Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

Abstract

A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with non-trivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.

31 pages, 12 figures, submitted to Physica D (21 September 2006, revised 23 April 2008)

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Cited by in corpus (10)

• Solitons in nonlinear lattices
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index
• Stabilization of multi-beam necklace solitons in circular arrays with spatially modulated nonlinearity
• Compactification tuning for nonlinear localized modes in sawtooth lattices
• Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrödinger lattices
• Multidimensional Discrete Compactons in Nonlinear Schrödinger Lattices with Strong Nonlinearity Management
• Breather mobility and the PN potential: Brief review and recent progress
• Variational Approximations of Bifurcations of Asymmetric Solitons in Cubic-Quintic Nonlinear Schroedinger Lattices