Dissipative surface solitons in a nonlinear fractional Schrödinger equation.

Abstract

We study the existence and stability of dissipative surface solitons supported by the nonlinear fractional Schrödinger equation (NLFSE) with an interface between a semi-infinite chirped lattice and a uniform Kerr medium. In such a system, the existence domain of dissipative surface solitons depends on an upper cutoff value of the linear gain coefficient at a fixed nonlinear loss. The results of the linear stability analysis are in good agreement with that of the propagation simulation in a fractional dimension. Stable dissipative surface solitons generally feature low energy and small propagation constants and adapt to a wide range of two-photon absorption. The instability of solitons can be suppressed by increasing the chirp rate of the lattice. Robust nonlinear dissipative surface states can be easily excited by a Gaussian input beam. Similar characteristics of the two-dimensional dissipative surface solitons are also addressed.