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Title: Periodic waves in fiber Bragg gratings
Authors: Chow, K. W.
Merhasin, Ilya M.
Malomed, Boris A.
Nakkeeran, K.
Senthilnathan, K.
Wai, Ping-kong Alexander
Subjects: Computer simulation
Energy gap
Light propagation
Optical Kerr effect
Time varying systems
Issue Date: 7-Feb-2008
Publisher: American Physical Society
Source: Physical review E, statistical, nonlinear, and soft matter physics, Feb. 2008, v. 77, no. 2, 026602, p. 1-8.
Abstract: 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.
Rights: Physical Review E © 2008 The American Physical Society. The Journal's web site is located at
Type: Journal/Magazine Article
DOI: 10.1103/PhysRevE.77.026602
ISSN: 1539-3755 (print)
1550-2376 (online)
Appears in Collections:EIE Journal/Magazine Articles

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