Propagation of the Hermite-Laguerre-Gaussian Schell-Model Beams Through Mode Converter

Mode converter is an astigmatic optical system that allows transforming the set of coherent Hermite-Gaussian modes with dislocation singularities into Laguerre-Gaussian one, which carries the OAM, and vice versa. The intermediate Hermite-Laguerre-Gaussian (HLG) modes are also obtained for a certain values of mode converter parameter. All these mode sets are used or can be used for information encoding in free space optical communication. Such mode transformation is well understood in the coherent case, however, the propagation of partially coherent HLG modes through the mode converter has not been addressed yet. Here, we derive a comprehensive closed-form expression for the evolution of the mutual intensity of HLG Schell-model beams (HLG-SMBs) during propagation through the mode converter. It is compared with the expression for HLG-SMBs propagation through rotationally symmetric system. We conclude that the mode converter also works for the partially coherent case, but only for intensity distribution. While the mutual intensity and, in particular, cross-correlation function are different in the output of the considered optical systems. This theoretical analysis is important for applications of the HLG sets in optical communication when the mode decoherence has to be taken into account.