The selection rule for angle-resolved polarized Raman (ARPR) intensity of phonons from standard group-theoretical method in isotropic materials would break down in anisotropic layered materials (ALMs) due to birefringence and linear dichroism effects. The two effects result in depth-dependent polarization and intensity of incident laser and scattered signal inside ALMs and thus make a challenge to predict ARPR intensity at any laser incidence direction. Herein, taking in-plane anisotropic black phosphorus as a prototype, we developed a so-called birefringence-linear-dichroism (BLD) model to quantitatively understand its ARPR intensity at both normal and oblique laser incidences by the same set of real Raman tensors for certain laser excitation. No fitting parameter is needed, once the birefringence and linear dichroism effects are considered with the complex refractive indexes. An approach was proposed to experimentally determine real Raman tensor and complex refractive indexes, respectively, from the relative Raman intensity along its principle axes and incident-angle resolved reflectivity by Fresnel’s law. The results suggest that the previously reported ARPR intensity of ultrathin ALM flakes deposited on a multilayered substrate at normal laser incidence can be also understood based on the BLD model by considering the depth-dependent polarization and intensity of incident laser and scattered Raman signal induced by both birefringence and linear dichroism effects within ALM flakes and the interference effects in the multilayered structures, which are dependent on the excitation wavelength, thickness of ALM flakes and dielectric layers of the substrate. This work can be generally applicable to any opaque anisotropic crystals, offering a promising route to predict and manipulate the polarized behaviors of related phonons.

由于双折射和线性二色性效应，来自各向同性材料中标准群论方法的角分辨偏振拉曼 (ARPR) 声子强度的选择规则将在各向异性层状材料 (ALM) 中失效。这两种效应导致入射激光的深度依赖性偏振和强度以及 ALM 内部的散射信号，因此对预测任何激光入射方向的 ARPR 强度提出了挑战。在此，以面内各向异性黑磷为原型，我们开发了一种所谓的双折射线性二色性 (BLD) 模型，通过同一组真实拉曼张量定量了解其在垂直和倾斜激光入射下的 ARPR 强度某些激光激发。不需要拟合参数，一旦考虑了复折射率的双折射和线性二色性效应。提出了一种通过菲涅耳定律从沿其主轴的相对拉曼强度和入射角分辨反射率分别通过实验确定真实拉曼张量和复折射率的方法。结果表明，通过考虑入射激光的深度依赖性偏振和强度以及由两者引起的散射拉曼信号，也可以基于 BLD 模型理解先前报道的在垂直激光入射下沉积在多层基板上的超薄 ALM 薄片的 ARPR 强度ALM 薄片内的双折射和线性二色性效应以及多层结构中的干涉效应取决于激发波长，ALM 薄片的厚度和基板的介电层。这项工作可以普遍适用于任何不透明的各向异性晶体，为预测和操纵相关声子的极化行为提供了一条有前途的途径。