激光正入射和斜入射下黑磷角分辨偏振拉曼光谱的理解

Understanding angle-resolved polarized Raman scattering from black phosphorus at normal and oblique laser incidences

由于双折射和二向色性效应,从群论方法得到的各向同性材料声子角分辨偏振拉曼(ARPR)强度的选择定则无法应用于各向异性层状材料(ALMs).这两种效应会导致入射激光和散射信号的偏振和强度在ALMs内部依赖于传输深度,使得预测任意激光入射方向下的ARPR强度面临巨大的挑战.本文以面内各向异性的黑磷作为范例,发展了所谓的双折射-二向色性(BLD)模型,定量理解了黑磷在正入射和斜入射时的ARPR强度.特定激发光下两者采用的是同一套实拉曼张量且不需要任何拟合参数,其中双折射和二向色性效应通过复折射率加以考虑.本文还提出了实拉曼张量和复折射率可分别通过主轴的相对拉曼强度及菲涅尔公式拟合入射角依赖的反射率得到.这些结果表明,在BLD模型基础上通过考虑由双折射和二向色性效应所导致的入射激光和散射信号深度依赖的偏振和强度以及多层结构的干涉效应,可定量理解前面报道的置于多层衬底上的ALMs超薄片在激光正入射时依赖于激发光波长、ALM厚度和衬底介质层厚度的反常ARPR强度.该研究可以广泛应用到任意不透明的各向异性晶体中,为预测和操控相关声子的偏振行为提供了一种有效的方法.

The selection rule for angle-resolved polarized Raman(ARPR)intensity of phonons from standard grouptheoretical 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.