Abstract
We analytically explore a wide class of optical similariton solutions to the nonlinear Schr\"odinger 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 Schr\"odinger 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 M\"obius transformation. Our procedure is applicable for both self-focusing and self-defocusing nonlinearities.
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