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A Fourier-invariant squared Laguerre-Gaussian vortex beam
E.S. Kozlova 1,2, A.A. Savelyeva 1,2, A.A. Kovalev 1,2, V.V. Kotlyar 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151;
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1285 kB

DOI: 10.18287/2412-6179-CO-1228

Pages: 367-373.

Full text of article: Russian language.

Abstract:
It is shown that a squared Laguerre-Gaussian (LG) vortex beam is Fourier-invariant and retains its structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into superposition of conventional LG beams, the number of which is equal to the number of rings in the squared LG beam. If there is only one ring, then the beam is structurally stable. A more general beam, which is a “product” of two LG beams, is also considered. Such a beam will be Fourier-invariant if the number of rings in two LG beams in the “product” is the same. The considered beams complement the well-known family of LG beams, which are intensively studied as they remain stable during their propagation in turbulent media.

Keywords:
optical vortex, topological charge, Laguerre-Gauss mode, Fourier invariance, Fourier transform, Fresnel diffraction.

Citation:
Kozlova ES, Savelyeva AA, Kovalev AA, Kotlyar VV. A Fourier-invariant squared Laguerre-Gaussian vortex beam. Computer Optics 2023; 47(3): 367-373. DOI: 10.18287/2412-6179-CO-1228.

Acknowledgements:
This work was supported by the Russian Science Foundation under grant No. 22-12-00137.

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