On the Behavior of Electromagnetic Field At Twisted Edges in Inhomogeneous Medium

Abstract

雖然，在早期文獻中對稜邊效應已有若干討論(1)(2)，直至Meixner研究電磁波衍射現象時，方始對邊稜條件加以界定(3)。晚近，有關數種不同介質具有共同邊稜之情況續有專文報導(5)至(7)；而在均勻介質中扭轉邊稜亦有研究成果(4)。適當的微分方程一經列出，所探察之結果隨之顯現。本文係探討在不均勻介質中扭轉稜邊左近電磁場之形態。但探討條件限於能量密度在一定區域內為具有可積分性者。列出Sturm-Liouville式微分方程，而以簡單列題表出具有本徵值之解。

The behavior of electromagnetic fields near a twisted edge in inhomogeneous medium is considered, starting from the condition that the energy density must be integrable over any finite domain. Differential equations of Sturm-Liouville type are then set up, which, together with relevant boundary conditions, determine the eigenvalues and accordingly the field behavior. Static fields are shown to have the same behavior in the neighborhood of such geometrical singularities. Media with pieceaise constant permeability and permittivity are discussed as application examples of the concept of "impedance" or "admittance" for solving the associated eigenvalue problems.