Linewidth of laser diodes with nonuniform phase-amplitude α-factor

The linewidth of a laser diode having a phase-amplitude factor α that varies arbitrarily along the path is calculated. For simplicity, an ideal single-mode ring-type laser diode with only one wave circulating is considered. The theory is exact in the limit of large injected currents, provided parameters such as the carrier temperature do not vary and the gain or loss per wavelength is small. It is found that when the electron-hole pairs are injected independently of each other (that is, when the pump fluctuations are spatially uncorrelated shot noises) the linewidth is half the value obtained earlier for the linear regime multiplied by (1+α²)_av where the round-trip averaging is affected with respect to the reciprocal of the power gain. Specific examples, in particular a sequence of amplifiers and partially reflecting mirrors, are considered