论文标题
电磁学中复杂的本征和本征频
Complex Eigenmodes and Eigenfrequencies in Electromagnetics
论文作者
论文摘要
对一般有损波电磁结构进行了对复杂本本型的首次全面处理，其中每单位长度繁殖相位移位（$β$）依赖性复杂的eigenfrequencies $ω（β）$映射到频率相关的复杂复杂的复合复杂的复合复杂的繁殖常量$γ（ω_0）$ for verlecter vertrole for Vertrol electermagnection colvery complectent $γ（β$）$。提出了严格的程序，以首先计算均匀和周期电磁结构的复杂本征模，它们使用全波模拟和已知的分析结果确认。对于任意统一和周期性结构，进一步提出了两个映射程序，其中已知的$ \ {ω-β\} $分别使用多项式和傅立叶级数扩展表示。因此，将$ \ {ω，〜jβ \} $替换为$ \ {ω_0，γ\} $在已知的$ \ {ω-β\} $之间的关系中，形成了一个特征方程，然后形成一个特征方程，然后将其数值求解，以表示两个未知数，代表了物理相关关系，代表了分散性关系$ω__0（频率）$ω_0（和频率）$ω_0（cypy）和频率β0（proveny）（和结构的$α（ω_0）$。在各种情况下，都证明了映射程序，包括无限均匀的介质，矩形波导，DRUDE分散式分离材料和周期性介电堆栈，在所有频率跨越频率的所有情况下，在所有情况下都成功地检索了确切的传播特性。
A first comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures where the per unit length propagation phase shift ($β$) dependent complex eigenfrequencies $Ω(β)$ are mapped to the frequency dependent complex propagation constant $γ(ω_0)$ for variety of electromagnetic structures. Rigorous procedures are presented to first compute the complex eigenmodes of both uniform and periodic electromagnetic structures which are confirmed using full-wave simulations and known analytical results. Two mapping procedures are further presented for arbitrary uniform and periodic structures, where the known $\{Ω-β\}$ relationship is expressed using polynomial and Fourier series expansions, respectively. Consequently replacing $\{Ω,~jβ\}$ with $\{ω_0, γ\}$ in the known $\{Ω-β\}$ relation, a characteristic equation is formed which is then numerically solved for the two unknowns, representing the physical dispersion relation $ω_0(β)$ and the frequency dependent propagation loss $α(ω_0)$ of the structure. The mapping procedure is demonstrated for variety of cases including unbounded uniform media, rectangular waveguide, Drude dispersive metamaterial and a periodic dielectric stack, where exact propagation characteristics have been successfully retrieved in all cases across both passbands and stopbands across frequency.
