Generalized vectorial Rayleigh–Sommerfeld diffraction integrals are developed for the cross-spectral-density matrices of spatially partially coherent beams. Using the Gaussian Schell-model (GSM) beam as an example, we derive the expressions for the propagation of cross-spectral-density matrices and intensity of partially coherent vectorial nonparaxial beams, and the corresponding far-field asymptotic forms, beyond the paraxial approximation. The propagation of the vectorial nonparaxial GSM beams are evaluated and analyzed. It is shown that a 3 × 3 cross-spectral-density matrix or a vector theory is required for the exact description of nonparaxial GSM beams.
© 2004 Optical Society of America
Kailiang Duan and Baida Lü, "Partially coherent vectorial nonparaxial beams," J. Opt. Soc. Am. A 21, 1924-1932 (2004)