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Algorithm for reconstructing complex coefficients of Laguerre–Gaussian modes from the intensity distribution of their coherent superposition

S.G. Volotovskiy 1, S.V. Karpeev  1,2, S.N. Khonina 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, 1395 kB

DOI: 10.18287/2412-6179-CO-727

Pages: 352-362.

Full text of article: Russian language.

Abstract:
In this paper, we consider a problem of reconstructing complex coefficients of the coherent su-perposition of Laguerre–Gaussian modes from the field intensity in a plane perpendicular to the propagation axis at a given distance using the Levenberg–Marquardt and Brent algorithm. The efficiency of using stage-by-stage optimization to restore complex coefficients of a superposition is demonstrated not only on model, but also on experimental intensity distributions. The algorithm can be used in optical information transmission through a turbulent atmosphere to process the received intensity distribution of the optical signal.

Keywords:
optical information transmission, Laguerre–Gaussian modes, optimization of approximation by a modes’ superposition, reconstruction of complex coefficients, Levenberg–Marquardt algorithm, Brent algorithm.

Citation:
Volotovskiy SG, Karpeev SV, Khonina SN. Algorithm for reconstructing complex coefficients of Laguerre–Gaussian modes from the intensity distribution of their coherent superposition. Computer Optics 2020; 44(3): 352-362. DOI: 10.18287/2412-6179-CO-727.

Acknowledgements:
This work was partly funded by the Ministry of Science and Higher Education within the government project of FSRC “Crystallography and Photonics” RAS under agreement 007-GZ/Ch3363/26 (theoretical part) and the Russian Foundation for Basic Research under grant No. 18-29-20045-mk (numerical calculations).

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