1. Introduction

Recently, there has been increasing demand for the heterogeneous integration of electronic/photonic devices and systems that cannot be realized in conventional semiconductor platforms [1]. Alternative schemes of flexible substrates combined with ultra-thin inorganic crystalline semiconductor nanomembranes (NMs) have thus been promoted and widely studied [2]. NMs with submicron thickness have been found to differ from their bulk counterparts (>200 µm), which feature distinctive material characteristics, such as weakened flexural rigidity, enhanced durability, and ease of transfer [3, 4]. Currently, the functional materials applied in the hybrid flexible platforms include organic polymers, inorganic III–V [5]/Si [6] NMs, metallic negative-index metamaterials [7], chalcogenides [8, 9], and assemblies of carbon nanotubes (CNTs) [10].

These proposed hybrid platforms enable researchers to gain an understanding of the device sensitivity and spatiotemporal response to realize the submicron or nanometer-scale structural deformation detections. The methodology of nanoscale detections can be divided into tuning the properties of the material or cavity physical structure. In the first approach, sensors based on metal-oxides [11], CNTs, and nanowire-polymer composites, have progressed rapidly [10, 12]. However, the limited mechanical response and signal-strain linearity of these materials usually lead to limited detection range and accuracy. In addition, for localized detection applications, ultra-small device footprints and ultra-high signal resolutions with a high contrast to environmental noise are required.

By contrast, for the second approach, nanolasers with tunable physical dimensions can be an ideal platform to provide nanoscale localized detection. Their cavity can be scaled to submicron sizes near the diffraction limit. Meanwhile, the characteristics of nanolasers strongly depend on the environment, as the resonances in the nanocavity are sensitive to changes in the cavity structural parameters, refractive index contrast, and environmental temperature. In addition, single-mode lasing with a high side-mode suppression ratio can provide unambiguous resonance signals to be monitored. In this approach, the idea has been expanded by proposing various types of nanocavities embedded in a deformable medium. In 2009, Shih et al. [13, 14] proposed flexible microdisk lasers embedded in polydimethylsiloxane (PDMS) operating at near-infrared (NIR) wavelengths, which could be applied to surface curvature detection. In 2013, Hsu et al. [15] demonstrated the mechanical wavelength tuning of a flexible photonic crystal (PhC) band-edge laser at NIR wavelengths. The wavelength tuning range was only a few nanometers. In 2016, Choi et al. [16] experimentally realized a high-resolution gauge using a nanorod-array PhC band-edge nanolaser with a wide wavelength tuning range of 26 nm. In 2017, Lu et al. [17] have reported a one-dimensional PhC nanolaser that exhibits a wide wavelength tuning range of 155 nm. The aforementioned flexible nanolasers have several points to be improved—first, flexible microdisk lasers are large (of the order of microns) and perform poorly in nanoscale detection; second, the Q factor and mode volume of flexible band-edge PhC nanolasers are not mechanically optimized; third, single-mode operation and tight mode confinement under different structural deformations are barely expected in these cavities. Meanwhile, a relative systematic and theoretical study of flexible PhC nanolasers has not yet been reported.

In this study, we propose and demonstrate a flexible bandgap PhC nanolaser cavity operating at approximately 686 nm with a III–V slab embedded in PDMS. In addition, the characteristics of the cavity mode and mechanical wavelength tunings are obtained from the finite-difference time-domain (FDTD) method. The proposed device holds potential in ultra-small biosensors and flexible laser projection displays.

2. Results and discussion

2.1 Device concept and theoretical model

PhC lasers were first defined in a 180-nm quaternary III–V slab containing InGaP multiple quantum wells (QWs) and InGaAlP barriers, supported by a 700-nm AlGaAs sacrificial layer, as shown in Fig. 1(a). The InGaP QWs were compressively strained to confine the light strongly into transverse electric (TE) modes. To obtain the flexible lasers, the whole process was divided into two steps: the first step involved the definition of the PhC pattern in the III–V slab, shown in Figs. 1(a) and 1(d), and the second involved the transfer of the pattern onto the flexible substrate, shown in Figs. 1(b) and 1(c). The optical characteristics of the proposed device structure were investigated theoretically by using the three-dimensional FDTD method.

