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Title: Periodic waves in fiber Bragg gratings

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and, in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ; ;  [5]
  1. Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road (Hong Kong)
  2. Department of Electrical and Electronics Engineering, The University Center of Judea and Samaria, Ariel (Israel)
  3. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
  4. School of Engineering, King's College, University of Aberdeen, Aberdeen AB24 3UE, Scotland (United Kingdom)
  5. Photonics Research Center and Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (China)
Publication Date:
OSTI Identifier:
21101953
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal Volume: 77; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevE.77.026602; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BRAGG REFLECTION; COMPUTERIZED SIMULATION; DIFFRACTION GRATINGS; EQUATIONS; FIBERS; INSTABILITY GROWTH RATES; KERR EFFECT; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; SOLITONS