HOMOGENEOUS AND INHOMOGENEOUS JONES MATRICES

The classification of polarization properties of polarization elements is studied to derive data-reduction equations for extracting the diat tenuation, retardance, and other polarization properties from their Jo nes matrices. Polarization elements, and Jones matrices as well, are d ivided into two classes: homogeneous, with orthogonal eigenpolarizatio ns, and inhomogeneous, with nonorthogonal eigenpolarizations. The basi c polarization properties, diattenuation and retardance, of homogeneou s polarization elements are straightforward and well known; these elem ents are characterized by their eigenvalues and eigenpolarizations. Po larization properties of inhomogeneous polarization elements are not s o evident. By applying polar decomposition, the definitions of diatten uation and retardance are generalized to inhomogeneous polarization el ements, providing an understanding of their polarization characteristi cs. Furthermore, an inhomogeneity parameter is introduced to describe the degree of inhomogeneity in a polarization element. These results a re then adapted to degenerate polarization elements, which have only o ne linearly independent eigenpolarization.