For citation:
Glazkov D. V. Qualitative analysis of one class of optoelectronic systems singularly perturbed models. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 4, pp. 167-181. DOI: 10.18500/0869-6632-2008-16-4-167-181
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 196)
Language:
Russian
Heading:
Article type:
Article
UDC:
517.929
Qualitative analysis of one class of optoelectronic systems singularly perturbed models
Autors:
Glazkov Dmitrij Vladimirovich, P. G. Demidov Yaroslavl State University
Abstract:
Two models of semiconductor laser with delayed optical feedback are studied. We consider singularly perturbed problem because of the large parameter presence. We construct and discuss quasinormal forms of models in trancritical cases.
Key words:
Reference:
- Khanin YI. Fundamentals of Laser Dynamics. Cambridge International Science; 2005. 400 p.
- Van Tartwijk GHM and Agrawal GP. Laser instabilities: A modern perspective. Progress in Quantum Electronics. 1998;22(2):43–122. DOI: 10.1016/S0079-6727(98)00008-1.
- Grigorieva EV. Quasiperiodicity in Lang–Kobayashi model of lasers with delayed optical feedback. Nonlinear Phenomena in Complex Systems. 2001;4(4):333–340.
- Ye J, Li H, McInerny JM. Period-doubling route to chaos in a semiconductor laser with weak optical feedback. Phys. Rev. A. 1993;47(3):2249–2252. DOI: 10.1103/PhysRevA.47.2249.
- Fischer I, Hess O, Elsasser W, and Gobel E. High-dimensional chaotic dynamics of an external cavity semiconductor laser. Phys. Rev. Lett. 1994;73(16):2188–2191. DOI: 10.1103/physrevlett.73.2188.
- Sacher J, Elsasser W, Gobel EO. Intermittency in the coherence collapse of a semiconductor laser with external feedback. Phys. Rev. Lett. 1989;63(20):2224–2227. DOI: 10.1103/physrevlett.63.2224.
- Sano T. Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback. Phys. Rev. A. 1994;50(3):2719–2726. DOI: 10.1103/physreva.50.2719.
- Tager AA, Petermann K. High-frequency oscillations and self-mode locking in short external-cavity laser diodes. IEEE J. Quantum Electron. 1994;30(7):1553–1561. DOI: 10.1109/3.299487.
- Wolfrum M, Turaev D. Instabilities of lasers with moderately delayed optical feedback. Opt. Commun. 2002;212(1–3):127–138. DOI: 10.1016/S0030-4018(02)01824-2.
- Heil T, Fischer I, Elsasser W, Krauskopf B, Green K, Gavrielides A. Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms. Phys. Rev. E. 2003;67(6):066214. DOI: 10.1103/physreve.67.066214.
- Tabaka A, Panajotov K, Veretennicoff I, Sciamanna M. Bifurcation study of regular pulse packages in laser diodes subject to optical feedback. Phys. Rev. E. 2004;70(3):036211. DOI: 10.1103/physreve.70.036211.
- Heil T, Fischer I, and Elsasser W. Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback. Phys. Rev. A. 1999;60(1):634–641. DOI: 10.1103/PhysRevA.60.634.
- Pieroux D, Mandel P. Bifurcation diagram of a complex delay-differential equation with cubic nonlinearity. Phys. Rev. E. 2003;67(5):056213. DOI: 10.1103/PhysRevE.67.056213.
- Lang R, Kobayashi K. External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. 1980;16(1):347–355. DOI: 10.1109/JQE.1980.1070479.
- Green K, Krauskopf B. Mode structure of semiconductor laser subject to filtered optical feedback. Opt. Commun. 2006;258(2):243–255. DOI: 10.1016/j.optcom.2005.08.005.
- Alsing P, Kovanis V, Gavrielides A, and Erneux T. Lang and Kobayashi phase equation. Phys. Rev. A. 1996;53(6):4429–4434. DOI: 10.1103/PhysRevA.53.4429.
- Kaschenko SA. Normalization in the systems with small diffusion. International Journal of Bifurcations and Chaos. 1996;6(6):1093–1109. DOI: 10.1142/S021812749600059X.
- Kashchenko SA. Cycle bifurcations in singularly perturbed nonlinear autonomous systems. Izv. RANS. Ser. MMMIU. 1998;2(4):5–53 (in Russian).
- Kashchenko SA. Local dynamics of nonlinear singularly perturbed systems with delay. Differential Equations. 1999;35(10):1360–1373.
- Kashchenko SA. Bifurcations in the vicinity of a cycle at small perturbations with a large delay. Computational Mathematics and Mathematical Physics. 2000;40(5):659–668.
- Kaschenko SA. Bifurcational features in systems of nonlinear parabolic equations with weak diffusion. International Journal of Bifurcation and Chaos. 2005;15(11)3595–3606. DOI: 10.1142/S0218127405014258.
- Vasilyeva AB, Butuzov VF. Asymptotic Expansions of Solutions of Singularly Perturbed Equations. Moscow: Nauka; 1973. 272 p. (in Russian).
- Levine AM, Tartwijk GHM, Lenstra D, and Erneux T. Diode lasers with optical feedback: Stability of the maximum gain mode. Phys. Rev. A. 1995;52(5):R3436–R3439. DOI: 10.1103/PhysRevA.52.R3436.
- Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from a chaotic signal. Phys. Rev. A. 1983;28(4):2591–2593. DOI: 10.1103/PhysRevA.28.2591.
- Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D. 1983;9(1–2):189–208. DOI: 10.1016/0167-2789(83)90298-1.
- Wolf A, Swift JB, Swinney HL, Vastano JA. Determining Lyapunov exponents from a time series. Physica D. 1985;16(3):285–317. DOI: 10.1016/0167-2789(85)90011-9.
- Glazkov DV. The simplest stable regimes in the Lang – Kobayashi model with a large delay. In: Proceedings of the XXVII Conference of Young Scientists MMF Lomonosov Moscow State University. Lomonosov Moscow State University; 2005. P. 27–33 (in Russian).
- Kolesov YS, Mayorov VV. A new method for studying the stability of solutions to linear differential equations with near-constant almost-periodic coefficients. Differential Equations. 1974;10(10):1778–1788 (in Russian).
- Kashchenko S.A., Mayorov V.V. An algorithm for studying the stability of solutions of linear differential equations with aftereffect and rapidly oscillating almost periodic coefficients. In: Collection of Articles. Research on Stability and Vibration Theory. Yaroslavl; 1977. С. 70–81 (in Russian).
- Mendez JM, Laje R, Giudici M, Aliaga J, and Mindlin GB. Dynamics of periodically forced semiconductor laser with optical feedback. Phys. Rev. E. 2001;63(6):066218. DOI: 10.1103/PhysRevE.63.066218.
Received:
29.03.2008
Accepted:
02.07.2008
Published:
31.10.2008
Journal issue:
Short text (in English):
(downloads: 73)
- 1593 reads