Cross-spectral density matrix of a random electromagnetic beam propagating through an apertured axially nonsymmetrical optical system

Using the fact that a hard-edged rectangular aperture function can be approximated by a two-dimensional multi-Gaussian series, analytic formulas for the elements of the cross-spectral density matrix of a random electromagnetic beam truncated by a rectangular aperture and passing through an axially nonsymmetrical optical system is derived. The analysis is illustrated by numerical examples relating to changes in the spectral degree of polarization of electromagnetic Gaussian Schell-model beams propagating through free space, focal system and dual-focus system. In particular, the effect of the size of the hard aperture on the spectral degree of polarization of the beam along its optical axis is discussed.