Optical similaritons in a tapered graded-index nonlinear-fiber amplifier with an external source

We analytically explore a wide class of optical similariton solutions to the nonlinear Schrodinger equation appropriately modified to model beam propagation in a tapered, graded-index nonlinear-fiber amplifier with an external source. Under certain physical conditions, we reduce the coupled nonlinear Schrodinger equations to a single-wave equation that aptly describes similariton propagation through asymmetric twin-core fiber amplifiers. The asymmetric twin-core fiber is composed of two adjoining, closely spaced, single-mode fibers in which the active one is a tapered, graded-index nonlinear-fiber and the passive one is a step-index fiber. We obtain these self-similar waves for different choices of tapered index profile, using a Mobius transformation. Our procedure is applicable for both self-focusing and self-defocusing nonlinearities.