteristics, and the inset shows the lasing spectrum at an injection current of 200 mA. The PCSEL exhibited single-mode lasing with a threshold current of 120 mA (threshold current density ≤ 0.68 kA/cm²), a differential resistance of 0.44 Ω at 300 mA, and a peak wavelength of 1320.8 nm. The threshold current under pulsed conditions with a pulse width of 10 µs and a duty cycle of 0.01% was confirmed to be comparable to that under CW conditions. Figure 23(b) shows near-field NFP and FFPs, including polarization states in the horizontal and vertical (Γ–M) directions of the PCSEL at an injection current of 200 mA under RT and pulsed conditions with a pulse width of 100 ns and a duty cycle of 0.01% for the same chip in Fig. 23(a). For the NFP, a uniform lasing beam profile from the PCSEL was confirmed, implying that uniform 2D oscillation occurred within the PC owing to the high optical coupling coefficients obtained due to the enhancement of coupling between the PC and active layers. The FFP for all polarizations generally exhibited a doughnut-like beam shape (with a slight distortion), which is theoretically predicted for the case of lasing in the mode of band edge A of a square-lattice PC with a circular hole structure, owing to the rotationally symmetric nature of the electromagnetic field as described in Section 3.1. The divergence angle in the horizontal and vertical directions were measured to be 1.0° and 0.8°, respectively, confirming that a narrow beam divergence was obtained. Note that side lobes appear in the FFP because the electric field was diffracted around edge the p-electrode (see the NFP in Fig. 23(b)); these side lobes can be removed by modifying the electrode structure appropriately. The horizontally-polarized FFP showed a node at the center owing to the cancellation of the radiative electric field from the upper and lower edges of the p-electrode, while the vertically polarized FFP showed a weaker single-lobed pattern with an antinode at the center owing to the partial coverage of the p-electrode, that is, to the incomplete cancellation of the radiative electric field from the left and right edges of the p-electrode.

Figure 23. (a) L–I–V characteristics at 15°C under CW conditions. The inset shows the lasing spectrum at an injection current of 200 mA under the same measurement conditions. (b) NFP and FFPs including horizontal and vertical polarization states of the PCSEL at an injection current of 200 mA under RT and pulsed conditions with a pulse width of 100 ns and a duty cycle of 0.01% for the same chip in Fig. 23(a). Reprinted from [77] © The Optical Society.

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Further studies [78] were carried out to realize high output power with a narrow-divergence, symmetric, single-lobed beam, which is essential to achieve high optical coupling to a single-mode fiber in optical communications and to achieve long-distance, eye-safe sensing in sensing applications. To attain high output power and single-lobed beam emission, concept of the double-lattice PC structure was employed in InP-based PCSELs. The double-lattice structure was used to strengthen the 180° diffraction of light within the PC by constructive interference. In addition, the asymmetry of the double-lattice structure was used to enhance the emission of light from the surface of the PC and to obtain a single-lobed beam.

A perspective-view schematic of the PCSEL structure with a double-lattice PC is shown in Fig. 24(a). A 3D image constructed from slice-and-view SEM observations of the air holes after regrowth is shown in Fig. 24(b). The formation of double-lattice air holes was confirmed, and the depths of the large and small air holes after regrowth were found to be 1060 nm and 670 nm, respectively. The aspect ratio of both air holes was over 6, which was around twice as large as that in the case of the single-lattice PC explained previously. Such deep air holes with a high aspect ratio further enhance the optical confinement within the PC layer. After the regrowth, a circular isolation mesa with a diameter of 200 µm was formed by photolithography and dry etching processes to remove the highly doped contact layer, and this was followed by chemical vapor deposition of an insulating film. The current injection area was restricted by this isolation mesa. After the formation of the mesa, a square p-electrode was deposited on the top of the device, and a n-electrode with a circular window was deposited on the back side of the device using photolithography and evaporation processes. The n-electrode allowed the light to be emitted through its circular window without obstruction, as illustrated in Fig. 24(a).

Figure 24. (a) Perspective-view schematic of the PCSEL structure and (b) 3D image constructed from slice-and-view SEM observations of the air holes after regrowth. Reprinted from [78] © Optica Publishing Group.

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The lasing characteristics of these PCSELs were evaluated under pulsed conditions first. Figure 25(a) shows the IL characteristic under pulsed conditions with a pulse width of 1 µs and a duty cycle of 0.1% at 25°C; the IL characteristic of a single-lattice PCSEL with a circular air hole and the same device configuration is also shown as a reference. It can be seen that the light output power of the double-lattice PCSEL is much higher than that of the single-lattice PCSEL, and that the slope efficiency of the double-lattice PCSEL is 25 times higher than that of the single-lattice PCSEL. These results indicate that the introduction of the double-lattice PC was effective to enhance the slope efficiency of surface emission owing to the asymmetric nature of the electromagnetic field in the double-lattice structure. The inset of Fig. 25(a) shows the FFPs of the double- and single-lattice PCSELs under pulsed conditions at an injection current of 400 mA. In the case of the single-lattice PC, an annular beam shape was observed due to the symmetric nature of the air hole and the electromagnetic field distribution as described in Section 3.1. On the other hand, the double-lattice PCSEL showed a single-lobed beam owing to the asymmetric nature of the electromagnetic field. The beam divergence angle was as narrow as 1.0° for the double-lattice PCSEL.

Figure 25. (a) I–L characteristics of PCSELs with double- and single-lattice PCs consisting of the same device structure under pulsed conditions with a pulse width of 1 µs and a duty cycle of 0.1% at 25°C. FFPs of PCSELs with double- and single-lattice PCs under pulsed conditions at an injection current of 400 mA are also shown in the insets. (b) L–I–V characteristics of the double-lattice PCSEL under CW conditions at a temperature of 25°C. (c) Lasing spectra of the double-lattice PCSEL under CW conditions at a temperature of 25°C (injection current: 400 mA and 800 mA). Reprinted from [78] © Optica Publishing Group.

