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This article is cited in 2 scientific papers (total in 2 papers)
DIFFRACTIVE OPTICS, OPTICAL TECHNOLOGIES
Double Laguerre-Gaussian beams
V. V. Kotlyarab, E. G. Abramochkinc, A. A. Kovalevab, A. A. Savelyevaab a Image Processing Systems Institute of the RAS - Branch of the FSRC "Crystallography and Photonics" RAS, Samara, Russia, Samara
b Samara National Research University
c Samara Branch of P. N. Lebedev Physical Institute, Russian Academy of Sciences
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
Received: 20.06.2022 Accepted: 13.08.2022
Citation:
V. V. Kotlyar, E. G. Abramochkin, A. A. Kovalev, A. A. Savelyeva, “Double Laguerre-Gaussian beams”, Computer Optics, 46:6 (2022), 872–876
Linking options:
https://www.mathnet.ru/eng/co1080 https://www.mathnet.ru/eng/co/v46/i6/p872
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