Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling
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...
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| Format: | Article |
| Language: | English |
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Saratov State University
2022-03-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
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| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2022/03/5-grigorieva_189-207.pdf |
| _version_ | 1818287112203534336 |
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| author | Grigorieva, Elena Viktorovna Kashchenko, Sergej Aleksandrovich |
| author_facet | Grigorieva, Elena Viktorovna Kashchenko, Sergej Aleksandrovich |
| author_sort | Grigorieva, Elena Viktorovna |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T01:35:18Z |
| format | Article |
| id | doaj.art-85a74ab3177b4b7395b2273c5228c5af |
| institution | Directory Open Access Journal |
| issn | 0869-6632 2542-1905 |
| language | English |
| last_indexed | 2024-12-13T01:35:18Z |
| publishDate | 2022-03-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj.art-85a74ab3177b4b7395b2273c5228c5af2022-12-22T00:03:54ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052022-03-0130218920710.18500/0869-6632-2022-30-2-189-207Local dynamics of laser chain model with optoelectronic delayed unidirectional couplingGrigorieva, Elena Viktorovna0Kashchenko, Sergej Aleksandrovich1Belarus State Economic University (BSEU), Republic of Belarus, 220070 Minsk, Partizansky Prospekt, 26P. G. Demidov Yaroslavl State University, 150000 Yaroslavl, Sovetskaya str., 14Purpose. 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.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2022/03/5-grigorieva_189-207.pdfbifurcation analysiswave structuresdelaylaser dynamics |
| spellingShingle | Grigorieva, Elena Viktorovna Kashchenko, Sergej Aleksandrovich Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling Известия высших учебных заведений: Прикладная нелинейная динамика bifurcation analysis wave structures delay laser dynamics |
| title | Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling |
| title_full | Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling |
| title_fullStr | Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling |
| title_full_unstemmed | Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling |
| title_short | Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling |
| title_sort | local dynamics of laser chain model with optoelectronic delayed unidirectional coupling |
| topic | bifurcation analysis wave structures delay laser dynamics |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2022/03/5-grigorieva_189-207.pdf |
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