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Figure 25(b) shows light–current–voltage characteristics, and Fig. 25(c) shows lasing spectra at injection currents of 400 mA and 800 mA, respectively, under CW conditions at a temperature of 25°C. Lasing oscillation occurred at an injection current (threshold current) of 320 mA. A light output power of over 100 mW was successfully achieved under CW conditions. The slope efficiency and differential resistance at injection currents of 400–600 mA were 0.20 W/A and 0.69 Ω, respectively. From the lasing spectra, single-mode lasing with a high SMSR of over 50 dB was confirmed even at a high injection current of over 800 mA. It is considered that the formation of deep air holes and the introduction of the double-lattice PC structure led to lasing operation with a high SMSR. Furthermore, very recently, the slope efficiency was increased even further by introducing a back reflector to a 200-µm-diameter InP-based PCSEL, with which a light output power of 400 mW was achieved under CW, single-mode operation.

The expected applications of the aforementioned InP-based PCSELs include fiber-based communications and also terrestrial and inter-satellite freespace communications. In addition, owing to its 1.3-µm wavelength, InP-based PCSELs with high peak output powers are suitable as eye-safe lasers for LiDAR applications.

3.5b Quantum Cascade PCSELs

In this subsection, we review quantum cascade PCSELs operating at far-infrared (terahertz) and mid-infrared wavelengths. These PCSELs are important for imaging, sensing, and optical communication applications. Intersubband transitions in quantum wells are used for far- to mid-infrared emission in quantum cascade PCSELs [16]. The light emitted in these transitions exhibit TM polarization. Therefore, TM band-edge modes of PC are employed for lasing. In 2008, Marshall et al. reported quantum cascade PCSELs in the terahertz region, by using a PC slab sandwiched by metallic layers, which acted as a planer waveguide to confine light [80]. A peak output power of 2 mW with an emission frequency (wavelength) of ∼2.75 THz (109 µm) was demonstrated under pulsed operation (10 kHz with a 1% duty cycle) at 10 K.

A mid-infrared quantum cascade PCSEL with a higher output power was reported by Liang et al. in 2019 [81]. A schematic of their quantum cascade laser is shown in Fig. 26(a). The active region was formed by InGaAs/AlInAs layers. The emission wavelength was designed to be ∼8.5 µm. A 800-nm-thick Si-doped InGaAs layer was grown on the active layer and was used to form the PC. SiN_x hard masks were used to deeply etch the InGaAs layer to fabricate rod-type PCs. They prepared square-lattice PCs with circular and right-angled isosceles-triangular rods for realizing doughnut-shaped and single-lobed beams, respectively. SEM images of the two rod shapes are shown in Fig. 26(b). After the PC rod formation, a Si-doped InP layer was grown to embed the rods. A cross-sectional view of the embedded rods is shown in Fig. 26(c). It is apparent that the rods were completely buried in the InP layer without defects nor voids. A square mesa with dimensions of ∼1.1 × 1.1 mm² was formed to define the lasing cavity size. A backside electrode was formed by deposition of a 3-µm-thick gold layer, and a front-side window electrode was formed by deposition of gold on top of the substrate. The finished PCSEL was mounted on a submount in the epi-down configuration.

Figure 26. (a) Schematic diagram of a quantum cascade PCSEL. (b) SEM images of SiN_x hard masks used to fabricate PCs. (c) Cross-sectional SEM image of rods embedded InP after regrowth (color is added to indicate each layer). Reprinted with permission from Liang et al., Appl. Phys. Lett. 114, 031102 (2019) [81]. Copyright 2019, AIP Publishing LLC.

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The light–current–voltage characteristics under pulsed operation at room temperature are shown in Fig. 27(a). Measurements were made for both circular-rod and triangular-rod devices. The threshold current density was found to be around 2 kA cm² for both devices. Figure 27(b) shows the spectra of the corresponding lasers, measured using Fourier-transform infrared spectrometers, with resolutions of 0.075 cm⁻¹ and 0.125 cm⁻¹ for the circular-rod and triangular-rod devices, respectively. It can be seen that lasing is observed at wavelengths of around 8.5 µm. As seen in Fig. 27(a), the maximum peak powers for the circular-rod and the triangular-rod devices were 176 mW and 333 mW, respectively, and their slope efficiencies were 7.8 mW/A and 17.5 mW/A, respectively. The slope efficiency of the triangular-rod device was higher than that of the circular-rod PCSEL, owing to the alleviation of destructive interference of the electric field at the center of the surface-emitted beam as explained in Section 3.2. The surface-emitted beam was found to be have an extremely small divergence angle (<1°) owing to the large-area single-mode oscillation. Since the reporting of these mid-infrared quantum cascade PCSELs, further improvements have been made, including the employment of a strain-balanced active region, the realization of a stronger effective index contrast by utilizing a 2-µm-thick PC layer, and the introduction of a grid-like top electrode to enhance the current injected into the middle of a large, 1.5 mm × 1.5 mm device. These improvements have led to increases of the slope efficiency to 130 mW/A and the light output power to 5 W under pulsed operation [82]. These laser sources are expected to play an important role in industry and research applications requiring high-power, high-beam quality laser light in the mid-infrared wavelength range.

Figure 27. (a) Light current voltage characteristics of circular-rod and triangular-rod quantum cascade PCSELs under pulsed operation. The peak power of light emitted from the surface of the devices are measured. (b) Measured spectra of the same quantum cascade PCSELs in Fig. 27(a) (operating conditions are mentioned in the legend). Reprinted with permission from Liang et al., Appl. Phys. Lett. 114, 031102 (2019) [81]. Copyright 2019, AIP Publishing LLC.

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4. Applications

As described in the previous sections, PCSELs have excellent features such as high-power, high-beam-quality, narrow-beam-divergence, single-mode operation, and, in addition, an extended wavelength range. Such features offer the potential for PCSELs to be used in a wide range of attractive applications, including next-generation remote sensing for smart mobility, laser processing for smart manufacturing, communications, medical applications, and even space applications. In this section, we focus on the use of PCSELs for two such applications: The first is their use in a compact LiDAR system for autonomous, smart mobility of robots, and the second is their use in a compact laser processing system for smart manufacturing.

