Determining Lang and Kobayashi Hopf bifurcation points

Thomas Erneux; Guido H.M. van Tartwijk; Daan Lenstra; Alfred M. Levine

doi:10.1117/12.212492

19 June 1995 Determining Lang and Kobayashi Hopf bifurcation points

Thomas Erneux, Guido H.M. van Tartwijk, Daan Lenstra, Alfred M. Levine

Proceedings Volume 2399, Physics and Simulation of Optoelectronic Devices III; (1995) https://doi.org/10.1117/12.212492
Event: Photonics West '95, 1995, San Jose, CA, United States

Abstract

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 (epsilon) which is defined as the ratio of the photon and carrier lifetimes. The remaining parameters are scaled with respect to (epsilon) . The critical feedback rate for a Hopf bifurcation is studied in terms of the pump parameter and is either an 0((epsilon) ) or an 0((epsilon) ^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.

Citation Download Citation

Thomas Erneux, Guido H.M. van Tartwijk, Daan Lenstra, and Alfred M. Levine "Determining Lang and Kobayashi Hopf bifurcation points", Proc. SPIE 2399, Physics and Simulation of Optoelectronic Devices III, (19 June 1995); https://doi.org/10.1117/12.212492

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