Operator for Describing Polarization States of a Photon

Based on the quantized electromagnetic field described by the Riemann-Silberstein complex vector $F$, we construct the eigenvector set of $$, which makes up an orthonormal and complete representation. In terms of $$ we then introduce a new operator which can describe the relative ratio of the left-handed and right-handed polarization states of a polarized photon .In $F^{\prime}s$ eigenvector basis the operator manifestly exhibits a behaviour which is similar to a phase difference between two orientations of polarization of a light beam in classical optics.