TY - JOUR
T1 - Ring-shaped solitons in a "dartboard" photonic lattice
AU - Hoq, Q. E.
AU - Kevrekidis, P. G.
AU - Frantzeskakis, D. J.
AU - Malomed, B. A.
N1 - Funding Information:
P.G.K. gratefully acknowledges support from the Eppley Foundation for Research, NSF-DMS-0204585 and NSF-CAREER, as well as numerous insightful discussions with Zhigang Chen about the experimental feasibility of the dartboard lattices.
PY - 2005/6/20
Y1 - 2005/6/20
N2 - We introduce a two-dimensional model of photorefractive media, with the usual saturable nonlinearity, and a cylindrical photonic lattice periodic in the radial direction. The saturable nonlinearity may be either self-focusing or self-defocusing, and the cylindrical lattice is introduced so that, in the former case, the potential has a maximum at the center. Ring-shaped solitons are constructed numerically. In the case of self-focusing, they are typically unstable against azimuthal perturbations, which is shown by means of numerical computations, and is also explained with the help of an analytical approximation. On the contrary, solitons of the same type may be stable if the saturable nonlinearity is self-defocusing.
AB - We introduce a two-dimensional model of photorefractive media, with the usual saturable nonlinearity, and a cylindrical photonic lattice periodic in the radial direction. The saturable nonlinearity may be either self-focusing or self-defocusing, and the cylindrical lattice is introduced so that, in the former case, the potential has a maximum at the center. Ring-shaped solitons are constructed numerically. In the case of self-focusing, they are typically unstable against azimuthal perturbations, which is shown by means of numerical computations, and is also explained with the help of an analytical approximation. On the contrary, solitons of the same type may be stable if the saturable nonlinearity is self-defocusing.
UR - http://www.scopus.com/inward/record.url?scp=20444389045&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2005.04.074
DO - 10.1016/j.physleta.2005.04.074
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AN - SCOPUS:20444389045
SN - 0375-9601
VL - 341
SP - 145
EP - 155
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1-4
ER -