Nonlinear property analysis of long-period fiber gratings using discretized coupled-mode theory

We present generalized mathematical expressions for coupled-mode equations for nonlinear pulse propagation in fiber gratings using discretized coupled-mode theory and quantitatively analyze the nonlinear properties of long-period fiber gratings, considering multimode coupling between the core mode and several cladding modes. The calculations yield nonlinear responses for the case of long-period fiber gratings, including pulse shaping and all-optical switching in the self- and cross-phase modulation regimes. In addition, we briefly discuss the group delay properties of long-period fiber gratings and present several numerical examples of nonlinear pulse compression, which is related to strong dispersion and soliton-like behavior in fiber gratings.