Modified Fabry–Perot and Rate Equation Methods for the Nonlinear Dynamics of an Optically Injected Semiconductor Laser

Modifications have been introduced to the Fabry– Perot (FP) and the rate equation methods to improve the accuracy of the analysis of the nonlinear dynamics of a laser with external optical injection. Comparison between the modified methods and the more accurate transmission-line laser model (TLLM) shows good agreement, while the computational time of the latter is larger by two or three orders of magnitude. In the FP method, the stimulated recombination term in the carrier density evolution equation is modified to include the backward propagating wave and the exponential longitudinal dependence of the electromagnetic field. In the rate equation method, the optical injection term is modified to account for the contribution of the amplification and losses of the injected light inside the cavity to the average photon density. The derivation explaining the validity of these changes and the mathematical relationship between the two methods is presented. Improved stability maps for different values of the injected optical power and frequency detuning are demonstrated and compared with those obtained by the TLLM. The gain compression effect is included in the FP model, and its effect on the stability properties is discussed.