Abstract
Stability of solitons in parity-time ()-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the lattice rises above a certain threshold (phase transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Third, we investigate the nonlinear evolution of unstable solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the lattice is below the phase transition point.
3 More- Received 12 January 2012
DOI:https://doi.org/10.1103/PhysRevA.85.023822
©2012 American Physical Society