Controllable generation and propagation of asymptotic parabolic optical waves in graded-index waveguide amplifiers

Abstract

The asymptotic properties of optical waves propagating inside the graded-index waveguide amplifier are studied in the framework of $(1+1)$-, $(2+1)$-, and $(3+1)$-dimensional nonlinear Schr\odinger equations. By employing a direct ansatz, we find that the parabolic optical waves can be generated from arbitrary input waves at the asymptotic limit. These waves possess linear chirps and can propagate self-similarly. It is found that the characteristics of the asymptotic parabolic optical waves is not only affected by the input power, but also affected by the inhomogeneity of the graded-index waveguide. Furthermore, the possibility of controlling the shape of output parabolic waves is demonstrated. Specifically, the existence of optical waves with elliptic and ellipsoidal profiles possessing nontrivial but isotropic quadratic phases are predicted. The theoretical results are confirmed by numerical simulations.