Spectra, coherence and polarization of diffracted electromagnetic Gaussian Schell-model beams

An approximate analytical formula for the cross-spectral density matrix of the electric field of diffracted electromagnetic Gaussian Schell-model (EGSM) beams is derived by using the method of the complex Gaussian function expansion. We show both analytically and by numerical examples the aperture effects of spectra, coherence and polarization of electromagnetic Gaussian Schell-model beams. It is shown that the larger the truncation parameter the spectral degree of polarization becomes non-uniform on propagation, the spectral density shape is more tightly. The spectral degree of coherence oscillates, and the larger the value of truncation parameter the spectral degree of coherence exhibits rapid oscillation.