±1/2阶快速Hankel变换及其在电磁场计算中的应用  

Fast Hankel Transforms with ±1/2 Order and Their Applications in Electromagnetic Calculating

作　　者：宋岁轩 陈桂波 张烨[1] 卢俊 SONG Suixuan;CHEN Guibo;ZHANG Ye;LU Jun(School of Physics,Changchun University of Science and Technology,Changchun 130022;Editorial Department of Journal,Changchun University of Science and Technology,Changchun 130022)

机构地区：[1]长春理工大学物理学院,长春130022 [2]长春理工大学学报编辑部,长春130022

出　　处：《长春理工大学学报（自然科学版）》2024年第4期9-17,共9页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：吉林省自然科学基金学科布局项目(20210101186JC)。

摘　　要：针对±1/2阶快速Hankel变换的滤波系数进行了设计研究,并将其用于水平层状正交各向异性介质中电磁场的计算。首先,利用Fourier变换以及传播矩阵法将空间域电磁场表示成二维无穷积分形式,并利用欧拉公式将其转化为包含±1/2阶Bessel函数的半无穷积分。然后,利用矩阵反演方法设计了三种不同长度的±1/2阶快速Hankel变换滤波系数,以提高电磁场计算效率。最后,通过设计一个五层正交各向异性介质模型计算了其电磁场分布,并与直接积分方法进行对比,从而检验了设计的±1/2阶快速Hankel变换的计算精度与效率。研究方法可用于复杂介质中电磁场的快速计算,也可为目标电磁成像提供一定基础,具有重要的理论与实际意义。In this paper,the filter coefficients of fast Hankel transforms with ±1/2 order were designed and studied,and used to calculate the electromagnetic fields in horizontal layered orthogonal anisotropic media.Firstly,Fourier transform and propagation matrix method were used to represent the electromagnetic fields in space domain into the form of twodimensional infinite integrals,and Euler's formula was used to transform them into semi-infinite integrals including ±1/2Bessel functions.Then,three different lengths of filter coefficients for Hankel transform with ±1/2 order were designed by using matrix inversion method to further improve the computational efficiency of electromagnetic fields.Finally,five-layered orthogonal anisotropic media model was designed to calculate the distributions of electromagnetic fields,and compared with the results calculated by direct integral method,thus verifying the calculation accuracy and efficiency of the fast Hankel transforms with ±1/2 order designed in this paper.The method presented in this paper can be used for the rapid calculation of the electromagnetic fields in complex media,and can also provide a certain basis for the electromagnetic imaging of the target,which has important theoretical and practical significance.

关 键 词：±1/2阶 BESSEL函数 快速Hankel变换 电磁计算 

分 类 号：O441.4[理学—电磁学]