Nonlinear optical coefficients of wurtzite-typeα-GaN determined by Raman spectroscopy

Abstract

Raman scattering on phonons in GaN with wurtzite structure ($\ensuremath{\alpha}$-GaN) is used to determine the coefficients of second-harmonic generation (SHG) and the linear electro-optic effect (LEO) in the region of optical transparency for excitations below the band gap. For wurtzite-type crystals, the symmetry requires that three SHG coefficients ${d}_{31}, {d}_{33}$, and ${d}_{24}$ and three LEO coefficients ${r}_{31}, {r}_{33}$, and ${r}_{42}$ be considered. In this work, the dependence of these SHG and LEO coefficients on the Raman scattering intensities of the polar transverse optical (TO) and longitudinal optical (LO) phonon modes in wurtzite-type crystals and their corresponding Faust-Henry coefficients is derived. In the case of GaN, the obtained SHG coefficients are $\left|{d}_{31}\right|$ = 2.46 pm/V, $\left|{d}_{33}\right|$ = 3.97 pm/V, and $\left|{d}_{24}\right|$ = 2.48 pm/V, which agree well with results measured by other methods. Also, all three LEO coefficients of GaN have been determined: $\left|{r}_{13}^{S}\right|$ = 0.72 pm/V, $\left|{r}_{33}^{S}\right|$ = 1.31 pm/V, and $\left|{r}_{42}^{S}\right|$ = 0.38 pm/V. Contrary to previous reports, our results indicate an important contribution of the ionic lattice displacements to the linear electro-optic effect. The ratios of the three SHG coefficients or the three LEO coefficients, which correspond to different nonlinear susceptibility tensor elements, depend on the relative intensities of the polar TO and LO phonon modes connected with different Raman tensor elements.