SEMICONDUCTOR-LASER DYNAMICS BEYOND THE RATE-EQUATION APPROXIMATION

Starting from the density-matrix equations, we have obtained a new set of generalized macroscopic Maxwell-Bloch equations for semiconductor lasers which can be used to study ultrafast phenomena at femtosecond time scales where the conventional rate equations are no longer valid. The band-structure details are included in these Maxwell-Bloch equations through two parameters kappa and zeta which can be determined numerically by using their definitions or obtained experimentally by fitting the measured data. In the limit of ultrafast intraband relaxation (the rate-equation approximation), these equations reduce to the conventional rate equations. As an illustration of the usefulness of the new Maxwell-Bloch equations we have obtained the analytic expressions for several important laser parameters such as the differential gain, the linewidth enhancement factor and the nonlinear gain coefficient, in terms of the parameters kappa and zeta when the semiconductor laser is operating continuously (the cw operation). The results obtained from these analytic expressions agree with those obtained numerically from the density-matrix equations under steady-state conditions by integrating over the density of states.