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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.