Nonlinear propagation of light in one-dimensional periodic structures

We consider the nonlinear propagation of light in an optical fiber waveguid e as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The wavegu ide is assumed to have an index of refraction that varies periodically alon g its length. The wavelength of light is selected to be in resonance with t he periodic structure (Bragg resonance). The AMLE system considered incorpo rates the effects of noninstantaneous response of the medium to the electro magnetic field (chromatic or material dispersion), the periodic structure ( photonic band dispersion), and nonlinearity. We present a detailed discussi on of the role of these effects individually and in concert. We derive the nonlinear coupled mode equations (NLCME) that govern the envelope of the co upled backward and forward components of the electromagnetic field. We prov e the validity of the NLCME description and give explicit estimates for the deviation of the approximation given by NLCME from the exact dynamics, gov erned by AMLE. NLCME is known to have gap soliton states. A consequence of our results is the existence of very long-lived gap soliton states of AMLE. We present numerical simulations that validate as well as illustrate the l imits of the theory. Finally, we verify that the assumptions of our model a pply to the parameter regimes explored in recent physical experiments in wh ich gap solitons were observed.