基于麦克斯韦方程的亥姆霍兹方程推导及电磁波极化规律研究
Derivation of the Helmholtz Equation Based on Maxwell\'s Equations and Research on Polarization Laws of Electromagnetic Waves
胡敏慧 1朱敏 1张敏1
作者信息
- 1. 辽宁工程技术大学电子与信息工程学院，辽宁省兴城市，125100
- 折叠
摘要
本文系统梳理了从麦克斯韦方程组到亥姆霍兹方程的理论推导，并深入研究了均匀平面波的极化规律。依托均匀无耗无源各向同性介质模型，利用矢量微分恒等式与时谐场复数表示法，严格推导了齐次亥姆霍兹方程。以沿z轴正向传播的均匀平面波为对象，通过调控正交电场分量的振幅与相位差，系统分析了线极化、圆极化和椭圆极化的形成机理。研究证实，亥姆霍兹方程是频域电磁分析的核心控制方程，全部极化形态均可由两路正交线极化波相干叠加生成，线极化和圆极化分别是椭圆极化在特定参数下的两类极限形式。文中辅以逻辑流程图、极化轨迹示意图及量化对比表格，为理论研究提供了直观支持。研究成果可为射频天线优化、卫星通信极化匹配及微波遥感探测等工程应用提供理论依据
Abstract
This paper systematically derives the Helmholtz equation from Maxwell\'s equations and investigates the polarization laws of uniform plane waves. Based on the model of lossless, source-free, and isotropic homogeneous medium, the homogeneous Helmholtz equation is rigorously derived using vector differential identities and the complex representation of time-harmonic electromagnetic fields. Taking uniform plane waves propagating along the positive z-axis as the research object, the formation mechanisms of linear, circular, and elliptical polarizations are systematically analyzed by adjusting the amplitude ratio and phase difference of orthogonal electric field components. The research verifies that the Helmholtz equation is the core governing equation for frequency-domain electromagnetic analysis, that all polarization modes can be generated by the coherent superposition of two orthogonal linearly polarized waves, and that linear and circular polarizations are two limiting forms of elliptical polarization under specific parameters. The paper is supplemented with logic flowcharts, schematic polarization trajectory diagrams, and quantitative comparison tables to provide intuitive support for theoretical research. The results can provide theoretical basis for engineering applications such as radio frequency antenna optimization, polarization matching in satellite communication, and microwave remote sensing detection.关键词
麦克斯韦方程组/亥姆霍兹方程/均匀平面波/电磁波极化/轴比/通信天线Key words
Maxwell\'s equations/Helmholtz equation/uniform plane wave/electromagnetic wave polarization/axial ratio引用本文复制引用
胡敏慧,朱敏,张敏.基于麦克斯韦方程的亥姆霍兹方程推导及电磁波极化规律研究[EB/OL].(2026-06-22)[2026-06-24].http://www.paper.edu.cn/releasepaper/content/202606-57.学科分类
电工基础理论/通信
