Passively mode-locked semiconductor laser under self phase modulation

In this work, the existing theory for the passively mode-locked laser diode in the frequency domain is extended to include higher order mode coupling and the carrier density dependencies of the gain, carrier recombination rate, and refractive index change. Our recent study showed that the specific carrier density dependencies of the material gain and the carrier recombination rate are the key parameters determining the gain saturation. The linewidth enhancement factor is also known to be a function of the carrier density and the operation conditions. Therefore, the more accurate dependencies of the differential gain, carrier lifetime, and the linewidth enhancement factor on the amplifier current or the absorber reverse bias enabled us to predict device characteristics over a wide operation range. It was shown that the inclusion of the self phase modulation (SPM) accompanying the mode coupling reduces the possible operation range of the mode-locking. The resultant mode-locking can be obtained only when the SPM due to the amplifier is almost compensated by that of the absorber, which explains the experimentally observed transform-limited pulses under SPM.