Application of the Finite Element Method to the Scattering of a Two-Dimensional, Semi-Infinite Periodic Structure

摘要

Infinite periodic structures have been studied heavily because of their efficient filtering capabilities. They generally exhibit sharp frequency roll-offs at the frequency band of interest. In the RF region of the electromagnetic spectrum, periodic structures find applications such as radomes and photonic bandgap materials. Most studies have been done with infinitely periodic arrays because it is convenient to collapse an infinite array into one representative period using Floquet Analysis. This thesis formulates a Finite Element Method (FEM) solution of a semi-infinite periodic array consisting of infinite cylinders. The array elements sufficiently far from the edge are implemented using the concept of a Physical Basis Function (PBF). The PBF concept is based on an a priori knowledge that the amplitudes of the currents in the periodic elements that are sufficiently far from an edge are constant. Implementation of the PBF concept allows the solution domain of the FEM to be bounded by introducing a periodic boundary that represents the truncated portion of the periodic array. The periodic boundary is implemented by relating the fields there with a Floquet phase factor based on one periodic element external to the FEM domain. Performance of the periodic boundary at normal incidence is promising. At off-normal incidence, the implemented boundary performs poorly. Implementation of a periodic boundary by relating the fields there with a Floquet phase factor with one interior periodic element is the next stage in improving off-normal incidence performance.