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Determining Lang and Kobayashi Hopf bifurcation points

par Erneux, Thomas ;Van Tartwijk, Guido;Lenstra, Daan;Levine, Alfred
Référence Proceedings of SPIE - The International Society for Optical Engineering, 2399, page (170-181)
Publication Publié, 1995

Article révisé par les pairs

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Résumé :

The Hopf bifurcation points for single mode solutions of the Lang and Kobayashi equations are determined using asymptotic methods. The approximation is based on a small parameter ε which is defined as the ratio of the photon and carrier lifetimes. The remaining parameters are scaled with respect to ε. The critical feedback rate for a Hopf bifurcation is studied in terms of the pump parameter and is either an 0(ε) or an 0(ε 1/2 ) quantity. At a fixed value of the pump parameter, we obtain an expression of the Hopf bifurcation point in terms of the effective feedback strength and the feedback phase. In addition, we investigate the Hopf bifurcation point near and at the lasing threshold.