PMID: 15244767Jul 13, 2004Paper

Symmetric and asymmetric solitons in linearly coupled Bragg gratings

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
William C K MakPak L Chu

Abstract

We demonstrate that a symmetric system of two linearly coupled waveguides, with Kerr nonlinearity and resonant grating in both of them, gives rise to a family of symmetric and antisymmetric solitons in an exact analytical form, a part of which exists outside of the bandgap in the system's spectrum, i.e., they may be regarded as embedded solitons (ES's, i.e., the ones partly overlapping with the continuous spectrum). Parameters of the family are the soliton's amplitude and velocity. Asymmetric ES's, unlike the regular (nonembedded) gap solitons (GS's), do not exist in the system. Moreover, ES's exist even in the case when the system's spectrum contains no bandgap. The main issue is the stability of the solitons. We demonstrate that some symmetric ES's are stable, while all the antisymmetric solitons are unstable; an explanation is given to the latter property, based on the consideration of the system's Hamiltonian. We produce a full stability diagram, which comprises both embedded and regular solitons, quiescent and moving. A stability region for ES's is found around the point where the constant of the linear coupling between the two cores is equal to the Bragg-reflectivity coefficient accounting for the linear conversion betwee...Continue Reading

References

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Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·William C K MakPak L Chu
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Nov 1, 1993·Optics Letters·C J Herbert, M S Malcuit

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Citations

Apr 8, 2006·Chaos·B A MalomedS González
Feb 7, 2007·Physical Review Letters·Andrey A Sukhorukov, Yuri S Kivshar
Jun 24, 2017·Scientific Reports·S A M Saddam Chowdhury, Javid Atai
Jan 20, 2018·Physical Review. E·Tanvir Ahmed, Javid Atai
Jun 5, 2007·Optics Letters·Sangwoo HaYuri S Kivshar
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Nir Dror, Boris A Malomed
Sep 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M D PetrovićB A Malomed
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wanneng Xiao

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