Problems in the self-consistent profile approach to the theory of laser mode-locking

We study the "self-consistent profile" approach to mode-locking theory, in the case of a laser medium with a short recovery time. Taking the case of mode-locking by synchronous pumping as our specific example, we compare the steady- state profiles derived from a commonly-used approximate method with those generated by an essentially exact numerical technique. Substantial discrepancies in the solutions are shown to arise from invalid assumptions in the standard approach, suggesting that results predicted by this method in other areas of mode-locking theory should be treated with caution.