Spectrum analysis for non-uniform ultra-long-period fiber grating

Based on the Fourier transforming of fiber grating refractive index modulation, a new analysis method is proposed from the spectral analysis, which is suitable for non-uniform ultra-long-period fiber grating (ULPFG). Also the coupled-mode equations are derieved for the non-uniform grid distribution and modulate depth. The method points out that the non-uniform ULPFG can be equivalent to the superposition of different uniform gratings. Numerical simulation and experiment about a non-uniform ULPFG indicated that this method, based on spectrum analysis, has an obvious advantages to analyze: 1) the effection on spectrum impacted by the grid number or the chirp size; 2) the phenomenon that one location with multiple resonance peaks.