Cross polarization in anisotropic gaussian light beams

Cross Polarization in anisotropic Gaussian light beams is derived within the framework of the Maxwell optics using the elegant Mukunda–Simon–Sudarshan matrix substitution rule for transition from Helmholtz scalar wave optics to the Maxwell vector wave optics. It is seen that the electromagnetic field components have certain interesting relations to each other. Other properties such as the intensity distribution are also presented.