4.1 Application to LiDAR System

In this subsection, we describe the LiDAR applications of PCSELs. LiDAR [83–85] using a time-of-flight (ToF) method is one of the most important sensing technologies for smart mobility of robots and autonomous vehicles. In ToF LiDAR, a pulse of light emitted from a laser source is scanned by a beam-scanning device (e.g., a rotating mirror [86]) and irradiated onto an object. A portion of this light is reflected or scattered from this object and detected by a photodetector. A bandpass filter is placed in front of the photodetector to filter out background light from other sources, such as sunlight, in order to a reduce the detection noise. One can measure the distance between the LiDAR system and the object based on the time difference between the emission of the pulse and the detection of the reflected light. For long-distance, high-spatial-resolution ranging, a pulsed laser source with a high peak power and a narrow beam divergence is required. In addition, to improve the signal-to-noise (S/N) ratio, the use of a narrow bandpass filter is desirable, which requires that the spectrum of the laser source has a narrow linewidth and a small temperature dependence.

However, existing ToF LiDAR systems mostly rely on conventional, Fabry–Perot (FP)-type semiconductor lasers as the laser source, which struggle to meet the above requirements due to undesirable features inherent to their edge-emitting resonators. Specifically, the beams emitted from these lasers have large divergence angles and are largely asymmetric, and thus the beams must be carefully reshaped by using a complicated series of lenses. Furthermore, the spectra of these lasers have broad linewidths and a large temperature dependence, so broad bandpass filters, rather than a narrow one, must be used at the photodetectors, which cause the detected signal to be affected by background noise. PCSELs can solve these issues. In particular, the beam of a PCSEL is emitted from the surface of the device, which enables the beam to have a symmetric circular shape and a very narrow divergence angle that is inversely proportional to the coherent lasing area, and thus no external lenses are needed for beam reshaping and collimation. In addition, the narrow linewidth and small temperature dependence (≤1/3 of that of FP-type lasers) of the lasing spectrum [24], which is fixed by the lattice constant of the PC, allow the use of a narrow bandpass filter to filter out background light in front of the detector of the LiDAR system, leading to a higher S/N ratio operation. These unique features are desirable for LiDAR applications.

An actual LiDAR system using the 10-W-class, 500-µm-diameter PCSEL (shown in Section 3.3) was developed in 2020 for the first time [24], and a smaller system (smallest size of their class) was also developed in 2021. Figures 28(a) and 28(b) show schematic diagrams of LiDAR systems using a conventional FP-type laser and a PCSEL. The LiDAR system using the FP-type laser required a complex system of multiple lenses to reshape the beam as mentioned previously. On the other hand, the LiDAR system using the PCSEL required no such lenses. In particular, in the 2021 PCSEL-based LiDAR system [shown in Fig. 28(e)], owing to the compactness of its lens-free operation, the PCSEL was able to be placed in a hole in the center of the condenser lens, which allowed the projector and receiver to be placed on the same side of the enclosure. Figures 28(c) and 28(d) compare the scanned beams projected by the FP-type-laser-based and the PCSEL-based LiDAR systems onto a screen (set at a distance of ∼1 m from each LiDAR system). For the FP-type-laser-based system, the scanned beam patterns were overlapped due to the large beam diameter of the FP laser, whereas for the PCSEL-based system, there was no such overlap owing to the small beam divergence angle (∼0.1° at FWHM) of the PCSEL, and thus each beam spot was clearly resolvable. Figure 28(e) shows a photograph of the 2020 and 2021 PCSEL-based LiDAR systems and a demonstration of the latter system. As seen in the distance map in the right panel, two fingers are clearly resolved, indicating that the PCSEL-based LiDAR has a high spatial resolution in addition to its small size. These results indicate that, by replacing the FP-laser with the PCSEL as the light source of LiDAR systems, not only can the external lens system be eliminated, but so too can the spatial resolution and sensing performance of the LiDAR system be improved. Although Fig. 28(e) shows an example of measurement at a relatively short distance, measurements at longer distances are also possible owing to the narrow divergence angle of the PCSEL, which keeps the beam spot small with a circular diameter of <5 cm (at FWHM) even at a distance of 30 m [24]. A compact LiDAR system with such a measurement range is promising as a sensor for autonomous transfer robots in factories. Figure 29(a) shows photographs of autonomous transfer robots with 2021 PCSEL-based LiDAR systems. The compactness of the LiDAR systems allowed them to occupy only a small space on the robots. Figure 29(b) shows a demonstration of autonomous driving of these robots. In this demonstration, Robot 1 was set to follow a person and Robot 2 was set to follow Robot 1. As shown in these photos, by detecting their surroundings using the PCSEL-based LiDAR, the robots successfully detected and followed the person or other robot automatically. These results indicate that PCSELs will be key devices for future smart mobility.

Figure 28. Development and demonstration of PCSEL-based LiDAR systems. (a), (b) Schematic of ToF LiDAR system. The light source consists of either an FP-type laser with external lenses or a lens-free PCSEL. (c), (d) Beam patterns produced by scanning the beam at a pitch of 0.25° when the (b) FP-type laser or (c) PCSEL was used as the light source. (e) Photograph of the developed PCSEL-based LiDAR system and demonstration. (c),(d) Reprinted from [24] under a Creative Commons license.

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Figure 29. (a) Photograph of autonomous transfer robots with PCSEL-based LiDAR systems. (b) Demonstration of autonomous robots tracking. Robot 1 detected and followed the person, and robot 2 detected and followed robot 1.

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4.2 Application to Compact Processing Systems

Next, we describe the material processing applications of PCSELs. Specifically, we show the marking of a metal surface using a CW 10-W-class, 1-mm-diameter PCSEL (shown in Section 3.3) [87]. Figure 30(a) shows the laser marking system in which the PCSEL was integrated. The PCSEL was mounted onto a heat sink and installed to the top section of the system in an upside-down configuration. The narrow-divergence beam emitted from the PCSEL was focused by a simple focusing lens system, which was constructed from commercially available 0.5-inch optics and had a total height of under 4 cm. With this lens system, the laser beam could be focused to a small spot diameter of ∼10 µm on the metal surface owing to the high beam quality of the PCSEL. An XY stage was used to translate the metal surface with respect to the focused laser spot. The movement of this stage could be automated by computer-aided design (CAD), while the laser was turned on and off in synchronization with the CAD-based movement. Figure 30(b) shows a magnified image of a stainless steel plate being marked with the logo of Kyoto University. The bright shine of the focused laser spot on the metallic surface indicated that the laser light was reacting with the material. Figures 30(c) and 30(d) show finished examples of metal surfaces marked using this system. The characters “PCSEL” [Fig. 30(c)] and the logo of Kyoto University [Fig. 30(d)] were successfully drawn on the stainless steel surface. Such fine patterns can be clearly marked by the compact PCSEL-based marking system. In the future, even larger-area and higher-power PCSELs (such as the 3-mm-diameter PCSEL demonstrated in Section 3.4 and the 100-W-to-1-kW-class PCSELs predicted in Section 2.5), are expected to open the door to a wider variety of material processing applications, such as cutting, welding, and 3D printing.

