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Title: Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices

Journal Article · · Journal of Optics
 [1];  [2];  [3]
  1. Western New England Univ., Springfield, MA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. Furthermore, we quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation of these instabilities to be the spontaneous rearrangement of the solution, for larger values of the coupling, into localized waveforms typically centered over fewer sites than the original unstable structure. In weak coupling, the instability appears to result in a robust breathing of the relevant waveforms.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1258008
Report Number(s):
LA-UR-15-24940
Journal Information:
Journal of Optics, Vol. 18, Issue 2; ISSN 2040-8978
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

References (18)

Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics text January 2008
Discretizing light behaviour in linear and nonlinear waveguide lattices journal August 2003
Spatial photonics in nonlinear waveguide arrays journal January 2005
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Many-body physics with ultracold gases journal July 2008
Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics journal December 2008
Observation of double-charge discrete vortex solitons in hexagonal photonic lattices journal April 2009
Symmetry-breaking diffraction and dynamic self-trapping in optically induced hexagonal photonic lattices journal February 2012
Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices journal June 2012
Topological Creation and Destruction of Edge States in Photonic Graphene journal September 2013
Observation of unconventional edge states in ‘photonic graphene’ journal November 2013
Unveiling pseudospin and angular momentum in photonic graphene journal February 2015
Multi-component quantum gases in spin-dependent hexagonal lattices journal February 2011
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Discrete flat-band solitons in the kagome lattice journal June 2013
Stability of discrete solitons in nonlinear Schrödinger lattices journal December 2005
Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators journal November 1994
Persistence and stability of discrete vortices in nonlinear Schrödinger lattices journal December 2005

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