ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Grigorieva E. V., Kashchenko S. A. Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 2, pp. 189-207. DOI: 10.18500/0869-6632-2022-30-2-189-207

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Article type: 
Article
UDC: 
517.9, 535.8

Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling

Autors: 
Grigorieva Elena Viktorovna, Belarus State Economic University (BSEU)
Kashchenko Sergej Aleksandrovich, P. G. Demidov Yaroslavl State University
Abstract: 

Purpose. The local dynamics of the laser chain model with optoelectronic delayed unidirectional coupling is investigated. A system of equations is considered that describes the dynamics of a closed chain of a large number of lasers with optoelectronic delayed coupling between elements. An equivalent distributed integro-differential model with a small parameter inversely proportional to the number of lasers in the chain is proposed. For a distributed model with periodic edge conditions, the critical value of the coupling coefficient is obtained, at which the stationary state in the chain becomes unstable. It is shown that in a certain neighborhood of the bifurcation point, the number of roots of the characteristic equation with a real part close to zero increases indefinitely when the small parameter decreases. In this case, a two-dimensional complex Ginzburg–Landau equation with convection is constructed as a normal form. Its nonlocal dynamics determines the behavior of the solutions of the original boundary value problem. Research methods. Methods for studying local dynamics based on the construction of normal forms on central manifolds are used as applied to critical cases of (asymptotically) infinite dimension. An algorithm for reducing the original boundary value problem to the equation for slowly varying amplitudes is proposed. Results. The simplest homogeneous periodic solutions of Ginzburg–Landau equation and corresponding to them inhomogeneous solutions in the form of traveling waves in a distributed model are obtained. Such solutions can be interpreted as phase locking regimes in the chain of coupled lasers. The frequencies and amplitudes of oscillations of the radiation intensity of each laser and the phase difference between adjacent oscillators are determined.

Acknowledgments: 
The work of S. A. Kashchenko was supported by the Russian Science Foundation (project No. 21-71-30011).
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Received: 
10.01.2022
Accepted: 
16.02.2022
Published: 
31.03.2022