Anomalous polarization dependence of Raman scattering and crystallographic orientation of black phosphorus

We investigated polarization dependence of the Raman modes in black phosphorus (BP) using five different excitation wavelengths. The crystallographic orientation was determined by comparing polarized optical microscopy with high-resolution transmission electron microscopy analysis. In polarized Raman spectroscopy, the B_2g mode shows the same polarization dependence regardless of the excitation wavelength or the sample thickness. On the other hand, the A_g¹ and A_g² modes show a peculiar polarization behavior that depends on the excitation wavelength and the sample thickness. The thickness dependence can be explained by considering the anisotropic interference effect due to the birefringence and dichroism of the BP crystal, but the wavelength dependence cannot be explained. We propose a simple and fail-proof procedure to determine the orientation of a BP crystal by combining polarized Raman scattering with polarized optical microscopy.