Figure 30. Demonstration of laser marking processing using a CW 10-W-class, 1-mm-diameter PCSEL. (a),(b) Compact laser marking system and demonstration. (c), (d) Results of laser marking process. The characters of “PCSEL” and the logo of Kyoto University were drawn on the metal (stainless) surface.

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5. Summary and Future Prospects

In this tutorial paper, we have first described the theory of PCSELs including their basic structure and lasing principle, simulation methods, and strategies to realize single-mode, high-power and high-beam quality operation (up to 1 kW). We then have presented experimental demonstrations, from pioneering works to the state of the art, including both pulsed and CW single-mode and high-brightness (1 GW cm^–2 sr^–1) operations. We have also discussed the extension of wavelengths of PCSELs to the telecommunications band and the mid-infrared regime, and referred to applications toward smart mobility and smart manufacturing.

Finally, we would like to note that in order to strengthen the research and development of the PCSELs, and to accelerate the social implementation of PCSELs, the Center of Excellence (COE) for PCSELs has been established in Kyoto University [88]. Start-up companies such as Vector Photonics from the University of Glasgow [89] and PHOSERTEK from National Chiao Tung University [90] have been also established. In the following, the activity of PCSEL COE at Kyoto University is briefly introduced. Over 1000 m² of floor space has been secured to provide an environment for conducting series of trial productions and evaluations of PCSELs and for collaborating with user companies and institutions, as well as companies interested in manufacturing. Due to the recent surge of interest in PCSELs, the number of companies inquiring to the COE has increased to over 100; these companies are based in both domestic and overseas markets and they are related not only to smart mobility and smart manufacturing, but also to mobile devices, telecommunications, lighting, and space applications (Fig. 31).

Figure 31. Future prospects of PCSELs.

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The social implementation of PCSELs at the COE is being accelerated in two ways. The first is through the provision of PCSELs as “Products.” Under the conditions of a material transfer agreement (MTA), PCSELs are provided to users for testing, and feedback from these tests is utilized to inform future development of the PCSELs. Such feedback has led to the development of applications described in Section 4 and to even further sophistication of PCSELs. The second way is through the transference of PCSEL “Technology,” such as data and intelligence related to PCSEL manufacturing. The COE is transferring technology to and collaborating with companies interested in expanding the development of PCSELs for various purposes, such as mobile and space communications, 3D printing, and laser emission at visible wavelengths. Recently, even a COE-centered ecosystem, enveloping partner companies and institutions related to nanostructure formation, crystal growth, device production and application, and global expansion, has been established.

On the international stage, collaboration has expanded to include institutions in Germany, who specialize in ranging sensors. The COE is even exploring opportunities to collaborate with research institutes in the US and in Australia for the expansion of PCSELs into aerospace applications. In addition, inquiries into joint research and technology transfer of PCSELs are being received from even more foreign companies and institutions. It is expected that these many collaborations will lead to the proliferation of PCSELs worldwide.

Funding

Council for Science, Technology and Innovation; Japan Society for the Promotion of Science (22H04915).

Acknowledgements

The authors thank various collaborating companies of Kyoto University on PCSELs through the center of excellence for PCSELs. This work was partially supported by the project of the Council for Science, Technology and Innovation; the Cross Ministerial Strategic Innovation Promotion Program (SIP) and Program for Bridging the Gap between R&D and the Ideal Society (Society 5.0) and Gathering Economic and Social Value (BRIDGE). This work was also partially supported by the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 22H04915).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. P. Crump, S. Böldicke, C. M. Schultz, H. Ekhteraei, H. Wenzel, and G. Erbert, “Experimental and theoretical analysis of the dominant lateral waveguiding mechanism in 975 nm high power broad area diode lasers,” Semicond. Sci. Technol. 27, 045001 (2012). [CrossRef]

2. C. J. Chang-Hasnain, M. Orenstein, A. Von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990). [CrossRef]

3. M. Winterfeldt, P. Crump, H. Wenzel, G. Erbert, and G. Tränkle, “Experimental investigation of factors limiting slow axis beam quality in 9xx nm high power broad area diode lasers,” J. Appl. Phys. 116, 063103 (2014). [CrossRef]

4. S. Rauch, H. Wenzel, M. Radziunas, M. Haas, G. Tränkle, and H. Zimer, “Impact of longitudinal refractive index change on the near-field width of high-power broad-area diode lasers,” Appl. Phys. Lett. 110, 263504 (2017). [CrossRef]

5. D. Bäuerle, Laser Processing and Chemistry (Springer Science & Business Media, 2013).

6. J. Hecht, “Lidar for self-driving cars,” Opt. Photonics News 29(1), 26–33 (2018). [CrossRef]

7. H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutor. 19, 57–96 (2017). [CrossRef]

8. Starshot. Breakthrough Initiativeshttps://breakthroughinitiatives.org/Initiative/3 (2018).

9. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999). [CrossRef]

10. S. Noda, N. Yamamoto, M. Imada, H. Kobayashi, and M. Okano, “Alignment and stacking of semiconductor photonic bandgaps by wafer-fusion,” presented at Workshop on Electromagnetic Crystal Structures (WECS), Laguna Beach, USA, 4-6 January (1999). Special issue was also published in J. Lightwave Technol.17, 1948–1955 (1999). [CrossRef]

11. S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77, 2310–2312 (2000). [CrossRef]

12. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001). [CrossRef]

13. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 195306 (2002). [CrossRef]

14. D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Opt. Express 12, 1562–1568 (2004). [CrossRef]

15. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Lasers producing tailored beams,” Nature 441, 946 (2006). [CrossRef]

16. M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic-crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett. 88, 191105 (2006). [CrossRef]

17. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319, 445–447 (2008). [CrossRef]

18. Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics 4, 447–450 (2010). [CrossRef]

19. S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express 19, 11963–11968 (2011). [CrossRef]

20. K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8, 406–411 (2014). [CrossRef]

21. S. Noda, K. Kitamura, T. Okino, D. Yasuda, and Y. Tanaka, “Photonic-crystal surface-emitting lasers: review and introduction of modulated-photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 23, 4900107 (2017). [CrossRef]

22. M. Yoshida, M. D. Zoysa, K. Ishizaki, Y. Tanaka, M. Kawasaki, R. Hatsuda, B. S. Song, J. Gelleta, and S. Noda, “Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams,” Nat. Mater. 18, 121–128 (2019). [CrossRef]

23. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999). [CrossRef]

24. M. Yoshida, M. De Zoysa, K. Ishizaki, W. Kunishi, T. Inoue, K. Izumi, R. Hatsuda, and S. Noda, “Photonic-crystal lasers with high-quality narrow-divergence symmetric beams and their application to LiDAR,” JPhys Photonics 3, 022006 (2021). [CrossRef]

25. T. Inoue, M. Yoshida, J. Gelleta, K. Izumi, K. Yoshida, K. Ishizaki, M. De Zoysa, and S. Noda, “General recipe to realize photonic-crystal surface-emitting lasers with 100-W-to-1-kW single-mode operation,” Nat. Commun. 13, 3262 (2022). [CrossRef]

26. M. Yoshida, S. Katsuno, T. Inoue, J. Gelleta, K. Izumi, M. De Zoysa, K. Ishizaki, and S. Noda, “High-brightness scalable continuous-wave single-mode photonic-crystal laser,” Nature 618, 727–732 (2023). [CrossRef]

27. R. Sakata, K. Ishizaki, M. DeZoysa, S. Fukuhara, T. Inoue, Y. Tanaka, K. Iwata, R. Hatsuda, M. Yoshida, J. Gelleta, and S. Noda, “Dually modulated photonic crystals enabling high-power high-beam-quality two-dimensional beam scanning lasers,” Nat. Commun. 11, 3487 (2020). [CrossRef]

28. R. Sakata, M. De Zoysa, M. Yoshikawa, T. Inoue, K. Ishizaki, J. Gelleta, R. Hatsuda, and S. Noda, “Dually modulated photonic crystal lasers for wide-range flash illumination,” Opt. Express 30, 26043–26056 (2022). [CrossRef]

29. R. Sakata, K. Ishizaki, M. De Zoysa, K. Kitamura, T. Inoue, J. Gelleta, and S. Noda, “Photonic-crystal surface-emitting lasers with modulated photonic crystals enabling 2D beam scanning and various beam pattern emission,” Appl. Phys. Lett. 120, 130503 (2023). [CrossRef]

30. R. Morita, T. Inoue, M. De Zoysa, K. Ishizaki, and S. Noda, “Photonic-crystal lasers with two-dimensionally arranged gain and loss sections for high-peak-power short-pulse operation,” Nat. Photonics 15, 311–318 (2021). [CrossRef]

31. T. Inoue, R. Morita, K. Nigo, M. Yoshida, M. De Zoysa, K. Ishizaki, and S. Noda, “Self-evolving photonic crystals for ultrafast photonics,” Nat. Commun. 14, 50 (2023). [CrossRef]

32. R. Morita, T. Inoue, T. Ueda, M. Masuda, K. Nigo, M. Yoshida, M. De Zoysa, K. Ishizaki, J. Gelleta, and S. Noda, “200-W short-pulse operation of photonic-crystal lasers based on simultaneous absorptive and radiative Q-switching,” Opt. Express 31, 31116–31123 (2023). [CrossRef]

33. K. Emoto, T. Koizumi, M. Hirose, M. Jutori, T. Inoue, K. Ishizaki, M. De Zoysa, and S. Noda, “Wide-bandgap GaN-based watt-class photonic-crystal lasers,” Commun. Mater. 3, 72 (2022). [CrossRef]

34. S. Noda, M. Yoshida, T. Inoue, M. De Zoysa, K. Ishizaki, and R. Sakata, “Photonic-crystal surface-emitting lasers,” Nature Rev. Elec. Engin., submitted for publication.

35. L. C. West and S. J. Eglash, “First observation of an extremely large-dipole infrared transition within the conduction band of a GaAs quantum well,” Appl. Phys. Lett. 46, 1156–1158 (1985). [CrossRef]

36. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2021).

37. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).

38. C. W. Hsu, B. Zhen, A. D. Stobe, J. D. Joannopoulos, and M. Soljacic, “Bound state in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). [CrossRef]

39. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991). [CrossRef]

40. S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A 21, 1769–1775 (2004). [CrossRef]

41. L.-L. Lin, Z.-Y. Li, and K.-M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811–821 (2003). [CrossRef]

42. A. Y. Song, A. R. K. Kalapala, W. Zhou, and S. Fan, “First-principles simulation of photonic crystal surface-emitting lasers using rigorous coupled wave analysis,” Appl. Phys. Lett. 113, 041106 (2018). [CrossRef]

43. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Methods for Electromagnetics (CRC Press, 1993).

