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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
The approximation of the ratio of Bessel functions of the second-order of the second-order variants to the adja- cent order of the adja- cent order is derived. Lentz-Thompson method is used to calculate the value of the Bessel function of the first order of the adja- Floating-point system, the least significant bit. Thus, the problem that the Bessel function overflows the range of double-precision floating-point expression is solved when solving the characteristic equation of the large-core and large-value step-size optical fibers. The conduction mode characteristic equations of the multimode quartz optical fiber and the large diameter large numerical aperture polymer optical fiber are respectively solved. The calculated results of the conduction mode eigenvalues of the quartz optical fiber are the same as that of Optiwave’s software. For the polymer optical fiber, the algorithm gives The calculation results for all modes, where the mode angle ordinal number is less than 70, are calculated in the same way as Optiwave’s software, and Optiwave’s software can not calculate modes with an angular ordinal number greater than 70