Lambert function methods for laser dynamics with time-delayed feedback

Abstract

Time-delayed differential equations arise frequently in the study of nonlinear dynamics of lasers with optical feedback and because the analytical solution of such equations can be intractable, one resorts to numerical methods. In this manuscript, we show that under some conditions, the rate equations model that is used to model semiconductor lasers with feedback can be analytically solved by using the Lambert W function. In particular, we discuss the conditions under which the coupled rate equations for the intracavity electric field and carrier inversion can be reduced to a single equation for the field, and how this single rate equation can be cast in a form that is amenable to the use of the Lambert W function.