Propagation properties of cosh-squared-Gaussian beam through fractional Fourier transform systems

Based on Collins integral formula and the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of cosh-squared-Gaussian beam passing through ideal and apertured FRFT systems have been studied, and some comparisons between using the methods of analytical formula and diffraction integral formula have been done. Further, the studies indicate that the normalized intensity distributions on FRFT plane depend on the fractional order, truncation parameter and initial beam parameter Ω. Variations of normalized intensity distributions with FRFT order are periodic: when the impact of aperture cannot be ignored, the variation period is 4; and when the impact of aperture can be ignored, the variation period is 2.