Modal gain in a semiconductor nanowire laser with anisotropic bandstructure

We investigate optical gain for the modes guided by semiconductor nanowires. We focus on optically anisotropic wurtzite-type semiconductors (such as GaN) and the situation when the optical axis of the crystal coincides with the geometrical axis of the nanowire. For GaN nanowire lasers, the calculation of the modal gain requires the knowledge of two confinement factors for a given mode and two gain coefficients for the bulk crystal. We show that the confinement factors for nanowire lasers are very large in comparison to those for heterostructure lasers, and can even exceed unity. To estimate the bulk gain in GaN we use the free-carrier model and emphasize the importance of accounting for anisotropy of gain. Using the calculated confinement factors and bulk gain, we predict that free-standing nanowires with small radius (R ≲ 70 nm) lase into the HE₁₁ mode, thicker nanowires (70 nm ≲ R ≲ 90 nm) lase into the TE₀₁ mode.