Fractional Fourier transform of Airy beams

Automatic Fourier transform and self-Fourier beams due to parabolic potential

“…[14][15][16] authors discussed the propagation and transformation of (finite-energy) Airy beams in a linear medium with a parabolic potential, in which periodic inversion, oscillation, and phase transition were reported. One should recall that in a parabolic potential, light propagation is equivalent to a fractional Fourier transform (FT) [17], the fact first noted by Mendlovic and his collaborators [18,19]. The fractional FT can be conveniently introduced through the propagation in gradient-index (GRIN) media, which can further be connected with the propagation in the parabolic potential and the automatic FT -as done in this article.…”

Propagation of an Airy-Gaussian beam passing through the ABCD optical system with a rectangular aperture

“…On the other hand, the fractional Fourier transform (FrFT) with its important applications in signal processing, optical image encryption, beam shaping and beam analysis has been widely investigated [30][31][32][33][34][35]. Recently, fractional fourier transform of Airy beams [36,37], Airy-Hermite-Gaussian beam [38], tunable dual airy beam [39], Airy-related beams [40] has been examined also. In this paper, our aim is to study the propagation properties of an AiG beam through a paraxial ABCD optical system with a rectangular aperture and the fractional Fourier transform (FrFT) system, the given model more really shows the propagation characteristics of an AiG beam.…”

The Fractional Fourier Transform of Hypergeometric-Gauss Beams Through the Hard Edge Aperture

“…1. The FRT transmission matrices for Lohmann I and Lohmann II optical systems can be expressed as [14,15] …”