Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes through complex ABCD optical systems

Abstract

The change of coherence and polarization of an electromagnetic beam modulated by a random anisotropic phase screen passing through any optical system is found within the framework of complex ABCD-matrix theory This means that the formalism can treat imaging and Fourier transform and free-space optical systems, as well as fractional Fourier transform systems, with finite-size limiting apertures of Gaussian transmission shape. Thus, the current paper shall be considered as a continuation, extension, and generalization of a previous work by Shirai and Wolf [J. Opt. Soc. Am. A21, 1907 (2004)]. It will be shown that the inclusion of apertures in the optical system strongly influences not only the propagation of spatial coherence but also the degree of polarization of a propagating field. Analytical expressions of coherence and polarization propagation will be given in terms of the matrix elements for any complex optical system.

Three-dimensional static speckle fields Part I Theory and numerical investigation

“…We also note, however, that the peak value decreases as ε increases. Equation (12) indicates that the out-of-plane displacement of the diffuser can be estimated in the observation plane using the off-axis speckle correlation values, by substituting the longitudinal camera displacement ε with the out-of-plane displacement of the object surface, while keeping the camera position steady. The quantitative relationship between the parameters in the equation is verified experimentally in Part II [21].…”

“…Recently, a generalized Yamaguchi correlation factor was derived using the Linear Canonical Transform and the associated ABCD matrix theory for a hard limiting aperture [7,8]. Such methods have been shown to be of great convenience when examining speckle size and controlling speckle characteristics in various paraxial optical systems [9][10][11][12][13][14][15].…”

3D polarisation speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams

“…for the field at 1 p in first observation plane after passing through a complex ABCD optical system and the field at 2 p in another plane displaced by a distance z Δ is connected to the mutual coherence matrix of the integral formulation 15,26 : ( ) ( )…”

“…where the modified polarization matrix ( ) 15) and the relationship between the revised polarization matrix t J and the coherence matrix…”

“…Therefore, a concept named polarization speckle has been introduced 6,7 to distinguish it from the conventional scalar laser speckle field with a uniform polarization. At the same time, the vectorial electromagnetic field description in terms of a 2 2 × beam coherence-polarization matrix 8,9 has shown to be a valuable tool in order to investigate the evolution of polarization and coherence states during propagation together with their spatial distribution [10][11][12][13][14][15] , especially after the setup of the unified theory of coherence and polarization 16,17 .…”