Discrete reduced-symmetry solitons and second-band vortices in two-dimensional nonlinear waveguide arrays

by Dr Johansson Magnus (Linköping University)

Tuesday 20 Jul 2010, 11:00 → 12:00 Europe/Stockholm

Considering a two-dimensional lattice of weakly coupled waveguides,where each waveguide may carry two orthogonal modes of dipolar character, we present a nonlinear discrete vector model for the study of Kerr optical solitons with profiles having a reduced symmetry relative to the underlying lattice. We describe analytically and numerically existence and stability properties of such states in square and triangular lattices and also reveal directional mobility properties of two-dimensional gap solitons which were recently observed in experiment. The model also describes one-site peaked discrete vortices corresponding to experimentally observed second-band vortex lattice solitons, for which oscillatory instabilities are predicted. We also introduce a concept of rotational Peierls-Nabarro barrier characterizing the minimum energy needed for rotation of stable dipole modes and compare numerically translational and rotational energy barriers in regimes of good mobility. A similar model has also recently been proposed as a mean-field model for p-band bosons in optical lattices, describing quantum states in the superfluid regime.