Abstract

We develop a statistical theory for laser operation with external optical feedback. The theory is applicable to a broad class of singlemode lasers including gas lasers and semiconductor lasers. We introduce a characteristic potential function in which each minimum corresponds to a possible mode frequency, while the corresponding second derivative is an immediate measure for the linewidth. The minima in this potential are shifted in position with respect to the power maxima by an amount mainly determined by the amplitudephase coupling or linewidth enhancement parameter. This explains why in highly dispersive lasers the preferred and most stable mode is not the one with highest power. A diffusion model is developed in which the spontaneous emission related quantum fluctuations are the driving noise forces. This leads to a Fokker-Pianck equation for the phase probability distribution function, which is the key equation for investigating dynamical stability, lifetimes and switching times. We determine the stationary probability distribution and calculate external mode lifetimes and hopping rates.

© 1990 Optical Society of America