General Lorentz transformation and its application to deriving andevaluating the Mueller matrices of polarization optics,

摘要

Abstract: We give a derivation of the explicit form of the general Mueller matrix of polarization optics for the case of arbitrary and uniform birefringence and dichroism. We first point out that the general Mueller matrix is essentially a Lorentz transformation. Then a set of complex Lorentz generator and a complex polarization vector is introduced. The complex generators are related to the usual Lorentz generators of special relativity, while the complex vector is related to the Stokes representation of the birefringence and dichroism vectors. Next, the explicit form of the general Lorentz transformation, and subsequently the general Mueller matrix for arbitrary and uniform berefringence and dichroism is derived. The general form is used to derive new Mueller matrices for three special cases. The special cases are (1) the Mueller matrix for a material with finite dichroism and weak birefringence, (2) the Mueller material with both finite birefringence and dichroism that are equal in magnitude and perpendicular in direction. Then, we derive an algorithm to determine the material parameters from the general Mueller matrix elements. Finally, we apply the algorithm to theoretical and experimental Mueller matrices. !6