On the Twistability of Partially Coherent, Schell-model Sources

The problem of assessing the twistability of a given bonafide cross spectral density is here tackled for the class of Schell-model sources whose shift invariant degree of coherence is represented through a real and symmetric function, say μ(−r)=μ(r). On employing an abstract operatorial language, the problem of the determination of the, highly degenerate spectrum of a twisted operator W^u is addressed through a modal analysis based on the complete knowledge of the spectrum of the sole twist operator T^u found by Simon and Mukunda [J. Opt. Soc. Am. A 15, 1361 (1998)]. To this end, the evaluation of the complete tensor of the matrix elements 〈n′,ℓ′|W^u|n,ℓ〉 is carried out within the framework of the so-called extended Wigner distribution function, a concept recently introduced by Van Valkenburgh [J. Mod. Opt. 55, 3537 - 3549 (2008)]. As a nontrivial application of the algorithm here developed, the analytical determination of the spectrum of saturated twisted astigmatic Gaussian Schell-model sources is also presented.