Jones Type Bispinors in Polarization Optics

Abstract

We shall present some facts relevant to solving the problems of polarization optics in the frames of Stokes’s vector and Jones’s spinor formalisms. It is known that the completely polarized light can be described by Stokes 4-dimensional vector or alternatively by Jones complex 2-dimensional spinor. It is known that the Stokes formalism may be extended to a partially polarized light, but Jones approach does not. In the present paper, we introduce the concept of 4-dimensional Jones type spinor, first for a completely polarized light. This approach is extended to the partially polarized light. From 4-dimensional spinor follow both 4-vector and antisymmetric tensor of Stokes type. Stokes vector depends on four parameters, whereas the Stokes tensor depends on five parameters. By this reason, we can assume that the Stokes tensor contains more information about the partially polarized light than the Stokes vector. We have found relationships between the four components of Stokes vector and five components of Stokes tensor in analytical form, they are studied numerically as well. In addition, we shortly discuss relationships between polarization of the light and space models with spinor structure.