Generalized matrix equivalence theorem for polarization theory

A generalized equivalence theorem for polarization theory is formulated and proven. It is shown that anisotropic properties of homogeneous nondepolarizing media can be presented as a combination of four basic mechanisms: linear and circular phase and linear and circular amplitude anisotropy. Expressions for the generalized effect operators of algebraic (or operator) optics are obtained and the inverse problem of crystal optics is solved in terms of physically realizable anisotropy parameters.