Computer simulation of amplifying phase-shifted Bragg gratings by the method of single expression

An advanced non-traditional method of single expression (MSE) is used to analyze uniform and phase-shifted amplifying fiber Bragg gratings (FBGs). In the MSE Helmholtz's equation solution is presented in the generalized form of a single expression, contrary to the widely accepted counter-propagating waves approach. Brief description of the principal statements of the MSE is presented. Uniform FBGs and FBGs with pi phase shift in the middle of the structure are considered. Spectral dependences of gainless and amplifying uniform and pi phase-shifted FBGs are obtained. Spatial distributions of the electric field amplitude, real part of permittivity and power flow density along the structure of FBG and in outside media are presented at central point of transparency. Simulations carried out on amplifying pi phase-shifted FBGs showed that they can be used as narrow-band pass-band filter-amplifiers for DWDM systems.