Synthesis of long-period fiber gratings with the inverted erbium gain spectrum using the multiport lattice filter model

This paper proposes an accurate modeling technique of concatenated long-period fiber gratings (LPFGs). The proposed technique,is then applied to the synthesis of LPFGs for the erbium gain equalization using both the simulated annealing and the steepest descent minimization technique. A piecewise-uniform LPFG is theoretically synthesized according to the inverted gain spectrum of a commercially available erbium-doped fiber amplifier (EDFA) over the range of 1525-1570 nm. Sensitivity analysis of the designed structure is presented by Monte Carlo simulation with regard to the manufactured amplitude mask. To verify a synthesizing technique using the proposed modeling, the piecewise-uniform LPFGs for gain flattening of EDFA are fabricated and their spectra are also presented experimentally.