Propagation of the relative phase shift of two-dimensional Hermite-cosh-Gaussian beams through rectangular apertured optical systems

Based on the fact that a hard-edge aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expressions for the relative phase shift of two-dimensional Hermite-cosh-Gaussian beams passing through a rectangular apertured ABCD optical system are derived. The approximate analytical expressions for the relative phase shift of the two-dimensional Hermite-Gaussian beams, cosh-Gaussian beams and Hermite-cosine-Gaussian beams are also deduced. It is shown that the relative phase shift is closely related to the beam parameters, optical system parameters and the size of apertures. Finally, some numerical examples are also illustrated.