Gap soliton dynamics in an optical lattice as a parametrically driven pendulum

A long wavelength optical lattice is generated in a two-level medium by low-frequency contrapropagating beams. Then a short wavelength gap soliton generated by evanescent boundary instability (supratransmission) undergoes a dynamics shown to obey the Newton equation of the parametrically driven pendulum, hence presenting extremely rich, possibly chaotic, dynamical behavior. The theory is sustained by numerical simulations and provides an efficient tool to study soliton trajectories.

Figure 1

(Color online) Graphs (a)–(c) display results of numerical simulation of Eq. (1) under boundary conditions [Eq. (23)] for the three incident wave amplitudes [Eq. (24)] generating optical lattice with slightly different depths. Graph (d) shows the pendulum angle evolution in model [Eq. (3)] corresponding to those three regimes. For sake of presentation, the gap soliton trajectories have been underlined with dashed lines.