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Title: Periodic waves in fiber Bragg gratings
Authors: Chow, K W
Merhasin, Ilya M
Malamod, Borris A
Nakeeran, K
Senthilnathan, K
Wai, P K A
Issue Date: 2008
Publisher: The American Physical Society
Citation: Physical Review E, Vol 77, Iss 2,
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 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 0, is identified. However, the sn waves with 0, as well as all cn solutions, are strongly unstable.
Description: Copyright for the published version belongs to APS
Appears in Collections:Journal Articles

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