Amplitude synchronization in a system of two coupled semiconductor lasers
- 45 Downloads
We consider a system of ordinary differential equations used to describe the dynamics of two coupled single-mode semiconductor lasers. In particular, we study solutions corresponding to the amplitude synchronization. It is shown that the set of these solutions forms a three-dimensional invariant manifold in the phase space. We study the stability of trajectories on this manifold both in the tangential direction and in the transverse direction. We establish conditions for the existence of globally asymptotically stable solutions of equations on the manifold synchronized with respect to the amplitude.
KeywordsPeriodic Solution Equilibrium Position Semiconductor Laser Invariant Manifold Stable Periodic Solution
Unable to display preview. Download preview PDF.
- 1.J. Piprek (editor), Optoelectronic Devices, Springer, New York (2005).Google Scholar
- 3.S. Yanchuk, K. R. Schneider, and L. Recke, “Dynamics of two mutually coupled semiconductor lasers,” Phys. Rev. E, 69, 056221 (2004).Google Scholar
- 4.S. Yanchuk, A. Stefanski, T. Kapitaniak, and J. Wojewoda, “Dynamics of an array of coupled semiconductor lasers,” Phys. Rev. E, 73, 016209 (2006).Google Scholar
- 5.I. V. Koryukin and P. Mandel, “Two regimes of synchronization in unidirectionally coupled semiconductor lasers,” Phys. Rev. E, 65, 026201 (2002).Google Scholar
- 8.R. Vicente, Shuo Tang, J. Mulet, C. R. Mirasso, and Jia Ming Liu, “Synchronization properties of two self-oscillating semiconductor lasers subject to delayed optoelectronic mutual coupling,” Phys. Rev. E, 73, 047201 (2006).Google Scholar
- 9.I. Wedekind and U. Parlitz, “Synchronization and antisynchronization of chaotic power drop-outs and jump-ups of coupled semiconductor lasers,” Phys. Rev. E, 66, 026218 (2002).Google Scholar
- 10.J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E, 65, 036229 (2002).Google Scholar
- 11.E. Wille, M. Peil, I. Fischer, and W. Elsäßer, “Dynamical scenarios of mutually delay-coupled semiconductor lasers in the short coupling regime,” in: D. Lenstra, G. Morthier, T. Erneux, and M. Pessa (editors), Proc. of the SPIE “Semiconductor Lasers and Laser Dynamics,” 5452 (2004), pp. 41–50.Google Scholar
- 14.F. Brauer and J. A. Nohel, Qualitative Theory of Ordinary Differential Equations, Benjamin, New York (1969).Google Scholar
- 15.M. Farkas, Periodic Motions, Springer (1994).Google Scholar