Kirchoff law for antennae: Solution of Maxwell's equation in the presence of metallic wire structures.


siu tat Chui

10:00:00 - 11:00:00

R202 , Astronomy and Mathematics Building

A modular and physical way to understand the interaction of electromagnetic waves and metallic wire structures consists of an equivalent circuit theory, which includes circuit parameters such as the inductances and the capacitances of the circuit. For uniform currents along each wire, the behavior of currents in a network is governed by Kirchoff's laws. In general, the current distribution along the wires is not uniform and the circuit element cannot be approximated by a single ``local'' lumped element; the modulation of the current along its path has to be taken into consideration. We have developed a method by expanding the current distribution along the wire not as finite elements but in terms of entire domain basis functions such as a Fourier series. Usually the electromagnetic waves are slowly varying. However, the boundary conditions of current conservation at wire ends and junctions involve many Fourier modes. We find a simple way of implementing the boundary condition by introducing auxiliary variables. We found that our approach provides for a physical and numerically very efficient way to understand metallic wire networks. For example, there is a folklore that, for a metallic wire of arbitrary shape of length L, the resonance wavelengths is close to twice its length divided by an integer, =2L/n, but no proof has ever been given. In our approach, we can show that this is true in the thin wire limit. We tested our code for some examples and find that it is two orders of magnitude faster than current commercial codes.