Complete Raman Tensor Determination in Birefringent $\beta$-Ga$_2$O$_3$ by Single-Stage Hyperspectral Analysis of Polarization Angle-Resolved Raman Spectra
The low symmetry of the monoclinic phase of Ga$_2$O$_3$ leads to pronounced optical anisotropy and, consequently, to birefringence, which strongly affects the Raman response. Because Raman scattering is fundamentally sensitive to the polarizability of a material, this anisotropy must be carefully accounted for in order to extract quantitative information - an effort that has only recently been shown to be feasible in such media. Here, we report Raman measurements from all three principal crystal planes $(100)$, $(010)$, and $(001)$, as well as from the $(\overline{2}01)$-plane of a $\beta$-Ga$_2$O$_3$ single crystal. By combining polarization angle-resolved Raman spectroscopy (PARRS) with a newly developed fitting procedure and explicitly accounting for birefringence, we achieve full spectral separation and quantitatively determine the energies and relative Raman tensor elements of all 15 Raman-active modes.