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

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 Schrödinger 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 Möbius transformation. Our procedure is applicable both for self-focusing and self-defocusing Kerr nonlinearities.

Figure 1

Evolution of cosine-similariton solution for $X_0=3$, $C_{01}=0.2$, and $W_0=1$.

Figure 2

Evolution of bright similariton solution for $X_0=3$, $C_{01}=0.2$, and $W_0=1$.

Figure 3

Evolution of sine-similariton solution for $X_0=3$, $C_{01}=0.2$, and $W_0=1$.

Figure 4

Evolution of kink-similariton solution for $X_0=2$, $C_{01}=0.25$, and $W_0=1$.