Sy. Lu et Ra. Chipman, HOMOGENEOUS AND INHOMOGENEOUS JONES MATRICES, Journal of the Optical Society of America. A, Optics, image science,and vision., 11(2), 1994, pp. 766-773
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.