Refractive indices and elasto-optic coefficients of GaN studied by optical waveguiding

Asymmetric GaN planar waveguides were grown on (0001) sapphire by molecular beam epitaxy or by metal-organic chemical vapor deposition. The GaN chromatic dispersion is measured in these samples by the prism coupling method at several discrete wavelengths over a large spectral domain (458–1550 nm). Two-term Sellmeier equations are adequate to fit the ordinary $no$ and extraordinary $ne$ refractive index curves as a function of wavelength. GaN waveguides were also grown on $AlxGa1−xN$ and AlN cladding layers, and the GaN refractive indices are further measured from these samples. On the other hand, the biaxial stress state of each sample is determined by measuring the A, B, and C free exciton transition energies by low temperature (10 K) reflectivity measurements. The refractive indices versus in-plane stress $σ1$ reveal linear variations in the studied range and the slopes $∂n/∂σ1$ are determined. It is found that these variations are more than seven times larger for the ordinary index than for the extraordinary index depending on the optical wavelength. We report here for the first time the measurement of the elasto-optic coefficients $(p11+p12)$ and $p13$ of GaN in the visible wavelength range.