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

摘要

Abstract: We give a derivation of the explicit form of thegeneral Mueller matrix of polarization optics for thecase of arbitrary and uniform birefringence anddichroism. We first point out that the general Muellermatrix is essentially a Lorentz transformation. Then aset of complex Lorentz generator and a complexpolarization vector is introduced. The complexgenerators are related to the usual Lorentz generatorsof special relativity, while the complex vector isrelated to the Stokes representation of thebirefringence and dichroism vectors. Next, the explicitform of the general Lorentz transformation, andsubsequently the general Mueller matrix for arbitraryand uniform berefringence and dichroism is derived. Thegeneral form is used to derive new Mueller matrices forthree special cases. The special cases are (1) theMueller matrix for a material with finite dichroism andweak birefringence, (2) the Mueller material with bothfinite birefringence and dichroism that are equal inmagnitude and perpendicular in direction. Then, wederive an algorithm to determine the materialparameters from the general Mueller matrix elements.Finally, we apply the algorithm to theoretical andexperimental Mueller matrices. !6