Decomposition of Jones and Mueller matrices in terms of four basic polarization responses

A simple new method is introduced to analyze the polarization of light by media. This method decomposes a Jones matrix into a linear combination of four basic matrices that represent different polarization responses. The Mueller matrix expressed in terms of the response coefficients of the basic matrices demonstrates a highly symmetric form that spells out the physical origins of each matrix element. Randomness in the response coefficients gives rise to depolarization that appears only in the diagonal elements of a Mueller matrix. The decomposition of a Mueller matrix gives both the depolarization and polarization characteristics relating directly to the anisotropic optical properties.