On the algebraic characterization of a Mueller matrix in polarization optics. II. Necessary and sufficient conditions for Jones-derived Mueller matrices

Abstract

We show that every Mueller matrix, that is a real 4 × 4 matrix M which transforms Stokes vectors into Stokes vectors, may be factored as M = L ₂ KL ₁ where L ₁ and L ₂ are orthochronous proper Lorentz matrices and K is a canonical Mueller matrix having only two different forms, namely a diagonal form for type-I Mueller matrices and a non-diagonal form (with only one non-zero off-diagonal element) for type-II Mueller matrices. Using the general forms of Mueller matrices so derived, we then obtain the necessary and sufficient conditions for a Mueller matrix M to be Jones derived. These conditions for Jones derivability, unlike the Cloude conditions which are expressed in terms of the eigenvalues of the Hermitian coherency matrix T associated with M, characterize a Jones-derived matrix M through the G eigenvalues and G eigenvectors of the real symmetric N matrix N = Mtilde]GM associated with M. Appending the passivity conditions for a Mueller matrix onto these Jones-derivability conditions, we then arrive at an algebraic identification of the physically important class of passive Jones-derived Mueller matrices.