Partially coherent sources with the combined quadratic phase

Abstract

We construct a class of partially coherent sources with a new phase, which is consisted of separable and inseparable quadratic phases. As examples, the Gaussian distribution and rectangular flat-topped Gaussian distributions are selected as weight functions, respectively. The analytical propagation formulas of anisotropic Gaussian Schell-model (AGSM) beams and rectangular multi-Gaussian Schell-model (RMGSM) beams with the combined quadratic phase are derived. We investigate the propagation characteristics of the AGSM beam and the RMGSM beam carrying the combined quadratic phase. The twist effects of the combined quadratic phase on the spectral density (SD) and the degree of coherence (DOC) of the AGSM beam are quantitatively analyzed, and a specific method for calculating the critical value of the phase parameter is proposed. In addition, we qualitatively analyze the twist effects of the combined quadratic phase on the SD and the DOC of the RMGSM beam. We find that the propagation of the RMGSM beam is similar to that of the AGSM beam. These results may provide new inspiration for applications of synthesizing rotating beams in optics.