On the Twistability of Partially Coherent, Schell-Model Sources - Riccardo Borghi (Photonics)
In this paper, the problem of assessing the twistability of a given bona fide cross-spectral density is tackled for the class of Schell-model sources, whose shift-invariant degree of coherence is represented by a real and symmetric function, denoted as <semantics>μ(−r)=μ(r)</semantics>. By employing an abstract operatorial language, the problem of determining the highly degenerate spectrum of a twisted operator <semantics><mover accent="true">W^</mover>u</semantics> is addressed through a modal analysis based on the complete knowledge of the spectrum of the sole twist operator <semantics><mover accent="true">T^</mover>u</semantics>, as found by R. Simon and N. Mukunda. To this end, the evaluation of the complete tensor of the matrix elements <semantics>⟨n′,ℓ′|<mover accent="true">W^</mover>u|n,ℓ⟩</semantics> is carried out within the framework of the so-called extended Wigner distribution function, a concept recently introduced by M. VanValkenburgh. As a nontrivial application of the algorithm developed here, the analytical determination of the spectrum of saturated twisted astigmatic Gaussian Schell-model sources is also presented.