Gap solitons in nonlinear periodic structures

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Abstract
In a medium with a dielectric constant periodic in one spatial direction, there are gaps in the dispersion relation of electromagnetic waves which propagate in the structure. If the index of refraction also contains a term proportional to the local-field intensity, we show that for frequencies within the gap, there exist soliton solutions to the nonlinear wave equation of the medium. This is demonstrated by analytic methods; the results agree with conclusions reached earlier, in numerical studies of power-dependent transmission through a finite superlattice, with a nonlinear element in each unit cell. DOI: http://dx.doi.org/10.1103/PhysRevB.36.947 © 1987 The American Physical Society