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A semiconductor laser model is presented, which resolves the full time, longitudinal and lateral space dependences. The model is applied to an investigation of the dynamical stability of an integrated master-oscillator power-amplifier (MOPA) device. The model captures the full gain and refractive index bandwidth as a function of total carrier density. Our simulation confirms, for the first time, some recent experimental observations of high frequency whole beam oscillations and experimental reports that complex transverse filamentation occurs at high power amplifier currents.