Semiconductor laser dynamics for feedback from a finite-penetration-depth phase-conjugate mirror

Most of the previous treatments of semiconductor lasers subject to optical feedback from a phase-conjugate mirror (PCM) have assumed that the PCM responds instantaneously. Furthermore, the mechanism responsible for phase conjugation does not usually enter into the analysis. In this paper, we derive the time-dependent reflectivity of a PCM created through nondegenerate four-wave mixing in a Kerr-type nonlinear medium. The resulting laser dynamics are compared with the case of the ideal PCM, as a function of the external-cavity length, the PCM reflectivity, and the PCM interaction depth. The PCM with a significant interaction depth tends to suppress otherwise chaotic output and produces pulses whose repetition rate is tunable by varying PCM reflectivity. At high feedback levels, it stabilizes the laser output. We use the circle-map formalism to explain our numerical results.