采用严格的耦合模理论,建立了镀金属膜和敏感膜的两层膜系长周期光纤光栅复特征方程,用微扰法对复数超越特征方程进行求解,结果和文献[5]给出的数据相符。理论模拟数据表明,金属的消光系数对功率密度和透射谱影响很大,低阶偶次模式在纤芯内的功率密度所占比重远大于奇次模式,其衰减峰幅度也比奇次模高,因此,金属镀层长周期光纤光栅实际应用时,需要选择偶次模作为研究对象。进一步理论分析了金属和敏感膜层参数对长周期光纤光栅谐振特性的影响,研究发现,金属膜厚、敏感膜厚和折射率对谐振波长有较大的影响,谐振波长随金属膜厚、敏感膜厚和折射率的增大向短波方向漂移。在某些区域谐振波长存在跳变现象,长周期光纤光栅实际应用时应避开此区域。

Based on the coupled-mode theory,the complex characteristic equation of long-period fiber gratings coated with metal film and sensing film is set up. By using the perturbation method,the complex roots are obtained. The results are coincident with the results of Reference[5]. The curves of intensity and the transmission spectrums are significantly influenced by the extinction coefficient. The proportion of the even mode′s intensity in core is much larger than that of the odd mode′s intensity. Also,the amplitude of the attenuation peak of the even mode is much larger than that of the odd mode. So the even mode is taken as the research object when the metal coated long-period fiber grating sensor is optimized. Furthermore,the influence of metal and sensitive film parameters on the resonant characteristics is analyzed in theory. The results show the metal film thickness,sensitive film thickness and refractive index influence the resonant wavelength,which shifts towards the short wavelength with the increase of the metal film thickness,sensitive film thickness and refractive index. And there is a jumping phenomenon for film parameters,so the film parameters corresponding to the jumping phenomena must be discarded in actual applications of long period fiber gratings (LPFG).