Exact Solution to Rate Equation with Time-Dependent Coefficients: Its Application in InGaAsP Lasers

By using the algebraic dynamics method, we obtain exact analytical solutions of rate equations with time-dependent coefficients, which might present an effective description of the physical mechanism of the practical semiconductor lasers. Based on the exact solutions, we investigate the dynamic behaviour and the emitted properties of the InGaAsP laser, which has been commonly used in long wavelength optical communication systems. It is found that when the cavity length varies with time exponentially, the output power of the laser will drop and approach its asymptote. When the cavity length is a sinusoid function of time, the intensity of the emitted optical pulses can be controlled by the amplitude of this function.