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建立了长周期光纤光栅傅里叶模式耦合理论.在分析同向模式耦合时,发现了同向耦合模式的振幅系数间存在傅里叶变换关系.推导了长周期光纤光栅的同向耦合谱和透射谱的通用表达式.该理论是用傅里叶变换分析得出长周期光纤光栅折射率微扰的空域谱,再对该空域谱进行模式同向耦合分析,从而得到长周期光纤光栅光谱特性的通用表达式.根据该理论模拟分析了长周期光纤光栅在不同长度和微扰幅值时的光谱特性,与传统耦合模理论进行了对比分析.结果表明,该长周期光纤光栅傅里叶模式耦合理论具有简单、精确和高效的特点,与实际长周期光纤光栅的透射谱特性一致.应用该理论可分析无过耦合的任意轴向折射率微扰分布的长周期光纤光栅光谱特性.
The Fourier-mode coupling theory of long-period fiber grating was established.Analyzing the coupling of co-directional modes, it was found that there was a Fourier transform relationship between the amplitude coefficients of the co-directional coupling mode.And the co-directional coupling spectra of long period fiber gratings The general expression of transmission spectra is obtained by using Fourier transform analysis to obtain the spatial spectrum of the perturbation of the refractive index of the long period fiber grating, and the mode coupling analysis of the spatial spectrum is carried out to obtain the spectral characteristics of the long period fiber grating Based on this theory, the spectral characteristics of long-period fiber gratings under different lengths and perturbation amplitudes are simulated and compared with the traditional coupled-mode theory.The results show that the Fourier transform The coupling theory is simple, accurate and efficient, which is consistent with the transmission spectrum characteristics of the actual long-period fiber gratings. The theory can be used to analyze the spectral characteristics of long-period fiber gratings without any coupling with any axial refractive index perturbation distribution.