长周期光纤光栅透射谱计算方法的比较与分析

长周期光纤光栅透射谱的求解方法有多种,本文以耦合模理论为基础,对常用的积分法、公式法、传输矩阵法求解长周期光纤光栅的透射谱进行比较与分析,指出这三种求解方法各自的特点和适用条件.积分法可在较宽波长范围内直接得到多个模式透射谱的精确解,但求解过程繁琐,运算量大;公式法虽然在表述和计算上较为方便,但只能在较小波长范围内直接求解单个模式的透射谱;传输矩阵法求解过程简便、准确度高、计算量相对较小,特别适合计算一些非均匀光纤光栅的透射谱.该研究为选择一种精确度高且理论和计算都较简单的计算长周期光纤光栅透射谱的方法提供理论依据.

Comparing and Analysis of Calculation Methods of Long-period Fiber Gratings Transmission Spectra

Many methods are considered for calculating long period fiber gratings (LPFGs) transmission spectra such as integral method, formula method and transfer matrix method. In this paper, these methods are analyzed based on the coupled mode theory and their characteristics and the conditions of application are pointed out. Exact solution for multi mode transmission spectra can be obtained directly by integral method in a wide wavelength range, however, the computation process of integral method is complicated. The formula method is convenient for calculating and expressing, but it can only solve single mode transmission spectra directly in a narrow wavelength range. The transfer matrix method is suitable for calculating some transmission spectra of non uniform fiber gratings, it is simple to implement, almost always sufficiently accurate, and general the fastest. Through the analysis and compare of the three methods, a best method with high precision and simple calculation is provided for long period fiber gratings transmission spectra in theory, which is important for the research and application of LPFGs.