- Access by Xinjiang University
Numerical stability analysis of a large-scale delay system modeling a lateral semiconductor laser subject to optical feedback
Phys. Rev. E 69, 036702 – Published 23 March, 2004
DOI: https://doi.org/10.1103/PhysRevE.69.036702
Abstract
This paper highlights the use of advanced numerical tools to study the stability of large-scale systems of delay differential equations (DDEs). Specifically, we consider a model describing a semiconductor laser subject to conventional optical feedback and lateral carrier diffusion. The symmetry of the governing rate equations allows external cavity mode solutions (ECMs) to be computed as steady state solutions. Using the software package DDE-BIFTOOL, branches of ECMs are computed as a function of varying feedback strength. The stability along these branches is computed by solving eigenvalue problems, the size of which is governed by a step-length heuristic. In this paper, we employ an improved heuristic which substantially reduces the size of these eigenvalue problems. This approach makes the stability analysis of large-scale systems of DDEs computationally feasible.
References (23)
- J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences Vol. 99 (Springer-Verlag, Berlin, 1993).
- K. Engelborghs, T. Luzyanina, and D. Roose, ACM Trans. Math. Softw. 28, 1 (2002).
- K. Verheyden, T. Luzyanina, and D. Roose, KU Leuven. Technical Report No. TW-383, 2003 (unpublished).
- K. Green and B. Krauskopf, Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, 2589 (2003).
- K. Green, B. Krauskopf, and K. Engelborghs, Physica D 173, 114 (2002).
- K. Green, B. Krauskopf, and G. Samaey, SIAM J. Dynamical Systems2, 254 (2003).
- B. Haegeman, K. Engelborghs, D. Roose, D. Pieroux, and T. Erneux, Phys. Rev. E 66, 046216 (2002).
- D. Pieroux, T. Erneux, B. Haegeman, K. Engelborghs, and D. Roose, Phys. Rev. Lett. 87, 193901 (2001).
- D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, Phys. Rev. E 63, 036211 (2001).
- R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
- E. Lacot, R. Day, and F. Stoeckel, Phys. Rev. A 64, 043815 (2001).
- M.S. Torre, C. Masoller, N.B. Abraham, and H.F. Ranea-Sandoval, J. Opt. B: Quantum Semiclassical Opt. 2, 563 (2000).
- M. Münkel, F. Kaiser, and O. Hess, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 951 (1998).
- M. Münkel, F. Kaiser, and O. Hess, Phys. Lett. A 222, 67 (1996).
- J.V. Moloney, in Nonlinear Laser Dynamics: Concepts, Mathematics, Physics, and Applications International Spring School, edited by Bernd Krauskopf and Daan Lenstra, AIP Conf. Proc. 548 (AIPMelville, NY, 2000), p. 149.
- D. Lenstra, B.H. Verbeek, and A.J. den Boef, IEEE J. Quantum Electron. 21, 674 (1985).
- G.H.M. Van Tartwijk and G.P. Agrawal, Prog. Quantum Electron. 22, 43 (1998).
- K. Engelborghs and D. Roose, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 40, 629 (2002).
- K. Verheyden, T. Luzyanina, and D. Roose, KU Leuven Technical Report No. TW-382, 2003 (unpublished).
- G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993).
- B. Krauskopf, G.H.M. Van Tartwijk, and G.R. Gray, Opt. Commun. 177, 347 (2000).
- K. Verheyden and K. Lust, KU Leuven Technical Report No. TW-357, 2003 (unpublished).
- J.L.A. Dubbeldam and B. Krauskopf, Opt. Commun. 159, 325 (1999).