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Double Laguerre-Gaussian beams
V.V. Kotlyar 1,2, E.G. Abramochkin 3, A.A. Kovalev 1,2, A.A. Savelyeva 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;
3 Lebedev Physical Institute, 443011, Samara, Russia, Novo-Sadovaya st. 221

 PDF, 897 kB

DOI: 10.18287/2412-6179-CO-1177

Pages: 872-876.

Full text of article: Russian language.

Abstract:
We show here that the product of two Laguerre-Gaussian (LG) beams, i.e. double LG beams (dLG), can be represented as finite superposition of conventional LG beams with certain coeffi-cients that are expressed via zero-argument Jacobi polynomials. This allows obtaining an explicit expression for the complex amplitude of the dLG beams in the Fresnel diffraction zone. Generally, such beams do not retain their structure, changing shape upon free-space propagation. However, if both LG beams are of the same order, we obtain a special case of a "squared" LG beam, which is Fourier-invariant. Another special case of the dLG beams is obtained when the azimuthal indices of the Laguerre polynomials are equal to n – m and n + m. For such a beam, an explicit expression is obtained for the complex amplitude in the Fourier plane. We show that if the lower indices of the constituent LG beams are the same, such a double LG beam is also Fourier-invariant. Similar to conventional LG beams, the product of LG beams can be used for optical data transmission, since they are characterized by azimuthal orthogonality and carry an orbital angular momentum equal to the topological charge.

Keywords:
Laguerre-Gaussian beam, product of complex amplitudes, Fourier-invariant beam, topological charge.

Citation:
Kotlyar VV, Abramochkin EG, Kovalev AA, Savelyeva AA. Double Laguerre-Gaussian beams. Computer Optics 2022; 46(6): 872-876. DOI: 10.18287/2412-6179-CO-1177.

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

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