Modeling multi-longitudinal-mode semiconductor lasers with incoherent feedback

Abstract

We study numerically the dynamics of a multi-longitudinal-mode semiconductor laser subject to incoherent optical feedback. The feedback scheme is such that the polarization state of the feedback light is rotated 90\ifmmode^\circ\else\textdegree\fi{}, so that the natural laser mode, TE, is coupled unidirectionally into the orthogonal, unsupported mode, TM. We use traveling-wave equations for the slowly varying complex amplitudes of the two counterpropagating optical fields circulating in the Fabry P\'erot cavity, both with TE polarization, coupled to an equation for the carrier population. The carrier equation contains a time-delayed term that takes into account the effect of the incoherent feedback. The model considers a parabolic frequency-dependent gain and does not assume a priori a fixed number of active longitudinal modes. We find that moderate feedback levels reduce the total power and increase the number of oscillating longitudinal modes. Larger feedback levels lead to instabilities at both the external cavity frequency ${f}_{\mathit{ext}}$ and the relaxation oscillation frequency ${f}_{\mathit{ro}}$. These findings are in good qualitative agreement with experimental observations by Houlihan et al. [Opt. Commun. 199, 175 (2001)]. For even stronger feedback there is square-wave periodic modulation of the total power, with a repetition period close to twice the delay time. In this regime, which consists of a sequence of turn-on and turn-off events driven by the incoherent feedback, the longitudinal modes show in-phase behavior at a frequency close to ${f}_{\mathit{ro}}$ accompanied by a slower out-of-phase drift, which is related to variations of the maximum and minimum values of the oscillation amplitude of the modal intensities.