大芯径大数值孔径阶跃光纤传导模特征方程求解

导出了相邻阶第二类变型贝塞尔函数的比值在小宗量的逼近形式，利用Lentz—Thompson方法计算相邻阶第一类贝塞尔函数的比值在小宗量的值，计算精度为浮点数系统的最低有效位。从而解决了求解大芯径、大数值孔径阶跃光纤的特征方程时．贝塞尔函数溢出双精度浮点数表示范围的问题。分别对多模石英光纤和大芯径大数值孔径的聚合物光纤的传导模特征方程进行了求解，石英光纤的传导模特征值计算结果与Optiwave公司的软件一致；对于聚合物光纤，算法给出了所有模式的计算结果，其中模式角向序数小于70的计算结果与Optiwave公司的软件一致，而Optiwave公司的软件不能计算角向序数大于70的模式。

Propagation Constant Solution for Large Core and High Numerical Aperture Step-Index Multimode Optical Fiber

Overflow of Bessel functions in numerical solution of characteristic equation with double precision for large core and high numerical aperture optical fibers is circumvented by evaluating the ratio of the n th order to the (n-1) th order modified Bessel functions of the second kind using a small argument approximation and by evaluating the ratio of n th order to the (n-1) th order Bessel function of the first kind using Lentz Thompson method. The evaluation error of the two methods is not larger than the minimum value of the floating point system used. Characteristic equations of multimode silica optical fiber and large core polymer optical fiber are solved using this algorithm and compared with commercial optical software (IFO Grating) from Optiwave Corp. The results for the silica optical fiber are good agreement with the commercial software. Authors' algorithm has solved all guided modes for the large core optical fiber and results for the guided modes with angular mode number smaller than 70 are same to that of IFO Grating, but IFO Grating failed to solve the eigenvalue for guided modes with angular mode number larger than 70.