Simulation of amplifying phase-shifted fiber Bragg gratings by the method of single expression

Abstract

An advanced method of single expression (MSE) is used for simulation of uniform and phase-shifted amplifying fiber Bragg gratings (FBGs) as potential narrowband transmission filters-amplifiers. In MSE the solution of Helmholtz's equation is represented in a special form of a single expression, which enables the exact solution of the corresponding boundary problem by means of numerical integration. Spectral dependences of amplifying uniform and π phase-shifted FBG are obtained. The electric field and power flow density distributions within and outside of amplifying FBGs permit to understand electrodynamically the process of amplification in modulated media. Amplification at transparency points of spectral dependences of uniform and π phase-shifted FBGs indicates essential gain accumulation against other parts of the spectrum. Amplification turns over uniform FBG from the stop-band filter to the narrow pass-band filter-amplifier with two sharp peaks at both edges of the stop-band region of corresponding FBG without gain. In amplifying π phase-shifted FBGs only one amplified narrow transmission peak appears at the center of the spectral dependences that is more acceptable for contemporary DWDM systems.