1. Introduction

The merging of silicon-on-insulation (SOI) based electronics with photonics probably be the next evolution in on-chip information since SOI processing technology is quite mature in industrial Metal-Oxide Semiconductor (CMOS) technology [1–4]. However, as an important part of the Si photonic integrated circuits, the on-chip coherent light source is a challenge since the optical feature of Si with the indirect band gap and comparatively low optical gain [5,6]. The semiconductor nanowire (NW) structure that can be grown directly on the Si substrate by bottom-up methods has been considered as one of the feasible ways to solve this challenge [7–10]. As a one-dimensional material, the NWs based on III-V semiconductor materials exhibit much less dislocations and defects due to the effective lateral stress relaxation and ultra-small footprint [11,12]. Besides, in comparison to top-down etched cavities, the vertical, atomically flat sidewall surface and the ability to form in situ passivation layers suppresses scattering and transmission losses, which preserves high radiative recombination efficiency [13–15]. Besides, the highly overlap of NW’s intrinsic Fabry-Perot (F-P) resonance cavity with gain material can offer a strong optical feedback.

Small-size surface-emitting lasers (SELs) are key components for optical interconnects due to the ease of testing and integration, good beam quality with a circular beam [16–18]. However, it is challenging to realize high-performance SELs just based on the traditional single NW laser. The traditional single NW lasers are constrained in terms of optical mode size and physical device dimension, due to the optical diffraction limit. The threshold gain of NW lasers is generally high as the result of the in-plane weak optical confinement. More importantly, single NW lasers typically display multimode behavior due to the lack of a mode selection capability in the F-P cavity. Photonic-crystal surface-emitting lasers (PCSELs) based on band-edge effects by diffraction are one of the ideal candidates to solve those problems simultaneously and achieve miniaturized low-threshold single-mode lasers [19–21]. By selective area growth, the vertical NWs can be arranged to construct photonic crystal (PhC) structures with band-edge effects to realize transverse scattering with low intrinsic loss by effective refractive index who is much less than 1 and slow group velocity near the photonic band edge of the First Brillouin Zone (FBZ) center [12,14,22]. Due to the dispersionless band structure (perfect or partial flat band), a surface-emitting lasing with a large area can be realized in PCSELs, without distributed Bragg reflector (DBR) [23–26]. The coupling of vertical F-P cavities of NWs and Bragg diffraction of PhC will enhance light-matter interactions to improve lasing performance.

Here, a low-threshold surface-emitting flat-band PhC laser with a small size based on GaAs/AlGaAs/GaAs NW arrays is designed and analyzed. We proposed a novel NW laser with a high-reflectivity bottom mirror by introducing an air gap between the NW and Si substrate, whose threshold gain and cut-off diameter are significantly reduced. A degenerate flat band mode is designed in the NW array PCSEL to realize the low-threshold surface-emitting lasing. The flat band not only can provide slow light with a high density of states and zero group over a broad range of Brillouin zone, but also can provide a mode selection mechanism for the single-mode lasing without DBRs. Sufficient periods are crucial to realize periodic modulation of a finite-size PhC. To miniaturize the PCSEL, we discuss the confinement factor, threshold gain and mode field distribution of the NW array PCSEL with different size. By numerical simulations, a single-mode lasing with a quality factor Q of 3940 and side-mode suppression ratio (SMSR) of 21 dB is obtained when the side length of the hexagonal structure are only five periods. In addition, a high confinement factor of 3.845, low threshold gain of 624 cm⁻¹ and little beam divergence of 7.5° are obtained due to the strong coupling of the F-P resonance cavity of NW and the band-edge mode of PhC.

2. Structures design

2.1 Traditional single NW lasers with different substrates

At first, A core-shell-gap GaAs (core/cladding)/AlGaAs/GaAs NW can be regard as a single NW laser due to the highly overlap of its natural F-P resonance cavity with the gain medium [9]. As shown in Fig. 1(a) (IV), the bottom-up single NW is made up of a GaAs core (radium of 25 nm), GaAs cladding (variable size), AlGaAs cladding (10 nm) and GaAs gap (5 nm) which can be obtained by the top-down selective-area epitaxial growth [9,10,14]. The length of NW laser is 8.7 um. As we all know, the GaAs core can be directly grown on the Si substrate due to the ultra-small footprint and the effective lateral stress relaxation [11,12]. The surrounding GaAs cladding layer will increase the gain medium to enhance the optical feedback and the photon confinement within the NW [9]. The AlGaAs shell is employed to decrease surface recombination, while the outermost thin GaAs gap prevents AlGaAs cladding layer form oxidation [27]. The core-shell-cap GaAs/AlGaAs/GaAs NW has been shown to be experimentally feasible [9,14]. It can be grown by a Metal-organic Chemical Vapor Deposition (MOCVD) reactor, where GaAs core, Al_0.5Ga_0.5As shell and GaAs cap can be grown sequentially.

