Sticking a twist to a partially coherent source cannot be done at will, since the result can violate the definiteness property of the corresponding cross-spectral density. As a matter of fact, the study of twisted sources has been mainly concentrated on the original case proposed by Simon and Mukunda [J. Opt. Soc. Am. A10, 95 (1993)JOAOD60740-323210.1364/JOSAA.10.000095] of circularly symmetric Gaussian Schell-model sources. Here, we discuss a modeling procedure that can be used to generate numberless genuine twisted sources without symmetry constraints. As geometrically simple examples, two cases of non-Gaussian twisted sources endowed with circular or rectangular symmetry are explicitly worked out.
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