  In-plane anisotropic layered materials (ALMs), such as black phosphorus (BP),
exhibit unique angle-resolved polarized Raman (ARPR) spectroscopy
characteristics, as attributed to birefringence, linear dichroism and complex
Raman tensor. Moreover, the ARPR intensity profiles of BP flakes deposited on
multilayer dielectrics are notably sensitive to their thickness, owing to
interference effects. The intricate anisotropic effects present challenges in
accurately predicting the ARPR intensity of BP flakes. In this study, we
propose a comprehensive strategy for predicting the ARPR intensity of BP flakes
by explicitly considering optical anisotropy, encompassing birefringence,
linear dichroism, and anisotropic cavity interference effects within
multilayered structures. Through this approach, we have identified the
intrinsic complex Raman tensors for phonon modes, independent of the BP flake
thickness. By leveraging this methodology, we have elucidated the flake
thickness-dependent effective complex Raman tensor elements, allowing for
precise prediction of the observed ARPR intensity profile for the BP flake.
This work provides a profound understanding of ARPR behaviors for ALM flakes.
