A unified formalism for polarization optics by using group theory

Abstract

A unified treatment of three polarization calculus methods - Jones matrix, Mueller matrix and Poincaré sphere - is accomplished by using the concept of the Lie group. In the case of the totally transparent system, it is related to the compact Lie group, and in the case of the partially transparent system, it is related to the homogeneous Lorentz group. The physical meaning of the Pauli's spin matrices is given and the generator is introduced and used extensively.