Self-induced transparency solitons in nonlinear refractive periodic media

Abstract

The behavior of two counter(co)propagating modes of the electromagnetic field inside a 1-D periodic nonlinear medium is represented by a pair of equations that are a generalization, by inclusion of the self-phase modulation, of the classical massive Thirring model in field theory which itself is integrable by means of the inverse scattering transform and therefore has soliton solutions. We have obtained a new class of solitonlike solutions for the optics model which are a generalization of the one soliton solutions of the integrable model on an addition of a nontrivial phase which can be computed by quadrature. This is a two parameter family of solutions and it contains as a subclass the recently obtained “slow Bragg solitons" of D. N. Christodoulides and R. I. Joseph. One remarkable feature is the self-induced transparency effect; that is, the waves can propagate undistorted even though the carrier frequency lies inside the forbidden gap. This effect, however, comes from a nonlinear interaction between the field and the periodic structure of the medium as opposed to the usual selfinduced transparency effect.