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Due to its low symmetry, $\beta$-Ga$_{2}$O$_{3}$ exhibits a stronglyanisotropic optical response. As a result, the absorption spectra changes withthe polarization state of the incoming photons. To understand this phenomenon,here we calculate the complete electromagnetic wave equation solutions as afunction of linear polarization angle and photon energy for$\beta$-Ga$_{2}$O$_{3}$ using its measured complex dielectric function tensor.The significant off-diagonal terms in this tensor result in a non-exponentialdecay in the photon flux, indicating that the Beer-Lambert law is not generallyvalid in this anisotropic material. However, over a limited spectral range (>5.8 eV (001 plane),>5.2 eV (010 plane)) an effective absorption coefficientwell approximates the photon flux decay with depth. Near the optical absorptionedge (4.9 - 5.8 eV (001 plane),4.65 - 5.2 eV (010 plane)) the photon flux decayexhibits a modified exponential decay, such that two effective absorptioncoefficients are necessary to model the optical spectrum. Using these results,we calculate the polarization-dependent photoresponsivity spectra for lightpolarized along different crystallographic directions and find that asignificant sub-bandgap photoresponse occurs spanning into the solar spectrum.Truly solar-blind photoresponsivity is only possible if the light is linearpolarized along the [010] direction as compared to (010) plane of$\beta$-Ga$_{2}$O$_{3}$.

Is the Beer-Lambert law in $\beta$-Ga$_{2}$O$_{3}$ applicable? Spectral and polarization dependent absorption and photoresponsivity