Lattice solitons in optical media described by the complex Ginzburg-Landau model withPT-symmetric periodic potentials

Abstract

We report the existence, stability, and rich dynamics of dissipative lattice solitons in optical media described by the cubic-quintic complex Ginzburg-Landau model with parity-time ($\mathcal{PT}$) symmetric potentials. We focus on studying the generic spatial soliton propagation scenarios by changing (a) the linear loss coefficient in the complex Ginzburg-Landau model, (b) the amplitudes, and (c) the periods of real and imaginary parts of the complex-valued $\mathcal{PT}$-symmetric optical lattice potential. Generically, it is found that if the period of the real part of the $\mathcal{PT}$-symmetric optical lattice potential is close to $\ensuremath{\pi},$ the spatial solitons are tightly bound and they can propagate straightly along the lattice, while if the period of the real part of the $\mathcal{PT}$-symmetric optical lattice potential is larger than $\ensuremath{\pi},$ the launched solitons are loosely bound and they can exhibit either a transverse (lateral) drift or a persistent swing around the input launching point due to gradient force arising from the spatially inhomogeneous loss. These latter features are intimately related to the dissipative nature of the system under consideration because they do not arise in the conservative counterpart of the dynamical model. These generic propagation scenarios can be effectively managed by properly changing the profile of the spatially inhomogeneous loss.