Propagation and transformation of four-petal Gaussian vortex beams in fractional Fourier transform optical system

Abstract

The propagation and transformation of four-petal Gaussian vortex beams in optical fractional Fourier transform system is investigated on the basis of the framework of Collins diffraction integral. The mathematical expression of propagation transformation is derived, and typical propagation and transformation characteristics are illustrated by numerical results. The effects of fractional Fourier order, beam order, vortex topological charge, beam width and lens focal length on the fractional Fourier transform of four-petal Gaussian vortex beams are discussed in detail. The four-petal Gaussian vortex beam has four petals rectangular symmetric intensity distribution in the source plane, which is different from the traditional circular symmetric vortex beam. The four-petal Gaussian vortex beam shows abundant transformation properties. The fractional Fourier transform system can be equivalent to other several optical systems, so the results obtained her e can be extended to other equivalent optical systems.