Open AccessSpectral limits for periodic pattern propagation in Kerr media
Author(s) -
N. Korneev,
Eduardo Tepichin Rodríguez
Publication year - 2004
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/opex.12.003297
Subject(s) - physics , optics , nonlinear system , amplitude , ordinary differential equation , wave propagation , nonlinear optics , kerr effect , refractive index , spatial frequency , motion (physics) , self phase modulation , mathematical analysis , differential equation , classical mechanics , mathematics , quantum mechanics
We consider the propagation of periodic waves with initially narrow spatial spectra in a Kerr medium. The set of constants of motion closely related to the order amplitudes is introduced. It is shown that the spatial spectrum remains uniformly narrow with propagation for both self-focusing and self-defocusing nonlinearity. In addition, for sufficiently weak nonlinearity, initially strong orders always remain strong. Thus the problem is shown to be essentially finite dimensional and well approximated by a proper set of coupled ordinary differential equations.