 

Fig. 1. (a) The schematic diagram of traditional single NW laser with different substrates. (b) The longitudinal-section normalized electric field distributions of NW lasers with the diameter of 300 nm in NW-Si, NW-SiO₂ and NW-air structures, respectively. (c) The cross-section normalized electric field distributions of HE₁₁, TE₀₁ and TM₀₁ modes of NW lasers with the diameter of 200 nm in NW-Si, NW-SiO₂ and NW-air structures, respectively.

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Due to the effective lateral stress relaxation and ultra-small footprint, the much less dislocations and defects of NW makes it can be grown directly on the Si substrate [10–12]. The NW laser vertically grown directly on the Si substrate is called NW-Si structure, shown in the Fig. 1(a) (I). However, the reflectivity of NW’s bottom mirror may be hampered by the similar refractive indices of GaAs and Si substrate. The NW-SiO₂ structure can be achieved by growing its GaAs core directly on the Si substrate via a small mask opening in SiO₂ interlayer, as shown in the Fig. 1(a) (II). By removing the SiO₂ interlayer which can be realized by wet etching with Buffered Hydrofluoric (BHF) solutions [28], the NW-air structure can be obtained, as shown in the Fig. 1(a) (III). The introduced SiO₂ interlayer and air layer between NW and Si substrate are expected to increase the reflectivity of F-P resonance cavity’s bottom mirror. The GaAs core directly on the Si substrate can ensure the vertical growth of NW even though the other layers are grown on different substrates [12].

The design and simulation were performed using 3D finite difference time domain (FDTD) method with the perfect matched layers (PML) boundary conditions. The refractive indices of AlGaAs and GaAs are 3.36582 and 3.54384, respectively. Figure 1(b) illustrates the longitudinal-section normalized electric field distributions of the NW lasers with the diameter of 300 nm in three different substrates. The optical energy is weakly confined in the F-P cavity of the NW-Si structure. However, much stronger optical resonances are obtained in the NW-air and NW-SiO₂ structure, which is contributed to the high reflectivity of NW’s bottom mirror. Similar results can be obtained in Fig. 1(c) which illustrates the cross-section normalized electric field distributions of the NW laser in the first three guide modes (HE₁₁, TE₀₁ and TM₀₁). For each mode, compared with only Si substrate, the resonance is remarkable enhanced by introducing a SiO₂ layer, and further enhanced by replacing the SiO₂ layer with air layer.

To more clearly show the performance of NW lasers with different substrates, the threshold gain ${g_{th}}$ is introduced to indicate the required gain per unit length for lasing, which is defined from the Eqs. (1) [29]:

A small cut-off diameter is crucial for the miniaturized lasers on chip. However, due to the great end-facet mirror loss and the optical diffraction limit, the light energy cannot be confined in the F-P resonance cavity of NW laser when the diameter is too small [30]. The introduced high-reflectivity bottom mirror of NW lasers are expected to reduce the cut-off diameter and threshold gain. The diameter of the proposed NW lasers can be changed by simply altering the thickness of the variable GaAs cladding. Figure 2(a) illustrates the diameters-dependent reflectivity of the NW bottom in three structures. For all three modes, the reflectivity of the bottom mirror in the F-P cavity in NW-air and NW-SiO₂ structure is significantly enhanced, compared with NW-Si structure. It can explain why the confinement factors of NW-Si structures are much lower and threshold gains are higher, compared with NW-SiO₂ structures, as shown in Fig. 2(b) and (c). The performance parameters are further significantly improved in the NW-air structure NW lasers. The confinement factor of NW lasers bigger than 1 can be explained by the strong wave guiding behavior due to the slower group velocity and larger model gain [9]. The minimum cut-off diameter can be obtained in the fundamental HE₁₁ mode, the NW-air structure NW laser exhibits a cut-off diameter of 180 nm, which is lower than 200 nm of NW-SiO₂ structure and 250 nm of NW-Si structure. The lowest threshold gain is obtained in the TE₀₁ mode with a large diameter, the NW-air structure NW laser exhibits a threshold gain of 384 cm⁻¹ with the diameter of 300 nm, which is lower than 837 cm⁻¹ of NW-SiO₂ and 8440 cm⁻¹ of NW-Si structure. Figure 2(d) illustrates the quality factor (Q) of NW lasers with three substrates, the maximum quality factor obtained in NW-Si, NW-SiO₂ and NW-air structures are 106,708 and 818, respectively. Due to the cut-off diameter and threshold gain significantly reduced in NW-air laser structure with the aid of high-reflectivity bottom mirror, we choose the NW-SiO₂ structure NW lasers to construct the PCSELs in the subsequent study.

