Longitudinal Mode Competition and Asymmetric Gain Saturation in Semiconductor Injection Lasers. II. Theory

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Abstract
Gain saturation in semiconductor lasers is analyzed using a density matrix formalism. A refined treatment of the density matrix formalism reveals that nonlinear gain has a component which is asymmetric with respect to the lasing frequency. The asymmetric component originates from refractive-index modulation due to a carrier-density pulsation induced by the optical-intensity beat. Based on the analysis, mode competition behavior is numerically examined using appropriate values of the linewidth enhancement factor and the intraband relaxation time. It is shown that the output power decreases at mode jumping from a shorter to a longer wavelength mode while it increases at mode jumping toward shorter wavelengths. The results agree with the features of the mode competition behavior observed in transverse-mode-controlled AlGaAs lasers.