Fundamental and vortex solitons in a two-dimensional optical lattice

Abstract

Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime the fundamental soliton is largely confined to one lattice site, whereas the vortex state comprises four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and the vortex solitons spread over many lattice sites. We further show that fundamental and the vortex solitons are stable against small perturbations in the strong localization regime.

Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity

“…Optical vortex solitons propagating in periodic media form another family of discrete spatial solitons with helical phase structures, as have been predicted earlier [13,14] and demonstrated in optical induced lattices with a self-focusing nonlinearity [15,16]. These are semi-infinite-gap vortex solitons.…”

Stable Higher-Charged Vortex Solitons in Optically-Induced Lattices

“…Stable vortices with charges lower than two are possible within certain ranges of lattice (transverse refractive index modulation) parameters [14,17,[21][22][23][24][25][26][27][28]. Different types of vortex solitons, such as discrete vortices [21], vortex-ring "discrete" solitons [28], and second-band vortices [22] were observed in experiments.…”

“…Successful alternatives are confined systems, such as graded-index optical fibers [12], nonlinear photonic crystals with defects [13], linear and nonlinear optical lattices [14][15][16][17][18][19], or optical lattices with defects [20], where the azimuthal instability of vortices can be suppressed by the corresponding confining potentials. Stable vortices with charges lower than two are possible within certain ranges of lattice (transverse refractive index modulation) parameters [14,17,[21][22][23][24][25][26][27][28].…”

Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices

“…Properties of single solitons and soliton complexes supported by one-and twodimensional optical lattices are now well established [7][8][9][10][11][12][13]. Lately we addressed properties of solitons supported by radially symmetric Bessel lattices [14].…”

“…(1) possess soliton solutions [7][8][9][10][11][12][13][14]. Here we recall basic properties of fundamental solitons.…”