The fractional Fourier transform of Airy beams using Lohmann and quadratic optical systems

Based on the generalized Huygens–Fresnel integral, the analytical expressions for Airy beams through three types of fractional Fourier transform (FRFT) optical systems (Lohmann I, Lohmann II and quadratic graded-index systems) are derived. Using the two analytical expressions, the propagation properties of Airy beams for the three types of FRFT optical systems are discussed in detail with numerical examples. Results indicate that the intensity of Airy beams periodically changes and remains form-invariant with the changing of fractional order p for the three types of FRFT optical systems.

► Propagation properties of Airy beams through varied fractional Fourier transform are studied.
► Three specific types of fractional Fourier transform optical systems are investigated.
► The propagation characteristics of Airy beams through FRFT optical systems are studied.
► The effects of a0 and fractional order pp are investigated as the critical parameters.
► The intensity of Airy beams periodically changes and remains form-invariant with the increase of pp.