镀金属四包层长周期光纤光栅特征方程的建立与求解

Establishment and solution of the characteristic equation of metal-coated quadruple clad long-period fiber grating

根据耦合模理论,建立了镀金属四包层长周期光纤光栅气体传感器的模型和特征方程,讨论了由于金属的复折射率虚部较大,引起特征方程中贝塞尔函数溢出的问题.提出了采用在贝塞尔函数源程序中乘上一个缩放因子解决溢出问题的方法,并给出了3种解决办法———积分法、幂级数法和渐进展开法.

Based on coupled-mode theory, the general model and characteristic euqation of metal-coated quadruple clad long-period fiber grating gas sensors are established. The problem of overflow of the Bessel functions caused by the big imaginary part of the complex refractive index of metal is discussed detailedly. The solution is given by a programmed scaling of each step of the calculation of the Bessel functions. In addition, three procedures （the integral method, the power series, and the asympotic expansion） are discussed detailedly.