44. M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13, 2869–2880 (2005). [CrossRef]

45. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 031104 (2010). [CrossRef]

46. T. Inoue, M. Yoshida, M. De Zoysa, K. Ishizaki, and S. Noda, “Design of photonic-crystal surface-emitting lasers with enhanced in-plane optical feedback for high-speed operation,” Opt. Express 28, 5050–5057 (2020). [CrossRef]

47. M. Toda, “Proposed cross grating single-mode DFB laser,” IEEE J. Quantum Electron. 28, 1653–1662 (1992). [CrossRef]

48. H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972). [CrossRef]

49. I. Vurgaftman and J. R. Meyer, “Design optimization for high-brightness surface-emitting photonic-crystal distributed-feedback lasers,” IEEE J. Quantum Electron. 39, 689–700 (2003). [CrossRef]

50. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89, 021101 (2006). [CrossRef]

51. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46, 788–795 (2010). [CrossRef]

52. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic crystal lasers with transverse electric polarization: a general approach,” Phys. Rev. B 84, 195119 (2011). [CrossRef]

53. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting lasers with transverse-electric polarization: finite-size effects,” Opt. Express 20, 15945–15961 (2012). [CrossRef]

54. Y. Liang, C. Peng, K. Ishizaki, S. Iwahashi, K. Sakai, Y. Tanaka, K. Kitamura, and S. Noda, “Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization,” Opt. Express 21, 565–580 (2013). [CrossRef]

55. Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Three-dimensional coupled-wave theory for the guided mode resonance in photonic crystal slabs: TM-like polarization,” Opt. Lett. 39, 4498–4501 (2014). [CrossRef]

56. T. Inoue, R. Morita, M. Yoshida, M. De Zoysa, Y. Tanaka, and S. Noda, “Comprehensive analysis of photonic-crystal surface-emitting lasers via time-dependent three-dimensional coupled-wave theory,” Phys. Rev. B 99, 035308 (2019). [CrossRef]

57. S. Katsuno, T. Inoue, M. Yoshida, M. De Zoysa, K. Ishizaki, and S. Noda, “Self-consistent analysis of photonic-crystal surface-emitting lasers under continuous-wave operation,” Opt. Express 29, 25118–25132 (2021). [CrossRef]

58. T. Inoue, T. Kim, S. Katsuno, R. Morita, M. Yoshida, M. De Zoysa, K. Ishizaki, and S. Noda, “Measurement and numerical analysis of intrinsic spectral linewidths of photonic-crystal surface-emitting lasers,” Appl. Phys. Lett. 122, 051101 (2023). [CrossRef]

59. K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982–7986 (1995). [CrossRef]

60. K.-B. Hong, L.-R. Chen, K.-C. Huang, H.-T. Yen, W.-C. Weng, B.-H. Chuang, and T.-C. Lu, “Impact of air-hole on the optical performances of epitaxially regrown p-side up photonic crystal surface-emitting lasers,” IEEE J. Sel. Top. Quant. Electron. 28, 1700207 (2022). [CrossRef]

61. X. Ge, M. Minkov, S. Fan, X. Li, and W. Zhou, “Low index contrast heterostructure photonic crystal cavities with high quality factors and vertical radiation coupling,” Appl. Phys. Lett. 112, 141105 (2018). [CrossRef]

62. M. Yoshida, M. Kawasaki, M. D. Zoysa, K. Ishizaki, T. Inoue, Y. Tanaka, R. Hatsuda, and S. Noda, “Experimental investigation of lasing modes in double-lattice photonic-crystal resonators and introduction of in-plane heterostructures,” Proc. IEEE 108, 819–826 (2019). [CrossRef]

63. P. Crump, G. Erbert, H. Wenzel, C. Frevert, C. M. Schultz, K.-H. Hasler, R. Staske, B. Sumpf, A. Maaßdorf, F. Bugge, S. Knigge, and G. Trankle, “Efficient high-power laser diodes,” IEEE J. Sel. Top. Quant. Electron. 19, 1501211 (2013). [CrossRef]

64. Y. Liang, T. Okino, K. Kitamura, C. Peng, K. Ishizaki, and S. Noda, “Mode stability in photonic-crystal surface-emitting lasers with large κ_1DL,” Appl. Phys. Lett. 104, 021102 (2014). [CrossRef]

65. J. Bravo-Abad, J. D. Joannopoulos, and M. Soljacic, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl Acad. Sci. 109, 9761–9765 (2012). [CrossRef]

66. S.-L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39, 2072–2075 (2014). [CrossRef]

67. B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015). [CrossRef]

68. R. Contractor, W. Noh, W. Redjem, W. Qarony, E. Martin, S. Dhuey, A. Schwartzberg, and B. Kanté, “Scalable single-mode surface-emitting laser via open-Dirac singularities,” Nature 608, 692–698 (2022). [CrossRef]

69. M.-A. Miri and A. Alù, “Exceptional points in optics and photonics,” Science 363, eaar7709 (2019). [CrossRef]

70. K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Commun. 23, 1335–1340 (2005). [CrossRef]

71. M. Yoshida, M. Kawasaki, M. De Zoysa, K. Ishizaki, R. Hatsuda, and S. Noda, “Fabrication of photonic crystal structures by tertiary-butyl arsine-based metal–organic vapor-phase epitaxy for photonic crystal lasers,” Appl. Phys. Express 9, 062702 (2016). [CrossRef]

72. D. M. Williams, K. M. Groom, B. J. Stevens, D. T. Childs, R. J. Taylor, S. Khamas, A. H. Hogg, N. Ikeda, and Y. Sugimoto, “Epitaxially regrown GaAs-based photonic crystal surface-emitting laser,” IEEE Photonics Technol. Lett. 24, 966–968 (2012). [CrossRef]

73. M. De Zoysa, M. Yoshida, M. Kawasaki, K. Ishizaki, R. Hatsuda, Y. Tanaka, and S. Noda, “Photonic crystal lasers fabricated by MOVPE based on organic arsenic source,” IEEE Photonics Technol. Lett. 29, 1739–1742 (2017). [CrossRef]

74. M. Nishimoto, K. Ishizaki, K. Maekawa, K. Kitamura, and S. Noda, “Air-hole retained growth by molecular beam epitaxy for fabricating GaAs-based photonic-crystal lasers,” Appl. Phys. Express 6, 042002 (2013). [CrossRef]

75. M. De Zoysa, M. Yoshida, B. Song, K. Ishizaki, T. Inoue, S. Katsuno, K. Izumi, Y. Tanaka, R. Hatsuda, J. Gelleta, and S. Noda, “Thermal management for CW operation of large-area double-lattice photonic-crystal lasers,” J. Opt. Soc. Am. B 37, 3882–3887 (2020). [CrossRef]

