Spectral analysis of scalar double multi-Gaussian Schell-model sources in the far-field

Abstract Multi-Gaussian Schell-model (MGSM) beam sources, due to their flattened correlations, has found various uses in many fields of optics such as in free space optical communications. Here, we introduce the double MGSM (DMGSM) source to redistribute the beam intensity profile of Schell-model beams. Theory of coherence and genuine spatial correlation functions are used to formulate the model. Specifically, we consider the multi-Gaussian functional form both in the spectral density and in the correlations part of the partially coherent beams. The model is called the DMGSM source in the sense that the source’s complete flatness helps the beam to have a localized and enhanced intensity in the far field relative to the source spectrum. The source model and the field expressions in the far-field are derived and analyzed numerically. The primary outcome of this study is the derivation of the far-field spectrum equation, which characterizes the far-field spectral properties of scalar DMGSM sources. This equation provides a comprehensive analytical framework for understanding spectral variations influenced by source parameters, with numerical evaluations serving to illustrate and elucidate the theoretical formula. Comparison of the DMGSM source to the MGSM source and to the Gaussian Schell-model source is presented.