Right Type Departmental Bulletin Paper

Optical solitons in fiber grating in which the dielectric constant varies periodically along it, are investigated. It is proved that the envelope of the Bloch wave obeys the nonlinear Schr\"odinger equation. As an application, gap solitons in a super-lattice are dicussed. The concept and method presented in this paper are useful not only for explaining recently observed Bragg grating soliton but for $\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{z}\mathrm{i}\backslash \mathrm{n}\mathrm{g} $ a large class of nonlinear periodic systems.