76. R. Morita, T. Inoue, M. Yoshida, K. Enoki, M. De Zoysa, K. Ishizaki, and S. Noda, “Demonstration of high-power photonic-crystal surface-emitting lasers with 1-kHz-class intrinsic linewidths,” arXiv, arXiv:2309.03457 (2023). [CrossRef]

77. Y. Itoh, N. Kono, N. Fujiwara, H. Yagi, T. Katsuyama, T. Kitamura, K. Fujii, M. Ekawa, H. Shoji, T. Inoue, M. De Zoysa, K. Ishizaki, and S. Noda, “Continuous-wave lasing operation of 1.3-µm wavelength InP-based photonic crystal surface-emitting lasers using MOVPE regrowth,” Opt. Express 28, 35483 (2020). [CrossRef]

78. Y. Itoh, N. Kono, D. Inoue, N. Fujiwara, M. Ogasawara, K. Fujii, H. Yishinaga, H. Yagi, M. Yanagisawa, M. Yoshida, T. Inoue, M. De Zoysa, K. Ishizaki, and S. Noda, “High-power CW oscillation of 1.3-µm wavelength InP-based photonic-crystal surface-emitting lasers,” Opt. Express 30, 29539–29545 (2022). [CrossRef]

79. Z. Bian, K. J. Rae, A. F. McKenzie, B. C. King, N. Babazadeh, G. Li, J. R. Orchard, N. D. Gerrard, S. Thoms, D. A. MacLaren, R. J. Tayler, D. Childs, and R. A. Hogg, “1.5 µm epitaxially regrown photonic crystal surface emitting laser diode,” IEEE Photonics Technol. Lett. 32, 1531–1534 (2022). [CrossRef]

80. O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93, 171112 (2008). [CrossRef]

81. Y. Liang, Z. Wang, J. Wolf, E. Gini, M. Beck, B. Meng, J. Faist, and G. Scalari, “Room temperature surface emission on large-area photonic crystal quantum cascade lasers,” Appl. Phys. Lett. 114, 031102 (2019). [CrossRef]

82. Z. Wang, Y. Liang, B. Meng, Y.-T. Sun, G. Omanakuttan, E. Gini, M. Beck, I. Sergachev, S. Lourdudoss, J. Faist, and G. Scalari, “Large area photonic crystal quantum cascade laser with 5 W surface-emitting power,” Opt. Express 27, 22708–22716 (2019). [CrossRef]

83. J.-F. Lalonde, N. Vandapel, D. F. Huber, and M. Hebert, “Natural terrain classification using three-dimensional ladar data for ground robot mobility,” J. Field Robot. 23, 839–861 (2006). [CrossRef]

84. U. Weiss and P. Biber, “Plant detection and mapping for agricultural robots using a 3D LIDAR sensor,” Robot. Auton. Syst. 59, 265–273 (2011). [CrossRef]

85. T. Luettel, M. Himmelsbach, and H.-J. Wuensche, “Autonomous ground vehicles—concepts and a path to the future,” Proc. IEEE 100, 1831–1839 (2012). [CrossRef]

86. I. Puente, H. González-Jorge, J. Martínez-Sánchez, and P. Arias, “Review of mobile mapping and surveying technologies,” Measurement 46, 2127–2145 (2013). [CrossRef]

87. Nature Research Custom Media and Kyoto University, “Semiconductor lasers: transforming manufacturing,” Nature Focal Point (2022). https://www.nature.com/articles/d42473-022-00101-5.

88. Center of Excellence (COE) for Photonic-Crystal Surface-Emitting Laser (PCSEL), Kyoto University, https://pcsel-coe.kuee.kyoto-u.ac.jp/.

89. Vector Photonics, https://www.vectorphotonics.co.uk/.

90. PHOSERTEK, https://en.phosertek.com/.

Susumu Noda received B.S., M.S., and Ph.D. degrees from Kyoto University, Kyoto, Japan, in 1982, 1984, and 1991, respectively, each in electronics. In 2006, he received an honorary degree from Gent University, Gent, Belgium. From 1984 to 1988, he was with the Mitsubishi Electric Corporation, and he joined Kyoto University in 1988. Currently he is a full Professor with the Department of Electronic Science and Engineering and a director of Photonics and Electronics Science and Engineering Center (PESEC), Kyoto University. His research interest covers physics and applications of photonic nanostructures based on PCs. He is the recipient of various awards, including the IBM Science Award (2000), the Japan Society of Applied Physics Achievement Award on Quantum Electronics (2005), the Optical Society of America Joseph Fraunhofer Award/Robert M. Burley Prize (2006), the Japan Society of Applied Physics Fellow (2007), IEEE Fellow (2008), The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (2009), the IEEE Nanotechnology Pioneer Award (2009), The Reo-Esaki Award (2009), Medal with Purple Ribbon (2014), the Japan Society of Applied Physics Outstanding Achievement Award (2015), and the Japan Academy Prize (2022).

Takuya Inoue received B.S., M.S., and Ph.D. degrees from Kyoto University, Kyoto, Japan, in 2012, 2014, and 2016, respectively, each in electronic science and engineering. From 2014 to 2016, he was a Research Fellow of the Japan Society for the Promotion of Science at Kyoto University. Since 2016, he has been an Assistant Professor in the Department of Electronic Science and Engineering, Kyoto University. His current research interest covers the exploration of novel optical phenomena inside photonic nanostructures and its device applications.

Masahiro Yoshida received B.S., M.S., and Ph.D. degrees in electronic science and engineering from Kyoto University, Kyoto, Japan, in 2015, 2017, and 2020, respectively. From 2017 to 2020, he was a Research Fellow of the Japan Society for the Promotion of Science, Kyoto University. He is currently an Assistant Professor with the Department of Electronic Science and Engineering, Kyoto University. His research interests include physics and applications of PCs and photonic nanostructures, such as the development of high-brightness PC lasers.

John Gelleta received B.Sc. degrees in Engineering Physics and Computer Science from the University of Saskatchewan, Saskatoon, Canada, in 2010, a M.A.Sc. degree in Engineering Physics from McMaster University, Hamilton, Canada, in 2013, and a Ph.D. degree in Electronic Science and Engineering from Kyoto University, Kyoto, Japan, in 2017. He is currently a program-specific researcher in the Department of Electronic Science and Engineering at Kyoto University. His research interests include light in periodic media, high-brightness and beam-steerable PC lasers, and novel phenomena in non-Hermitian systems.

