Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation

Abstract

We study the continuous-wave (cw) operation of a semiconductor laser subject to optical feedback from a Fabry-Perot resonator in a case where the emission is resonant to a reflection minimum of the resonator. This configuration is treated in the framework of Lang-Kobayashi equations. The nature of bifurcations and the stability of steady state solutions is analyzed in terms of the dependence on magnitude and phase of the feedback. In contrast to conventional optical feedback from a single mirror, the locus of external cavity modes is not elliptic but represents a tilted eight with possible satellite bubbles. Below a critical feedback strength, which is analytically given, only one single mode exists representing the completely unchanged cw emission of the laser. In this weak-feedback regime, the feedback phase allows noninvasive control of the cw emission and a tailoring of its small-signal response within wide limits. The results obtained are a prototype for all-optical realizations of delayed feedback control.

Control of unstable steady states by extended time-delayed feedback

“…Time-delayed feedback has been widely used in optical systems both to study the intrinsic dynamics and to control the stabilization of, for instance, a laser device [30,31,32,33,34,35]. In these systems, the optical phase is an additional degree of freedom.…”

Time-Delayed Feedback Control: From Simple Models to Lasers and Neural Systems

“…Suppression of the pulsations and non-invasive stabilization of the steady state is achieved by direct optical feedback from a properly designed external FP etalon. Although proposed one and a half decades ago [39,137] and despite of some numerical studies [137,138,139], such non-invasive all-optical control approach has not been implemented experimentally until recently [38]. A novel aspect of our analysis is that it addresses the role of the optical phase as a specific feature of the FP control configuration.…”

Control-Based Continuation of Periodic Orbits With a Time-Delayed Difference Scheme

“…Even more, the computation of the difference equation can often be implemented experimentally (for example, by two external mirrors in a laser experiment (see Tronciu et al [2005]). The fact that system (6) does not involve any linearization suggests that finding periodic orbits with many unstable directions and of complicated shape or long period is likely to be impossible with this approach.…”