Asymptotic methods applied to semiconductor laser models

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Abstract
Semiconductor lasers subject to a weak external perturbation (optical injection, optical feedback) are unstable devices that generate pulsating intensities. Most of our understanding of these instabilities comes from intensive numerical simulations of simple model equations. These computations are long and delicate because the solution of the laser equations exhibits several time scales. Asymptotic methods may either simplify the laser original equations or lead to useful approximations of the solution of these equations. We illustrate these techniques by reviewing the Hopf bifurcation problem of the well known Lang and Kobayashi equations modeling a laser subject to optical feedback. Basic approximations are reviewed, a low pump problem is examined in detail, and analytical approximations of the (multiple) Hopf bifurcation line in the case of a short cavity are derived for the first time.

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