Polarization characteristics of partially coherent beam passing through astigmatic fractional Fourier system

Abstract

The fractional Fourier transform is a powerful tool for analyzing optical resonators. The selection of fractional number and astigmatism coefficient determines the size of the resonator, and influences the polarization, far-field emission angle and focusing power of the laser beam. Researchers often pay more attention to the change of light intensity after the fractional Fourier transform system. However, the effect of polarization changes on the system is also critical. In this article, we took partially coherent electromagnetic Gaussian-Schell model beam as a research object. Based on Collins formula and the fractional Fourier transform system ABCD matrix, we deduced the polarization degree of electromagnetic Gauss Schell model beam passing through the astigmatic lens fractional Fourier transform, elliptical azimuth and ellipticity; and analyzed the distribution of polarization degree, elliptic azimuth and ellipticity output plane of the astigmatism fraction Fourier transform system by numerical simulation. The results show that the distribution of polarization degree, ellipse azimuth and ellipticity on the output plane are no longer uniform after the beam passing through the fractional Fourier transform system with an astigmatic lens. In the non-focal plane, affected by astigmatism, beam waist position in x and y directions do not coincide, and the bigger astigmatism is, the farther separation is. Therefore, the polarization properties are elliptically symmetrical, and the greater the astigmatism is, the greater the eccentricity of the ellipse is. In the focal plane, the beam coincides with the waist position in the x and the y direction, and the polarization characteristics are circularly symmetric. The larger the astigmatism coefficient is, the larger the radius is. The greater the astigmatism coefficient is, the faster the polarization changes on the axis. The astigmatism of the lens leads to the difference of the beam width between the x direction and the y direction. Therefore, the point polarization of the shaft will appear in doublet or double valleys, and the greater the astigmatism coefficient is, the greater the difference between the value with and without astigmatism is. The results of this study have some reference value for the selection of fractional Fourier transform order and astigmatism coefficient under different polarization characteristics, and have important guiding significance for the design of optical resonator.