Twisted vortex Gaussian Schell-model beams, generalized ABCD systems, and multidimensional Hermite polynomials

Abstract

We derive the cross-spectral density (CSD) function for a twisted vortex partially coherent beam at the output of a general ABCD system in terms of multidimensional Hermite polynomials (MDHPs). MDHPs, which to our knowledge have not been applied in classical optics, offer notational and computational advantages over prior CSD function representations, which use common (one-dimensional) Hermite polynomials. We explain how to compute MDHPs using the recurrence relation given in the literature and include MATLAB code to generate MDHPs of any order. Lastly, we validate our work experimentally by comparing the measured spectral density of a twisted vortex beam at the output of an asymmetric optical system to predictions from our theoretical CSD function.