## The low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback

Physical Review A 55 4443-4448, (1997)

#### G.D. Lythe and T. Erneux

Optique nonlinéaire théorique, Université Libre de Bruxelles CP231,
Bruxelles 1050 BELGIUM

#### A. Gavrielides and V. Kovanis

Nonlinear Optics Center, Phillips Laboratory PL/LIDN,
Kirtland AFB, NM 87117-5776

## Abstract

The conditions for a bifurcation to periodic intensities (Hopf bifurcation) for low values of the pump current are examined using asymptotic methods. We show that the frequency of the oscillations at the bifurcation point remains close to the relaxation oscillations frequency of the solitary laser until the pump parameter is close to its effective threshold value. This part of our analysis adds substance to previous approximations of the frequency of the oscillations which were guided by experiments. In the second part of our analysis, we show that, very close to threshold, the frequency exhibits a sharp transition from the relaxation oscillations frequency to a frequency proportional to the external cavity frequency (i.e., $2\pi /\tau ,$ where $% \tau$ is the external round-trip time). These two different behaviors of the frequency reveal distinct physical mechanisms controlling the onset of sustained oscillations in a semiconductor laser subject to optical feedback.