Effects of surface roughness of a waveplate on the development of diffractive polarization speckle

A rough-surfaced retardation plate is a particular polarization-dependent phase modulation device, whose performance is affected by its surface roughness structures. In previous research [J. Opt. Soc. Am. A32, 2346 (2015)JOAOD60740-323210.1364/JOSAA.32.002346], its decorrelation and depolarization effects have been investigated under an assumption of a rough surface model with large covariance of thickness fluctuations, giving a fully developed speckle field by transmission/reflection. This paper continues the analysis of the rough-surfaced retardation plate and then focuses 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 non-uniform spatial distribution of polarization state will be discussed in the form of the 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 in statistical features from fully developed polarization speckle are emphasized.