Complex Eigenmodes and Eigenfrequencies in Electromagnetics
| Autor: | Rahmeier, João G. Nizer, Tiukuvaara, Ville, Gupta, Shulabh |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A first comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures where the per unit length propagation phase shift ($\beta$) dependent complex eigenfrequencies $\Omega(\beta)$ are mapped to the frequency dependent complex propagation constant $\gamma(\omega_0)$ 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 $\{\Omega-\beta\}$ relationship is expressed using polynomial and Fourier series expansions, respectively. Consequently replacing $\{\Omega,~j\beta\}$ with $\{\omega_0, \gamma\}$ in the known $\{\Omega-\beta\}$ relation, a characteristic equation is formed which is then numerically solved for the two unknowns, representing the physical dispersion relation $\omega_0(\beta)$ and the frequency dependent propagation loss $\alpha(\omega_0)$ 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. Comment: 13 pages, 8 figures |
| Databáze: | arXiv |
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