 

Fig. 2. (a) (b) (c) and (d) Diameters-dependent Reflectivity, Confinement factor, Threshold gain and Quality factor of NW laser in HE₁₁, TE₀₁ and TM₀₁ modes with different substrates.

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2.2 Flat-band finite-size NW array PCSELs

We arrange the GaAs/AlGaAs/GaAs NW-SiO₂ NW lasers into the hexagonal lattice to access the flat-band PhC structure, which can be realized by the bottom-up selective-area epitaxial growth [9,12,14], as illustrated in Fig. 3(a). The thickness of air layer, the diameter of NW lasers and lattice constant of the PhC are h = 200 nm, d = 180 nm and a = 510 nm, respectively. The PCSEL is proposed with a hexagonal shape, whose side length consists of n NW lasers.

 

Fig. 3. (a) The schematic diagram of the NW array PCSEL. (b) Photonic band structure of the hexagonal lattice PhC obtained from a full-wave calculation.

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The slow light with zero group velocity and a high density of states can be realized in the flat-band PhC structure due to the dispersionless band [24]. In addition, compared with traditional band-edge modes which can only be realized at one point in Brillouin zone, the flat-band modes can be realized over a broad range [18,26]. Therefore, light-matter interactions can be significantly enhanced in the flat-band PhC [31]. Figure 3(b) illustrates the photonic band structure of the hexagonal lattice PhC obtained in the transverse magnetic (TM) polarized from a full-wave calculation. It is worth mentioning that the definitions of polarization modes (TE/TM) are opposite in two systems (guide modes of NW lasers and photonic crystals) [32]. The electric field vector is perpendicular to the direction of light propagation in the TM-polarized photonic band structure of the PhC and the TE₀₁ guide mode of vertical NW lasers. In the photonic band structure of the proposed non-Hermitian hexagonal lattice photonic crystal, Dirac cones and exceptional points are connected which causes a spawning ring of exceptional points out of the Dirac cone [18,31]. By tuning the lattice constant of photonic crystal with the diameter of nanowires unchanged, an accidental degeneracy in the Dirac cone (quadrupole modes and dipole modes) can be obtained. The real part and imaginary part of the eigenvalue are both degenerated to be constants in the wavevector points which makes the complex eigenvalues of the system are deformed into a two-dimensional flat band. The central inset shows the details about mode A, B and C around the Γ point in the band structure. The mode B exhibits a range of flat band between b₁ and b₂, which can be observed in the schematic of the first Brillouin zone (insert at the lower right corner). Due to the symmetry, the zero group velocity and the standing wave can be realized in the red area in the Brillouin zone. In addition, the flat band support a mode selection mechanism for the lasing. The lasing performance is further enhanced by the coupling of the F-P resonance mode of the NW and the flat-band resonance mode of the PhC.

3. Results and discussions

The size of the proposed NW array PCSEL can be controlled by the parameter n. A tiny size of the device is crucial to the high-density photonic integrated circuits on chips. Furthermore, more high-order transverse modes may be supported as the size of the PhC increase, which seriously thwarts the single-mode operation of lasers [33–35]. Figure 4(a) and (b) illustrates the confinement factors and the threshold gain of the designed PCSEL in the first three modes with different sizes. The resonance of flat-band mode is significantly enhanced due to the periodic modulation of PhC with the increase of n. The performance of lasers is further improved by the coupling of F-P cavities of NWs and the flat-band mode of PhC. When n = 5, the confinement factors are significantly increased from 1.35, 0.37 and 0.06 to 3.85, 3.56 and 0.94, in HE₁₁, TE₀₁ and TM₀₁ modes, respectively, compared with the traditional single NW laser (n = 1). The threshold gains are significantly reduced from 8715 cm⁻¹, 21170 cm⁻¹ and 167000 cm⁻¹ to 624 cm⁻¹, 1272 cm⁻¹ and 10325 cm⁻¹, in HE₁₁, TE₀₁ and TM₀₁ modes, respectively, when n increases from 1 to 5. Much stronger optical resonances as n increases can be observed in the normalized electric field distributions of the PCSEL, as shown in Fig. 4(c). However, the performance improvement is not obvious when n increases from 5 to 7, due to the relatively strong periodic modulation. It needs a great increase in size of PCSEL to noticeably boost lasing performance. For a higher cost-performance ratio, the n is decided to be 5 in our proposed finite-size low-threshold flat-band NW array PCSEL.

 

Fig. 4. (a) and (b) The confinement factors and threshold gains of the proposed PCSELs (diameter of 180 nm) with different sizes in the first three guide modes. (c) The cross-section normalized electric field (|E|²) distributions of PCSELs with different sizes.