Menaka De Zoysa received B.S., M.S., and Ph.D. degrees in Electronic Science and Engineering from Kyoto University, Kyoto, Japan, in 2007, 2009, and 2012 respectively. From 2010 to 2012, he was a Research Fellow of the Japan Society for the Promotion of Science with Kyoto University. From 2012 to 2014, he was a post-doctoral fellow in the Quantum Optoelectronics Laboratory. From 2014 to 2016, he was an Assistant Professor at the Hakubi Center for Advanced Research, Kyoto University. He is currently a Senior Lecturer at Department of Electronic Science and Engineering. His research interests include thermal emission control based on manipulation of electronic and photonic states, development of PC introduced thin-film solar cells, and development and improvement of PC lasers.

Kenji Ishizaki received B.S., M.S., and Ph.D. degrees in Electronic Science and Engineering from Kyoto University, Kyoto, Japan, in 2005, 2007, and 2010, respectively. From 2007 to 2010, he was a Research Fellow of the Japan Society for the Promotion of Science with Kyoto University, and from 2010 to 2012, he was a Postdoctoral Fellow in the Department of Electronic Science and Engineering, Kyoto University. From 2012 to 2019 he was an Assistant Professor, and from 2019 to 2022 a Program-Specific Associate Professor, in the Department of Electronic Science and Engineering. He is currently a Program-Specific Associate Professor in the Photonics and Electronics Science and Engineering Center, Kyoto University. His research interests include manipulation of photons based on PCs and photonic nanostructures, such as the development of high-brightness/smart semiconductor lasers and highly efficient photovoltaic devices based on the resonant effects in PCs, realization of arbitrary manipulation of photons in three dimensions using 3D PCs.

High-power and high-beam-quality photonic-crystal surface-emitting lasers: a tutorial

Abstract

1. Introduction

2. Theory

2.1 Basic Structure and Lasing Principle of PCSELs

2.2 Simulation Method of PCSELs

2.2a Plane-Wave Expansion Method

2.2b Rigorous Coupled-Wave Analysis

2.2c Finite-Difference Time-Domain Method

2.2d Coupled-Wave Theory

2.3 Basic Design Guideline of PCSELs

2.4 Introduction of Double-Lattice PCs for 10-W-Class High-Brightness Single-Mode Operation

2.5 Hermitian and Non-Hermitian Control in Double-Lattice Structures for 100-W-to-1-kW High-Brightness Single-Mode Operation

2.5a Hermitian and Non-Hermitian Optical Couplings Inside PCSELs

2.5b Conditions for Increasing the Threshold Gain Difference Between Different Band-Edge Modes

2.5c Conditions for Increasing the Threshold Gain Difference Between Band-Edge Modes within the Same Band in an Ultra-Large-Area Device

2.5d Concrete Design of Single-Mode Ultra-Large-Area PCSELs and Lasing Stability Analysis Considering Carrier–Photon Interactions

3. Experiments

3.1 Initial Demonstration and Vector Beam Generations

3.2 Introduction of Asymmetric Unit-Cell Structure and Watt-Class Operation

3.3 Introduction of Double-Lattice Structure and 10-Watt-Class Operation

3.4 Hermitian/Non-Hermitian Control and Realization of CW 50-W-Class Output Power with CW Brightness of 1 GW cm^–2 sr^–1

3.5 Extension of Emission Wavelength Range of High-Power PCSELs

3.5a InP-Based PCSELs Operating in the Optical Communication Band

3.5b Quantum Cascade PCSELs

4. Applications

4.1 Application to LiDAR System

4.2 Application to Compact Processing Systems

5. Summary and Future Prospects

Funding

Acknowledgements

Disclosures

Data availability

References

Data availability

Cited By

Figures (31)

Equations (30)

Advances in Optics and Photonics

Abstract

1. Introduction

2. Theory

2.1 Basic Structure and Lasing Principle of PCSELs

2.2 Simulation Method of PCSELs

2.2a Plane-Wave Expansion Method

2.2b Rigorous Coupled-Wave Analysis

2.2c Finite-Difference Time-Domain Method

2.2d Coupled-Wave Theory

2.3 Basic Design Guideline of PCSELs

2.4 Introduction of Double-Lattice PCs for 10-W-Class High-Brightness Single-Mode Operation

2.5 Hermitian and Non-Hermitian Control in Double-Lattice Structures for 100-W-to-1-kW High-Brightness Single-Mode Operation

2.5a Hermitian and Non-Hermitian Optical Couplings Inside PCSELs

2.5b Conditions for Increasing the Threshold Gain Difference Between Different Band-Edge Modes

2.5c Conditions for Increasing the Threshold Gain Difference Between Band-Edge Modes within the Same Band in an Ultra-Large-Area Device

2.5d Concrete Design of Single-Mode Ultra-Large-Area PCSELs and Lasing Stability Analysis Considering Carrier–Photon Interactions

3. Experiments

3.1 Initial Demonstration and Vector Beam Generations

3.2 Introduction of Asymmetric Unit-Cell Structure and Watt-Class Operation

3.3 Introduction of Double-Lattice Structure and 10-Watt-Class Operation

3.4 Hermitian/Non-Hermitian Control and Realization of CW 50-W-Class Output Power with CW Brightness of 1 GW cm–2 sr–1

3.5 Extension of Emission Wavelength Range of High-Power PCSELs

3.5a InP-Based PCSELs Operating in the Optical Communication Band

3.5b Quantum Cascade PCSELs

4. Applications

4.1 Application to LiDAR System

4.2 Application to Compact Processing Systems

5. Summary and Future Prospects

Funding

Acknowledgements

Disclosures

Data availability

References

Data availability

Cited By

Figures (31)

Equations (30)

Advances in Optics and Photonics

3.4 Hermitian/Non-Hermitian Control and Realization of CW 50-W-Class Output Power with CW Brightness of 1 GW cm^–2 sr^–1