Comprehensive analysis of photonic-crystal surface-emitting lasers via time-dependent three-dimensional coupled-wave theory

We develop a time-dependent three-dimensional coupled-wave theory (3D-CWT) for the transient analysis of photonic-crystal surface-emitting lasers (PCSELs). Our model takes into account the temporal evolution of both the photon and carrier distribution inside PCSELs, which enable the analysis of various above-threshold lasing characteristics including the relaxation oscillation, spatial hole burning, and multimode lasing. With the developed time-dependent 3D-CWT, we perform transient analysis of the high-power, high-beam-quality PCSELs with double-lattice photonic crystals and reproduce the experimental results of near-field patterns and lasing spectra under high current injection. Our theory enables the comprehensive understanding of the device physics of PCSELs toward the realization of higher-power continuous-wave lasing and short-pulse lasing.

Figure 1

Schematics of (a) cross-section of a typical PCSEL device and (b) top view of a square-lattice PC. (c) Bloch wave states represented by wave vectors (arrows) in reciprocal space including four basic waves (red arrows), high-order waves, and radiative waves.

Figure 2

(a) Schematic of a double-lattice PC. (b) 3D shape of the air holes embedded by MOVPE, which has been reconstructed from scanning electron microscope images. (c) Calculated photonic band diagram near the Γ point. (d) Calculated threshold gain of the fundamental and high-order modes in the mode A group in a device with $L=300\mu \mathrm{m}$. The color maps show the photon distributions of the first, second, and third modes, which have been calculated using the conventional 3D-CWT.

Figure 3

(a) Calculated temporal change of the carrier density in the center of electrode (upper) and the output power (lower) at two different current injection levels. (b), (c) Calculated carrier density distribution and photon distribution at two different current injection levels, respectively. At the higher injection level $(I=2.8I_{\mathrm{th}})$, SHB arises in the center of the electrode, and the photon distribution becomes more uniform. (d) Experimentally measured near-field patterns of the double-lattice PCSEL.

Figure 4

(a), (b) Calculated lasing spectra of the double-lattice PCSEL at three different injection current levels. The carrier-induced refractive index change is taken into account in (a) but not in (b). The transition from single-mode to two-mode lasing is observed only in (a). (c) Experimentally measured lasing spectra of the fabricated double-lattice PCSEL. (d) Schematic of the spatial distribution of the carrier density (upper) and band-edge frequency (lower). In the case of upward convex band A, a photonic band gap (shown in blue) is formed above the band-edge frequency $\left(f_{\mathrm{edge}}\right)$, which more strongly confines photons with the lasing frequency $\left(f_{\mathrm{lase}}\right)$ inside the electrode. A small band gap is also formed in the center of the electrode for photons with $f_{\mathrm{lase}}$, which makes the photon distribution more uniform.