Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source

Abstract

We present exact analytical solutions describing spatial bright, trigonometric, and kink-type of self-similar waves, as well as the trains of such waves to the nonlinear Schroedinger equation appropriately modified to model beam propagation in graded-index, nonlinear fiber amplifier with an external source. We show that this model is appropriate for the self-similar propagation in asymmetric twin-core fiber amplifier. The asymmetric twin-core fiber is composed of two adjoining, closely spaced, single mode fibers in which the active one is a graded-index nonlinear fiber and the passive one is a step-index fiber. We obtain these self-similar waves using a Moebius transformation. Our procedure is applicable both for self-focusing and self-defocusing Kerr nonlinearities.