  Based on the quantized electromagnetic field described by the
Riemann-Silberstein complex vector $F$, we construct the eigenvector set of $%
F$, which makes up an orthonormal and complete representation. In terms of $% F
$ 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.
