Fractional Fourier transform of Airy-related beams generated from flat-topped Gaussian beams

●We investigated the fractional Fourier transform (FrFT) of the newly proposed Airy-related beams generated from flat-topped Gaussian beams.●Analytical expression for Airy-related beams propagating through a paraxial ABCD optical system is derived.●Several influence parameters of both the Airy-related beams and the FrFT optical system are discussed in detail.●Results show that the FrFT optical system provides a convenient way for modulating the Airy-related beams.

The analytical expression for Airy-related beams generated from flat-topped Gaussian beams propagating through a paraxial ABCD   optical system is derived and used to investigate its properties in the fractional Fourier transform (FrFT) optical system. The influences of the Airy-related beam order NN and the fractional order pp on the evolution of the beam intensity distribution in the FrFT system are examined in detail. Results show that the FrFT optical system provides a convenient way for modulating the beam profile of Airy-related beams by properly choosing optical parameters: lower order Airy-related beams have a longer non-spreading FrFT range, in which the Airy-related beams can maintain their original intensity distribution with no measurable spreading; and it is also found that the Airy-related beam intensity distribution versus the fractional order is symmetrical about p=1p=1. Moreover, the Airy-related beam intensity distribution versus the fractional order is periodical, and the period is 2. The results obtained in this work are valuable for Airy-related beam shaping.