The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)
（临沂大学 自动化与电气工程学院，山东 临沂276005） 摘要：基于光纤光栅的模式耦合理论，用传输矩阵法对长短周期级联光纤光栅的传输谱特性进行分析。先由耦合模方程分别得到长周期光纤光栅（LPFG）、连接光纤段和短周期光纤光栅（FBG）的传输矩阵，然后将它们相乘得到总的传输矩阵，最后再结合边界条件即可求得长短周期级联光纤光栅（CLBG）的传输谱。进一步对CLBG的传输谱进行了数值模拟，并通过实验进行了验证。实验结果表明, CLBG的传输谱中出现了由纤芯模和包层模耦合形成的两个谐振峰，与模拟计算的结果一致，证明了传输矩阵法求解CLBG传输谱的可行性，为CLBG在多参量传感和测量领域的广泛应用提供了理论支持。
Based on the mode coupling theory of fiber gratings, the transmission spectrum characteristics of cascaded long and short- period fiber grating are analyzed by transmission matrix method.The transmission matrices of long period fiber grating (LPFG), connected fiber and short period fiber grating (FBG) are obtained by the coupling mode equation, and then the total transmission matrix of cascaded fiber gratings can be obtained by multiplying them. Finally, the transmission spectrum can be obtained by combining boundary conditions. Further, the transmission spectrum of CLBG is simulated and verified by the experiment.The experimental results show that there are two resonant peaks formed by the coupling of core mode and cladding modes in the transmission spectrum of CLBG, which are consistent with the simulation results. It proves the feasibility of the transmission matrix method to solve the transmission spectrum of CLBG, and provides theoretical support for the wide application of CLBG in the field of multi-parameter sensing and measurement.