Journal
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Volume 9, Issue 2, Pages 519-535Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090751335
Keywords
Lang-Kobayashi; large delay; external cavity modes; stability; pseudocontinuous spectrum
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Funding
- DFG Research center MATHEON Mathematics for key technologies [D21]
- DFG Sonderforschungsbereich [555]
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The Lang-Kobayashi model is a system of delay differential equations (DDEs) describing the dynamics of a semiconductor laser under delayed optical feedback. In this paper, we study the stability of so-called external cavity modes (ECMs), which are harmonic oscillations corresponding to stationary lasing states. We focus on experimentally relevant situations, when the delay is large compared to the internal time scales of the laser. In this case, both the number of ECMs and the number of critical eigenvalues is large. Applying a newly developed asymptotic description for the spectrum of linearized DDEs with long delay, we are able to overcome this difficulty and to give a complete description of the stability properties of all ECMs. In particular, we distinguish between different types of weak and strong instabilities and calculate bifurcation diagrams that indicate the regions with different stability properties and the transitions between them.
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