Use of the fractional Fourier transform in π/2 converters of laser modes

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic π/2 converters of Hermite–Gaussian modes to donut Laguerre–Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared.