Effects of surface roughness of a wave plate on the development of diffractive polarization speckle

A rough-surfaced retardation plate is a particular polarization-dependent phase modulation device, the performance of which is affected by its surface roughness structures. In previous research[1], its decorrelation and depolarization effect have been investigated under an assumption of a rough surface model with large covariance of thickness fluctuation, giving fully developed speckle field by transmission/reflection. In this paper, the analysis of the rough-surfaced retardation plate will continue but be focused on a smooth roughness model. When the thickness fluctuation is relatively small, partially developed speckle will be generated. The statistics of partially developed polarization speckle with nonuniform spatial distribution of polarization state will be discussed in the form of matrix elements of the coherence-polarization matrix. The propagation of the partially developed speckle field will be traced within the framework of the complex-valued ABCD matrix theory under paraxial approximation to reveal the evolution of its degree change of coherence and polarization on propagation. This means that Gaussian apertures are included in the optical train of elements. The differences for the statistical features to the fully developed polarization speckle are emphasized.