Electromagnetic Circuits

TL;DR

This paper constructs electromagnetic circuits analogous to elastic networks, characterizing their response matrices and demonstrating how structured ladder networks can exhibit novel, non-Maxwellian electromagnetic behaviors at a macroscopic level.

Contribution

It introduces electromagnetic circuits with a complete characterization of their response matrices and shows how ladder networks can produce unique macroscopic electromagnetic responses.

Findings

Complete characterization of response matrices $ ext{BW}$ for electromagnetic circuits.

Electromagnetic ladder networks can have non-Maxwellian continuum responses.

Structured networks exhibit novel electromagnetic behaviors.

Abstract

The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of them. They consist of thin triangular magnetic components joined at the edges by cylindrical dielectric components. (There are also dual electromagnetic circuits consisting of thin triangular dielectric components joined at the edges by cylindrical magnetic components.) Some of the edges can be terminal edges to which electric fields are applied. The response is measured in terms of the real or virtual free currents that are associated with the terminal edges. The relation between the terminal electric fields and the terminal free currents is governed by a symmetric complex matrix $\BW$. In the case where all the terminal edges are disjoint, and the frequency is fixed, a complete characterization is obtained of all possible response matrices $\BW$ both in the lossless and lossy cases. This is done by introducing a subclass of electromagnetic circuits, called electromagnetic ladder networks. It is shown that an electromagnetic ladder network, structured as a cubic network, can have a macroscopic electromagnetic continuum response which is non-Maxwellian, and novel.