Fig. 1. Modeled microdisk laser. (a) Schematic cross-section of the disk with labeled dimensions. (b) Strain across the layer stack, along a vertical axis near the periphery of the disk, where the optical field of whispering gallery ground modes is maximal. (c) Measured thresholds reported by Stange et al. [29] at a 1064 nm pump wavelength (Nd:YAG).

Fig. 2. Flat-band energy diagram at 20 K. (a) Conduction band energy levels, with quantization levels in the wells (the gray curve shows the non-quantized EΓ band edge energy, the blue curves the quantized EΓ1 and EΓ2 levels, and the red curve EL1 inside the wells and the non-quantized EL inside the barriers). (b) Valence band energy levels, with quantization levels in the wells (the gray curve shows the non-quantized EHH band edge, the blue curves the EHH1, EHH2, and EHH3 levels, and the red curve ELH1 inside the wells and the non-quantized ELH inside the barriers).

Fig. 3. Net gain as a function of pump power density. The experimentally determined thresholds are indicated by the vertical lines. (a) Lifetimes equal to 217 ps and 80 ps at 50 K and 100 K, respectively. Positive net gains equal to 267 cm−1 and 342 cm−1 are observed at the experimental thresholds at 50 K and 100 K, respectively. (b) Directness ΔEL−Γ reduced by 30 meV and lifetimes uniformly set to 80 ps. The net gain at threshold is close to zero for both temperatures and rolls over at 100 K. Pump power densities indicated on the x axes can be converted into carrier concentrations averaged across the thin film stack by taking the assumed lifetimes and stack thickness (690 nm) into account. QW dependent carrier concentrations at threshold are reported in Fig. 6.

Fig. 4. (a) Field profiles for the TE3, TM0, and TM3 modes, with Er, Ez, and Ep the E-field components along the radial, z, and azimuthal directions. While TM3 is a quasi-TM mode, it also has strong in-plane field components Er and Ep away from the disk’s symmetry plane. This explains why it is the quasi-TM mode with the highest gain at low temperatures (50 K), at which the TE material net gain is the highest. At higher temperatures (100 K), the TM material net gain is highest, and TM0 becomes the dominant lasing mode. (b) TE and TM confinement factors ΓTE and ΓTM as a function of QW number for each of these three modes. The pronounced off-symmetry-plane ΓTE for TM3 is readily apparent.

Fig. 5. Carrier concentrations versus vertical position for (a) 20  kW/cm2 pump intensity at 50 K and (d) 150  kW/cm2 pump intensity at 100 K along the axis indicated in Fig. 1. Barrier layers and buffer are shown as gray regions. Conduction and valence band energies at (b), (c) 50 K and (e), (f) 100 K, with the same color coding as in Fig. 2. In addition, quasi-Fermi levels are shown in green. To reduce the number of curves, the red curves in (b) and (e) show the EL band edge in the barriers, but the EL1 subband edge in the wells. Similarly, the purple curves in (c) and (f) show ELH in the barriers and ELH1 in the wells.

Fig. 6. (a), (b) Electron and (d), (e) hole concentrations for each of the wells at (a), (d) 50 K and at the 20  kW/cm2 threshold pump intensity and (b), (e) 100 K and 150  kW/cm2. Electrons are classified as (total) Γ- and L-valley electrons, holes as (total) HHs and LHs. Confined Γ-valley electrons, HHs, and LHs are also separately shown. (c), (f) Carrier densities integrated over the entire stack and broken down in Γ- and L-valley electrons inside the wells, total electron density in the barriers, and total electron density in the buffer. Similarly, holes are broken down in HHs and LHs inside the wells, total holes in the barriers, and total holes in the buffer.

Fig. 7. Gain at 50 K and 100 K, respectively, at 20  kW/cm2 and 150  kW/cm2 threshold pump intensities. (a) Material gain for each well, for both polarizations. (b) Modal gain for each well. The TE3/TM3 modes have the highest gain at 50 K, and the TE3/TM0 modes at 100 K. (c) Total modal gain of the TE3 and TM0 modes, respectively, at 50 K and 100 K. (d) Breakdown of the modal gain for the TM0 mode at 100 K across quantum wells.

Fig. 8. Calculated absorption losses at 50 K and 100 K and at respective lasing thresholds 20  kW/cm2 and 150  kW/cm2. (a) FCA as predicted by the modified Drude model and (b) IVBA, calculated for both TE and TM polarizations.

Table 1. Summary of Assumed Material Properties in the 50–100 K Range

Table 2. Summary of Gain Modeling Assumptions