Periodic waves in fiber Bragg gratings

K. W. Chow, Ilya M. Merhasin, Boris A. Malomed, K. Nakkeeran, K. Senthilnathan, Ping Kong Alexander Wai

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)


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 (ω<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 ω>0, is identified. However, the sn waves with ω<0, as well as all cn solutions, are strongly unstable.
Original languageEnglish
Article number026602
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 7 Feb 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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