Surface Solitons in Three Dimensions

Abstract

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site "horseshoe"-shaped structure, which is always unstable in the bulk, while at the surface it is stable near the anti-continuum limit. We also examine effects of the surface on lattice vortices. For the vortex placed parallel to the surface this increased stability region feature is also observed, while the vortex cannot exist in a state normal to the surface. More sophisticated localized dynamical structures, such as five-site horseshoes and pyramids, are also considered.

10 pages, 12 figures, submitted to Phys. Rev. E

References in corpus (11)

• Observation of surface gap solitons in semi-infinite waveguide arrays
• Observation of two-dimensional surface solitons in anisotropic waveguide arrays
• Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays
• Surface vortex solitons
• Multipole-mode surface solitons
• Nonlocal surface dipoles and vortices
• Discrete surface solitons in two dimensions
• Dynamics of surface solitons at the edge of chirped optical lattices
• Discrete surface solitons in two-dimensional anisotropic photonic lattices
• Surface modes and breathers in finite arrays of nonlinear waveguides
• Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice

Cited by in corpus (5)

• Interface solitons in one-dimensional locally-coupled lattice systems
• Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas
• Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices
• Surface solitons in trilete lattices
• (2+1)D surface solitons at the interface between a linear medium and a nonlocal nonlinear medium