本文详细研究了扇形截面柱状谐振腔与波导的亥姆霍兹方程求解问题．通过分离变量法，对电磁波在这类谐振腔及波导中的谐振与传播模式进行了系统分析，详细探讨了各种边界条件下电磁场的分布，并通过理论推导及数值仿真验证了分析的正确性和实用性．本文的研究对扇形截面柱状谐振腔与波导的设计和制造提供了理论基础．

This paper presents a detailed study on the solution of the Helmholtz equation for sectorial cylindrical resonators and waveguides. By employing the method of separation of variables, we systematically analyze the resonance and propagation modes of electromagnetic waves within such resonators and waveguides. The electromagnetic field distributions under various boundary conditions are thoroughly investigated. The correctness and practicality of the analysis are verified through theoretical derivations and numerical simulations. This study provides a theoretical foundation for the design and fabrication of sectorial cylindrical resonators and waveguides.