Optical Fourier transform of pseudo-nondiffracting beams

We investigate the generation of the Fourier transform of nondiffracting beams modulated by Gaussian envelope and the propagation through free space of these new generated beams. We exploit the ability of the converging thin lens to perform optical Fourier transform of any arbitrary beam. In the framework of the paraxial approximation, we use Huygens-Fresnel diffraction integral to calculate the expression of the electric field or the Fourier transform of the pseudo-nondiffracting beams (pNDBs) in the focal plane of the thin lens. The propagation of the resulting field in free space after the thin lens is studied by using the same diffraction integral. Analysis of the obtained results illustrates that by selecting convenient parameters, the Fourier transform can be identified to the image of the angular spectrum of nondiffracting beams given by the Whitaker integral as the circular ring for Bessel beams or two light points for cosine beams. Results on the propagation of the Fourier transform beams demonstrate that these later diffract after the focal plane because of the presence of the Gaussian envelope. Finally, our results may be beneficial for generating new and particular kinds of beams in the focal plane of the thin lens as perfect vortex beams or two-light-spot beams. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates the generation of Fourier transforms of nondiffracting beams modulated by Gaussian envelopes and their propagation through free space. The research demonstrates that by selecting appropriate parameters, the Fourier transform can be related to the image of the angular spectrum of nondiffracting beams, such as circular rings for Bessel beams or two light points for cosine beams. Additionally, results show that the Fourier transform beams diffract after the focal plane due to the presence of Gaussian envelopes.