 

Fig. 1 Proposed design of the flexible PhC nanolaser cavity and fabrication procedure. (a) Schematic of the compositional epitaxial layer of the wafer. The photonic crystal lasers are fabricated in a 180-nm slab layer. The active layer provides a wavelength of approximately 670 nm. (b), (c) Schematic of the PhC slab layer transferred to and embedded in a flexible PDMS substrate. (d) SEM image of the fabricated laser cavity. The PhC slab is split along the cleavage plane from the suspended structure, enabling easy transfer into the PDMS. (e) Fabricated flexible laser, with PhC cavity embedded in the PDMS, demonstrating the flexibility and transparency of the fabricated sample.

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2.2 Theoretical study of the flexible PhC lasers

The physical design of the two-dimensional PhC slab was carried out with a triangular lattice of air holes with lattice constant a ( = 0.16 µm). The thickness of the slab and radii of the air holes were 1.125a (0.18 µm) and 0.26a (0.0416 µm), respectively. The light field could thus be concentrated two-dimensionally by Bragg reflection and vertically in the slab (n_slab = 3.4) with a high index contrast to the surrounding PDMS (n_PDMS = 1.4). The Q factor of the PhC nanocavity was optimized mechanically by shifting the two adjacent holes near the L3 line defect (removing three air holes), as proposed by Noda’s group [18]. The basic mechanism of this method involves tailoring the vertical confinement by designing the momentum space inside the cavity [19,20]. First, the x and y axes are defined as the directions parallel or perpendicular to the L3 line defect, respectively, and the z-axis is defined as the direction vertical to the slab plane. The light confinement in the vertical direction (z-direction) is obtained by total internal reflection (TIR). This vertical confinement can be investigated by performing a spatial Fourier transformation (FT) of the electric field in the cavity, which decomposes the field into various plane-wave components with different k-vectors. If the in-plane k-vectors (k_//) lie in the leaky region (|k_//|<2π/λ₀, where λ₀ is the wavelength in air), the TIR condition (or k_// conservation law) is broken, leading to weak vertical confinement. Inversely, the k_//-vectors outside the leaky region (|k_//|>2π/λ₀) indicate strong vertical confinement. If the envelope function of the mode, as determined by the physical dimension of the cavity, changes abruptly at the cavity edge, it would generate more components inside the leaky region, leading to weaker vertical confinement and lower Q factors. In our work, to reduce this change, the two adjacent holes at the L3 cavity edge were shifted outward by 0.2a, changing the phases of the reflections at the moved holes. The phase-mismatch leads to reduced electric field variations.

The fundamental mode distributions and far-field patterns of the L3 defect cavity mode at approximately 686 nm without any strain are depicted in Fig. 2, and are obtained with a high theoretical Q factor of 8539 and mode volume of 7.40468 x 10⁻³ µm³. The mode patterns shown in Fig. 2 have almost the same symmetries and distributions for all simulated structures under different strains along the x and y directions. Figure 2(a) presents the simulated electric field intensity distribution. The mode is strongly confined in the L3 defect with two adjacent holes shifted. The shift of holes has little influence on the mode pattern and mode volume but greatly improves the Q factors. Figures 2(b) and 2(c) illustrate the E_y and E_x field distributions, respectively, both of which exhibit clear symmetries. The E_y field pattern in Fig. 2(b), due to its even mirror symmetries, will exhibit y-polarized emission in the vertical direction. However, in the E_x field pattern, the mode distribution has odd mirror symmetry as no x-polarized emission is allowed in the vertical direction. The resultant vertical emission is mainly characterized by the E_y field and the y-directional polarization should be collected in the objective. The vertical magnetic field (H_z) is shown in Fig. 2(d). Meanwhile, the calculated far-field pattern of the fundamental mode is shown in Fig. 2(e). The far-field pattern is obtained from the Fourier transform of the in-plane field distributions in the FDTD model. The fundamental mode exhibits the strongest emission 50° from the vertical direction (z-direction). However, the emitted photons are barely collected within the angle range of 0–40°. Since the cavity is designed to be operated with high Q factors, the k_//-vectors located in the leaky region (|k_//| < 2π/λ₀) in the wavevector space should be minimized as the mode components near the point k_x = k_y = 0 are negligible. The L3 PhC slab, to some degree, performs poorly in the vertical emission and collection, but in turn, this mode will couple efficiently to some specific waveguides.

 

Fig. 2 Near-field and far-field patterns of the L3 cavity at approximately 686 nm. (a) Electric field intensity profile. The white circles indicate the air holes and the two adjacent holes near the defect are shifted. (b) E_y field. (c) E_x field. (d) Vertical magnetic field (H_z). (e) Far-field pattern. The mapping coordinate (u_x, u_y) is obtained from (sinθcosφ, sinθsinφ), and θ is the angle from the direction vertical to the slab (x, y plane). The center (0, 0) indicates the vertical emission, while the red solid boundary indicates the horizontal emission. The white dotted line represents the 40° emission angle.

