Title: Origin of the Anisotropic Beer-Lambert Law from Dichroism and Birefringence in $β$-Ga$_2$O$_3$ Show Chinese title

Title: $β$-Ga$_2$O$_3$中各向异性 Beer-Lambert 定律的起源来自吸收和双折射

Abstract: The anisotropic optical absorption edge of $\beta$-Ga$_2$O$_3$ follows a modified Beer-Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in $\beta$-Ga$_2$O$_3$, which arises from the anisotropy and spectral splitting of the physical absorbers i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of $\beta$-Ga$_2$O$_3$. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer-Lambert law arises from the interplay of both the dichroic and birefringent properties of $\beta$-Ga$_2$O$_3$. Show Chinese abstract

Abstract: $\beta$-Ga$_2$O$_3$的各向异性光学吸收边遵循一个修正的比尔-兰伯特定律，具有两个有效的吸收系数。 线偏振光的吸收系数在超过临界穿透深度后会降至最小吸收方向，而该深度本身取决于偏振和波长。 为了理解这种行为，进行了斯托克斯矢量分析，以跟踪深度函数的偏振状态。 吸收系数的减弱与平面内线偏振逐渐转向最小吸收晶体学方向有关，这在(010)平面中沿着a激子方向，在(001)平面中沿着b激子方向。 我们表明，在$\beta$-Ga$_2$O$_3$的光学吸收边附近，强线性二向色性导致了这种转变，这是由物理吸收体（即激子）的各向异性和光谱分裂引起的。 线性偏振的偏移伴随着椭圆度的变化，这是由于$\beta$-Ga$_2$O$_3$的双折射特性所致。 对入射电场与某一深度处电场之间的相位关系进行分析，揭示了相速度作为有效折射率，其沿不同的晶体学方向而变化。 临界穿透深度被证明与椭圆度最大的深度有关。 因此，各向异性的比尔-朗伯定律源于$\beta$-Ga$_2$O$_3$的二向色性和双折射特性的相互作用。