White polarization sandwiches: optical elements with non-orthogonal eigenpolarizations

Optical elements with non-orthogonal eigenpolarizations have complex anisotropic properties, which are not yet well understood. As an example of such elements, we studied theoretically the class of white polarization sandwiches. Light passing successively through two identical white sandwiches preserves its polarization state, so that, following the terminology of Berry and Dennis, white polarization sandwiches can be regarded as non-trivial square roots of unity. This paper presents a general Jones matrix of white polarization sandwiches and discusses its spectral properties. It further discusses a way to synthesize white sandwiches. Our analysis shows that a general white polarization sandwich has complex anisotropic properties comprising all four basic anisotropy mechanisms: linear and circular dichroism and linear and circular birefringence. Several simple examples of synthesized white sandwiches show, however, that the form, orientation and rotation direction of their eigenpolarization ellipses can be easily controlled by changing a single parameter of the constituent elements. The results could contribute to understanding the properties of optical elements with non-orthogonal eigenpolarizations and, more generally, elements with anisotropic absorption.