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On the 70th birthday of L.P. Shilnikov
Quasiperiodic regimes in multisection semiconductor lasers
S. V. Gonchenkoa, K. R. Schneiderb, D. V. Turaevc a Institute for Applied Mathematics and Cybernetics,
10, Uljanova Str. 603005 Nizhny Novgorod, Russia
b Weierstrass Institute for Applied Analysis and Stochastics,
Mohrenstr. 39, 10117 Berlin, Germany
c Ben-Gurion University of the Negev,
Beer-Sheva 84105, Israel
Abstract:
We consider a mode approximation model for the longitudinal dynamics of a multisection semiconductor laser which represents a slow-fast system of ordinary differential equations for the electromagnetic field and the carrier densities. Under the condition that the number of active sections $q$ coincides with the number of critical eigenvalues we introduce a normal form which admits to establish the existence of invariant tori. The case $q = 2$ is investigated in more detail where we also derive conditions for the stability of the quasiperiodic regime.
Keywords:
multisection semiconductor laser, averaging, mode approximation, invariant torus, normal form, stability.
Received: 29.07.2005 Accepted: 14.09.2005
Citation:
S. V. Gonchenko, K. R. Schneider, D. V. Turaev, “Quasiperiodic regimes in multisection semiconductor lasers”, Regul. Chaotic Dyn., 11:2 (2006), 213–224
Linking options:
https://www.mathnet.ru/eng/rcd669 https://www.mathnet.ru/eng/rcd/v11/i2/p213
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