电子学报2025，Vol.53Issue(12)：4288-4295,8.DOI:10.12263/DZXB.20250644
球坐标系下异形金属谐振腔电磁特性的解析分析
Analytical Analysis of Electromagnetic Properties of Shaped Metal Resonant Cavity in Spherical Coordinate System
摘要
Abstract
As the general solution of the Helmholtz equations for spherical resonant cavities analyzed with the sepa⁃rated-variable method only takes the integer-order first-type associated Legendre function,it is confined to characterize the electromagnetic properties of the shaped-metal resonant cavity derived from this structure invalidly.To address the afore⁃mentioned drawbacks,in this study,a universal analytical analytical framework of electromagnetic properties of shaped met⁃al resonant cavity is proposed.The first and the second type of arbitrary order and degree of associated Legendre functions are constructed by introducing the generalized hypergeometric function,so as to complete the general solution of Helmholtz equations.Based on this,the analytical solutions of the electromagnetic fields of the fundamental and higher-order modes in the transverse magnetic and transverse electric modes are derived based on the Borgins'method of potential function,as well as verified by finite element numerical simulations.The results indicated that the relative errors between the analytical and numerical solutions for the resonance frequencies of fundamental and higher-order modes are 0.070％and 0.069％,re⁃spectively.Furthermore,the normalized electromagnetic field distributions of both solutions are mutually consistent,with root-mean-square errors of only 1.670×10-3 and 2.667×10-3,respectively,validating the accuracy and reliability of the re⁃search method.This study not only successfully extends the conclusion of classical spherical cavities to shaped structures,but also expands the application scope of analytical modeling of electromagnetic fields,which is instrumental to precise de⁃sign of novel microwave and optical devices.关键词
异形金属谐振腔/分离变量法/球坐标/亥姆霍兹方程/任意阶、次连带勒让德函数/伯格尼斯位函数Key words
shaped metal resonant cavity/separate variables method/spherical coordinates/Helmholtz equation/ar⁃bitrary order and degree of associated legendre functions/Borgins'potential function分类
信息技术与安全科学引用本文复制引用
李德贵,孙琦,马子寅,梅中磊..球坐标系下异形金属谐振腔电磁特性的解析分析[J].电子学报,2025,53(12):4288-4295,8.基金项目
国家重点研发计划(No.2019YFA0405403) National Key Research and Development Program of China(No.2019YFA0405403) （No.2019YFA0405403）
