The Effects of Nonlinear Gain on the Stability of Two-Element Evanescently Coupled Laser Arrays

Abstract

Arrays of semiconductor lasers have become widely used as compact sources of intense radiation, generating watts of power in diffraction limited beams. [1] Their high power makes them attractive as potential sources for optical fibers. However, their dynamical behavior is not well understood. Ordinarily, the problem is handled by solving a set of coupled nonlinear differential equations which are descriptive of the coupling of the carrier and photon populations in a single device as well as the the coupling between the individual devices. When writing these equations, one generally assumes that the optical gain is independent of the intensity. However, from a physical perspective, it is reasonable to postulate that the gain will begin to decrease significantly for sufficiently large photon populations. Several models have been utilized in order to describe the phenomenon of gain saturation [2]. One formalism assumes that the gain may be described by g = g L (1 − ϵX2), where X is a normalized electric field and X2 is proportional to the photon density in the laser cavity. This formalism is, however, only valid for low power levels. A second phenomenological form uses g = g L (1 + ϵX2)−1. This model has its origins in the two-level model and, since a semiconductor laser connot be described completely by the two-level model, a third model, which is taken from a non-perturbative density matrix calculation, has been formulated in which g = g L 1 + ε X 2 − 1 2 . It is clear that the presence of nonlinear gain will be a stabilizing influence on arrays of lasers, but to what degree is unclear. In the present study, we determine stability criteria for a two-element evanescently coupled laser array using each of the three models mentioned above in an effort to predict the effect of nonlinear gain on these arrays.