基于耦合模理论，利用传输矩阵法求解出长周期光纤光栅(Long Period Fiber Gratings，LPFGs)的透射谱表达式，模拟分析了LPFGs的光谱特性与光栅参数如周期、刻写长度以及折射率调制深度之间的关系。研究结果表明：LPFGs谐振波长随着周期和折射率调制深度的增大向长波方向移动，且高次模谐振波长对光栅周期更为敏感；光谱带宽的变化主要取决于光栅的刻写长度，随着光栅刻写长度的增加，带宽逐渐变窄，且当光栅刻写长度大于5.2 cm时，光栅存在过耦合区域；随着折射率调制深度的增加，光栅存在不完全耦合、完全耦合和过耦合现象，且谐振损耗最大值位置随着折射率调制深度的增加逐渐向低次转移。该研究结论对长周期光纤光栅的理论分析和实际应用中的参数设计具有重要参考价值。

Based on the coupled-mode theory, the equation for the transmission spectrum of Long Period Fiber Gratings (LPFGs) is solved by using the transmission matrix method and the relationship between the spectral characteristics of LPFGs and grating parameters (such as grating period, writing length and the depth of refractive index modulation) is simulated. The results show that the resonant wavelength of LPFGs is red-shifted with an increase in the grating period and refractive index modulation depth, and that the resonant wavelength with higher-order mode is relatively more sensitive on the grating period. At the same time, the change in the spectral bandwidth mainly depends on the writing length of the grating. The bandwidth narrows gradually with an increase in the length of the grating and over-coupling occurs when the grating length is higher than 5.2 cm. With an increase in the refractive index modulation depth, the grating has the phenomena of incomplete coupling, complete coupling and over-coupling, and the position of the maximum resonance loss will gradually transfer to the lower-order mode. The results of this research have important referential significance for the theoretical research of LPFGs and parameter designs in practical applications.