Mueller-Stokes Matrix Formulation of Fresnel's Equations

Abstract

The Mueller-Stokes matrices for Fresnel's reflection and transmission equations at a dielectric surface are derived and the basic properties of these matrices are discussed. A corresponding pair of matrices for Fresnel's reflection and transmission coefficients are also derived. The matrix forms are shown to simplify considerably at the Brewster angle and their special properties are demonstrated. In order to simplify matrix multiplications a diagonal matrix is constructed. The significance of the eigenvalues and the eigenvectors of the Mueller-Stokes polarizing matrix is noted. The relationship between the Mueller-Stokes polarizing matrix and the diagonal polarizing matrix is developed. Finally, Chandrasekhar's phase matrix is shown to be a special case of the diagonal polarizing matrix.