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Title: Solitons in Bragg gratings with saturable nonlinearities
Authors: Merhasin, IM
Malomed, BA
Senthilnathan, K
Nakkeeran, K
Wai, PKA 
Chow, KW
Keywords: Cladding (coating)
Control nonlinearities
Energy gap
Mathematical models
Photorefractive materials
Issue Date: 1-Jul-2007
Publisher: Optical Society of America
Source: Journal of the optical society of America B: optical physics, 1 July 2007, v. 24, no. 7, p. 1458-1468 How to cite?
Journal: Journal of the optical society of America B: optical physics 
Abstract: We introduce two different systems of coupled-mode equations to describe the interaction of two waves coupled by the Bragg reflection in the presence of saturable nonlinearity. The basic model assumes the ordinary linear coupling between the modes. It may be realized as a photorefractive waveguide, with a Bragg lattice permanently written in its cladding. We demonstrate the presence of a cutoff point in the system’s bandgap, with gap solitons existing only on one side of it. Close to this point, the soliton’s norm diverges with power −3/2. The soliton family between the cutoff point and the edge of the bandgap is stable. In this model, stationary bound states of two in-phase solitons are found too, but they are unstable, transforming themselves into breathers. Another model assumes a photoinduced longitudinal bulk grating, with the corresponding intermode coupling subject to saturation along with the nonlinearity. In that model, another cutoff point is found, with the soliton’s norm diverging near it with power −2. Solitons are stable in this model too (while it does not give rise to two-soliton bound states). Collisions between moving solitons are always quasi-elastic, in either model.
ISSN: 0740-3224
DOI: 10.1364/JOSAB.24.001458
Rights: © 2007 Optical Society of America. This paper was published in Journal of the Optical Society of America B and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.
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