Waves in nonlinear lattices: Ultrashort optical pulses and Bose-Einstein condensates

Y. Sivan, G. Fibich, M. I. Weinstein

Research output: Contribution to journalArticlepeer-review

97 Scopus citations

Abstract

The nonlinear Schrödinger equation i ∂ zA(z,x,t)+ x,t2A+[1+m(κx)]|A|2A=0 models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate x, and also the evolution of 2D Bose-Einstein condensates in which the scattering length varies in one dimension. Stability of bound states depends on the value of κ=beamwidth/lattice period. Wide (κ+/1) and κ=O(1) bound states centered at a maximum of m(x) are unstable, as they violate the slope condition. Bound states centered at a minimum of m(x) violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of m(x). Even in that case, the stability region is so small that these bound states are "mathematically stable" but "physically unstable."

Original languageEnglish
Article number193902
JournalPhysical Review Letters
Volume97
Issue number19
DOIs
StatePublished - 16 Nov 2006
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (all)

Fingerprint

Dive into the research topics of 'Waves in nonlinear lattices: Ultrashort optical pulses and Bose-Einstein condensates'. Together they form a unique fingerprint.

Cite this