Complex-order fractional Fourier transforms in optical schemes with Gaussian apertures

Several optical schemes performing the complex-order fractional Fourier transform are considered. It is shown that these schemes, containing only Gaussian apertures or their combination with lenses, have eigenbeams represented by Hermite–Gaussian modes with transverse indices m, n≤1 and Laguerre–Gaussian modes with p = 0 and l = 1. The wave front of the eigenbeams is, as a rule, spherical.