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First, the FDTD simulation is performed to study the effects of the mechanical deformation on the optical properties of the PhC cavity embedded in PDMS. The calculation boundary, as determined by the mechanical stability of the slab containing III–V QWs, is primarily investigated. For the III–V membranes, the maximum structural deformation that could be applied is estimated by ε_max = Young’s Modulus/Yield strength, which gives a relative compressive or stretched strain limit of ± 1%. In the simulation, the lattice spacing (a), porosity factor (r/a), and hole-shift ratio (shift/a) are set to 0.16 µm, 0.26, and 0.2, respectively. As mentioned before, the QWs inside the slab are compressed to generate the TE-polarized modes, so in the FDTD model, magnetic dipole cloud sources are placed inside the PhC cavity to excite the TE-like bandgap modes. To quantify the PhC cavity structural deformation, the displacement of air holes induced by the applied stretched/compressive force is assumed to be linear with the cavity strain, i.e., a 1% x-directional stretched strain will enlarge the x-directional period a_x to 1.01a_x, with y-directional period a_y unchanged, as shown in the inset of Fig. 3(a). Other circumstances of strains are consistent with this setting. Moreover, when the PhC structure is deformed, it is true that the PhC air holes may also be distorted, making the circular holes elliptical, which should affect the optical properties of the PhC nanocavity. However, further simulation results that we perform showed that hole distortion had negligible influence on cavity characteristics, e.g., resonant wavelength, Q factor, and mode volume within the strain limit of ± 1% that we considered. The resonant spectra of the TE modes under different structural strains are depicted in Figs. 3(a) and 3(b). As shown in the inset of Fig. 3(b), only three resonant peaks are observed in the visible range (400–760 nm), corresponding to peaks of approximately 600, 650, and 686 nm. The strongest resonance is located at approximately 686 nm without any strain, and its magnetic field pattern is shown in Fig. 3(e). Similar to Fig. 2(d), the magnetic field pattern of the fundamental mode is largely determined by the H_z components, while the pattern of electric field E_z (not shown here) exhibits few symmetries or periodical features, which suggests a strong TE mode resonance in the L3 cavity.

 

Fig. 3 Simulated resonant spectra of the L3 defect PhC cavity as a function of wavelength and mode field distributions. Relative strains in the (a) x-direction (parallel to L3 defect) and (b) y-direction (perpendicular to L3 defect). The negative values of the strain (–1 to –0.1%) represent the compressed state of the cavity, while the positive values (0.1 to 1%) represent the stretched state within the yield strength limit of the III–V slab. Inset left: schematic of the linear displacement of each hole in the PhC cavity under stretched structural deformation; right (white curves): featured simulated spectrum of the L3 defect cavity. (c)–(e) Magnetic field profiles of the three resonant modes of the hybrid PhC L3 cavity: (c) mode I, (d) II, and (e) III, corresponding to approximately 600, 650, and 686 nm.

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With the cavity compressed or stretched along the x or y-direction, a significant blue shift (corresponding to compression) or red shift (corresponding to stretch) for all resonant modes is observed. In addition, in the hybrid cavity, with the consideration of a wide range of structural deformations within the yield strength ( ± 1% strain) of the flexible III–V slab, single-mode operation can be achieved with a spectral range of approximately 9 nm (681–690 nm), which reveals the theoretical feasibility of the strain sensor, providing an ambiguous optical signal under each mechanical strain. Meanwhile, the other two resonant modes, presented in Figs. 3(a) and 3(b), are located at approximately 600 and 650 nm, which are approximately 35-nm or 85-nm separated from the fundamental mode, which further guarantees single-mode lasing when the cavity is compressed or strained. Their mode patterns are depicted in Figs. 3(c) and 3(d).

The numerical analysis of the resonant mode is depicted in Fig. 4. Here, the fundamental mode at approximately 686 nm near the emission peak of approximately 670 nm of the InGaP/InGaAlP QWs is selected and analyzed, and is considered to be more easily transformed into lasing and provide higher resolutions for strain detection compared with the other two modes. The resonant wavelength is plotted as a function of the applied strain. As predicted, the curves in Fig. 4(a) exhibit a linear relationship between the wavelength shifts and strains, yielding a corresponding theoretical optical strain sensitivity of approximately 4.5 and 3 nm per ε (1% strain for both) for the x and y directions, respectively, theoretically surpassing the 1.27 nm per ε (1% strain) reported by Choi et al. [16]. This improved sensitivity results from the ultra-small footprint of the L3 defect cavity and the ultra-compact mode confinement, as any tiny structural deformation would lead to large modal changes. This indicates that the reduced cavity sizes, in nanoscale localized detections, are more conducive to the sensitivity enhancement.

