# Nonlinear Dynamics in Semiconductor Lasers - Abstract

**Erneux, Thomas**

*Secondary bifurcation from sustained relaxation oscillations in the large delay limit*

For a semiconductor laser subject to optical feedback, the relaxation oscillation (RO) frequency of the solitary laser, fro, and the round-trip frequency, fdelay = 1/T, are our guidelines in all studies. As early as 1969, R.F. Broom [1] reported on a resonant interaction between these frequencies. He stated that "the interaction would be strongest when fro = nfdelay where n is an integer". Quite recently, this resonance question was revived by a series of experiments carried on a quantum dot laser subject to optical feedback and partial filtering [2]. The delay was large and the ratio fro/fdelay was close to an integer. The authors reported on a Hopf bifurcation to sustained RO oscillations followed by a secondary bifurcation to quasi-periodic oscillations. The latter exhibited the RO frequency and the round-trip frequency verifying the ratio fro/fdelay = n where the integer n goes from 3 to 9 depending on the pump parameter. Rate equations appropriate for the QD laser have substantiated this particular scenario but are too complicated for analytical studies. We have considered the laser rate equations for both the laser subject to an optoelectronic feedback on the pump and the laser subject to coherent optical feedback. In the limit of large delays, we have found that there is always a secondary bifurcation from a primary branch of sustained relaxation oscillations. We determined analytically a scaling law for the secondary bifurcation point in terms of the feedback rate k, namely ksb 1/n, where n is a large integer close to the product (2pifro)T. 1. R.F. Broom, Electr. Lett. 5, 571 - 572 (1969) 2. J. B. Tykalewicz, D. Goulding, S. P. Hegarty, G. Huyet, T. Erneux, B. Kelleher, E. A. Viktorov, Opt. Express 24, 4239-4246 (2016)