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We have further performed detailed studies of the proposed NW PCSEL with different design parameters, shown in Table 1 and Fig. 5(a). The PCSELs with lattice constants of a = 460 nm and a = 560 nm can be obtained by adjusting only the distance between neighboring NWs and remaining other parameters unchanged, shown in Fig. 5(a). Compared with the PCSEL with a = 510 nm, the flat band mode is weakened by decreasing or increasing a, which results in a lower mode confinement and a higher threshold gain, shown in the Table 1. The confinement factors are reduced from 3.85, 3.56, 0.94 (a = 510 nm) to 2.98,2.83, 0.75 (a = 460 nm) and 3.27, 2.98, 0.83 (a = 560 nm) in HE₁₁, TE₀₁ and TM₀₁ modes, respectively. The threshold gains are increased from 624 cm⁻¹, 1272 cm⁻¹, 10325 624 cm⁻¹ (a = 510 nm) to 870 cm⁻¹, 1625 cm⁻¹, 12579 cm⁻¹ (a = 460 nm) and 790 cm⁻¹, 7496 cm⁻¹, 11867 624 cm⁻¹ (a = 560 nm) in HE₁₁, TE₀₁ and TM₀₁ modes, respectively. Figure 5(a) illustrates the cross-section normalized electric field (|E|²) distributions of NW PCSELs (n = 5) with different lattice constants in the first three guide modes. It is obvious that much stronger optical resonance in the flat-band mode when a = 510 nm. The quality factor is much increased with the aid of flat-band mode, shown in Fig. 5(b).

 

Fig. 5. (a) The cross-section normalized electric field (|E|²) distributions of NW array PCSELs with different lattice constants in the first three guide modes. (b) The output spectra of the conventional NW laser and the PCSELs (n = 5) with different lattice constants. (c) The detailed spectrum of the NW array PCSEL with a of 510 nm.

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Table 1. The confinement factors and threshold gain of PCSELs (n = 5) with different lattice constants

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A new mode selection mechanism is introduced in the NW array PCSEL, compared with the traditional NW laser. There are multiple modes supported in the F-P cavity of NW, as shown in Fig. 5(b). However, a single-mode lasing is observed in the PCSEL by the coupling of the flat-band mode and F-P modes. The quality factor of resonance mode is significantly increased to 3940 with the center wavelength of 873.4 nm. Figure 5(c) illustrates the details of the output spectrum of the designed PCSEL. The side mode suppression ratio (SMSR) and full-width at half-maximum (FWHM) are 21 dB and 0.22 nm, respectively. There is only one other resonance mode at the wavelength of 857.31 nm in the spectrum, whose confinement factor and threshold gain are 0.83 and 32107 cm⁻¹, as illustrated in Fig. 5(c). This is crucial for the sing-mode PCSEL at high pump powers, as the other resonance mode's threshold gain is over 48 times bigger than our working mode's.

In the proposed NW array PCSEL, a range of flat band appears around the Γ point (center of the Brillouin zone) which makes it easier for the light coherently increased in flat-band resonance cavities in the PhC plane to be coupled to the vertical F-P cavities by Bragg diffraction [36]. Additionally, the in-plane weakly guiding waveguide characteristic of PhC makes the far-filed divergence angle further reduced [37]. An angle divergence ∼7.5° is observed in the far field projection for the designed PCSEL with n of 5, as Fig. 6(a) shown. The far-filed divergence beam is a function of the size of the finite-size PCSEL by increasing the parameter n, as shown in Fig. 6(b), due to the intensity of the periodic modulation [14,33]. The beam divergence significantly drops with parameter n increasing from 2 to 5, which can be explained by the fact that more light is coupled into the vertical F-P resonance cavity of NW due to the strong mode confinement of flat-band mode. The resonance intensity of the flat-band mode is relatively strong with n of 5, which makes the increase of flat-band mode confinement not obvious with n increasing from 5 to7. In addition, the decrease of beam divergence is no longer sensitive to the increasing of size of the PCSEL when the divergence angle is tiny enough. A surface-emitting lasing with ∼7.5° beam divergence is obtained in the proposed NW array PCSEL.

 

Fig. 6. (a) Far field projection for the proposed NW array PCSEL with n of 5, resulting in the approximate 7.5° beam divergence. (b) Beam divergence angle as a function of n.

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4. Conclusion

In conclusion, a flat-band single-mode Si-based NW array PCSEL was proposed and analyzed. By introducing high-reflectivity bottom mirrors and flat-band mode, strong optical mode confinement and low lasing threshold were obtained. A surface-emitting single-mode lasing was realized with tiny SMSR, high Q factor, low threshold gain, and small beam divergency angle. This work provides a route towards low-threshold miniaturized surface-emitting lasers for high-density Si-based photonic integrated circuits.