Gap solitons in nonlinear periodic structures

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.