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

Abstract

Abstract 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 N and the fractional order p 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 = 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.