We propose a new method for synthesizing piecewise-uniform long-period fiber gratings (LPFGs) by using an extended fundamental matrix model with thermal changes. The proposed synthesis method is then applied to the design of the LPFG tuned by the thermal changes for erbium gain equalization by using the simulated-annealing and steepest-descent optimization techniques. We describe how a piecewise-uniform LPFG can be constructed by utilizing the inverted gain spectrum of erbium-doped fiber amplifiers (EDFAs), from the thermal change parameters’ search process. A sensitivity analysis also is done to study the tolerance of our approach against possible error sources, such as the temperature controller, the fabrication of the LPFG, and the EDFA spectrum, by using Monte Carlo simulations. To verify the validity of the proposed synthesis method experimentally, we manufactured the piecewise-uniform LPFG with thermal changes by using a divided coil heater. We observe that the spectrum designed by the proposed synthesis method is close to the corresponding measured spectrum in the wavelength band of interest. We also compare the performance of the proposed method with traditional approaches, such as Newton-like methods.
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