Spectral intensity characteristics of partially coherent flattened multi-Gaussian beams with an axial shadow passing though paraxial ABCD optical systems

Based on the beam model for the flattened multi-Gaussian beams (FMGBs) with an axial shadow and partially coherent theory, the expression for cross-spectral density of partially coherent FMGBs with an axial shadow has been given, and the analytical expression for the spectral intensity of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems has been derived. The spectral shift of partially coherent FMGBs with an axial shadow focused by a thin lens has been analyzed quantitatively. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed in detail. Our results show that the spectral intensity and the spectral shift of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems depend on the source spectral density, the generalized Fresnel number of the system, the transverse coordinate, the spatially coherence parameter, as well as the beam orders.