Eigen generalized Jones matrix method

A differential generalized Jones matrix method (dGJM) was recently introduced by Ortega-Quijano and colleagues to derive the GJM for modelling uniaxial and biaxial crystals with arbitrary orientations in laboratory coordinate systems. Later, we propose an eigen generalized Jones matrix method to simulate the phase and polarization of fully polarized light propagating in an anisotropic crystal when the optical axis orientations and light directions are both arbitrary. In our method, we use physics that are equivalent in principle to those of Ortega-Quijano, but we use a modified mathematical technique. We introduce the eigen generalized Jones matrix in the intrinsic coordinate system to precisely calculate the phase and polarization of the light, which overcomes the limitations of the differential generalized Jones matrix method. The simulation results indicate that our method can be used to calculate the polarization distribution, regardless of how the light beam and optical axis positioned, or whether the light beam has a vortex.