Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers

Abstract

The dynamic response of semiconductor lasers is generally studied by solving the single-mode rate equations which assume an instantaneous relaxation of carriers within the conduction and the valence bands. Even though the intraband relaxation time is typically ~0.1 ps, it can affect laser dynamics significantly. To the first order, the effects of a finite intraband relaxation time are included in the rate equations by assuming that the modal gain g decreases linearly with the intracavity mode intensity I, i.e., g = g0 (1–εI). This functional form of the nonlinear gain becomes questionable at high intensities. A nonperturbative solution of the densitymatrix equations shows that the modal gain saturates with the intensity as g = g0(I + I/Is)−1/2, where Is is the intraband saturation intensity. At the same time, the modal refractive index also becomes intensity dependent. We include the intensity dependence of both the gain and the refractive index in the single-mode rate equations and study how their inclusion affects the dynamic response of semiconductor lasers by considering the laser parameters such as the modulation bandwidth and the damping time of relaxation oscillations.