 

Fig. 4 Characteristic analysis of the PhC L3 defect cavity. (a) Resonant wavelength as a function of the relative strain of the cavity in the x and y directions. (b) Q factors (black curves) and mode volumes (red curves) as a function of strain.

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The Q factor and mode volume V_m under different deformations were also studied, and are plotted in Fig. 4(b). The Q factors increase with the y-directional stretched strain, while they decrease monotonously with the y-directional compressed strain. For x-directional strains, the Q factors increase monotonously with both the compressed and stretched strains. The increase in Q factors could be due to the change in the momentum space, i.e., when the cavity is compressed or stretched, the rearrangement of air holes smoothens the change in the original abrupt envelope function at the cavity edge, leading to fewer mode components in the leaky region. The opposite is true for the decrease in Q factor. The Q factors maintain relatively high values of the order of 10⁴, as relatively low lasing thresholds can be obtained.

V_m is defined as the ratio of the total electric field energy density to the peak energy density of the mode and can be given by the following equation:

The effect of the slab bending curvature on the cavity performance was also investigated. In Fig. 5, the Q factor degrades significantly when a large bending deformation is applied to the cavity. However, the energy confinement remains strong in the cavity, as predicted in the inset of Fig. 5. Most of the field energy distributes inside the 180-nm slab despite the large bending deformation. This indicates the worsened condition for the cavity modes to turn into lasing because of the severe energy leakage induced by cavity structure bending.

 

Fig. 5 Q factor of the PhC L3 cavity with different bending curvatures. Inset: Field power distributions in the vertical half plane with a bending curvature of 0.11 µm^–1.

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3. Proposed fabrication procedure

To realize the proposed device, detailed fabrication procedure is provided here. The epitaxial wafer was first coated with a 120-nm SiO₂ hard mask, grown via plasma-enhanced chemical vapor deposition, and a 180-nm ZEP 520A electron beam resist. The designed PhC pattern was first lithographically defined on the e-beam resist and then transferred onto the hard mask by CHF₃-based reactive ion etching (RIE). After removing the resist, the PhC pattern was further transferred through the 180-nm slab layer containing QWs by chlorine-based, inductively coupled plasma RIE (ICPRIE). To form the suspended structure, which would efficiently prevent the light field from dissipating into the surrounding dielectric, time-controlled oxidation and wet etching of the sacrificial layer, were subsequently performed. The definition of the PhC laser in the rigid substrate was finalized by the dissolution of the residual SiO₂ hard mask with 10:1 buffered HF. The suspended structure enables the easy transfer of the pattern with little mechanical damage to the device. The flexible material PDMS was then coated onto the III–V wafer and the sample was then placed in a vacuum chamber for 30 min to get rid of any tiny bubbles around the PhC cavities. The sample coated with PDMS was baked at 60 °C for 12 h. Finally, the PDMS was peeled off from the substrate along with the PhC slab. Figure 1(e) demonstrates the fabricated PhC nanolaser with PhC cavities embedded in the PDMS, exhibiting the flexibility and transparency of the fabricated sample.

4. Conclusions

The authors propose a flexible PhC nanolaser cavity emitting at approximately 686 nm with high theoretical Q factors of the order of 10⁴ and compact mode volumes of the order of 10⁻³ µm³. Theoretical optical strain sensitivities of approximately 4.5 and 3 nm per ε (1% strain for both) for the x and y directions, respectively, were predicted. This sensitivity was improved by scaling down the sizes of the laser cavity operating with a fundamental bandgap mode. The current study focuses on the characteristics of the TE mode in the cavity. For further investigation, the characteristics of the TM-polarized cavity modes including the transmission spectrum, photonic band diagrams, Q factor, and mode volume can be obtained in the similar FDTD model, if required. In addition, during the fabrication process, to achieve a more robust and flexible platform, one can improve the quality of the PDMS by optimizing the current conditions or coat another PDMS layer onto the fabricated devices to ensure that the PhC slab is fully embedded. We expect the red flexible PhC lasing cavity to be used in flexible light emitters as well as the nanoscale detection of local structural deformations in the future.