Properties of electromagnetic scattering from periodic metallic structures: Application to frequency-selective and bandgap structures

The focus of this dissertation is the scattering of electromagnetic plane waves by infinite periodic structures composed of electrical conductors. The periodicity is two dimensional (planar), but the periodic scatterer need not be two dimensional. Although the problem is infinite in extent, the use of Floquet's Theorem can reduce the extent of the problem to one periodic cell. Floquet's Theorem reduces the scattered fields to an infinite summation of plane waves (modes), of which only a finite set is propagating (the rest of the modes are decaying or evanescent). In this dissertation, the main focus is on the behavior of the lowest order (dominant) mode as a function of frequency and angle of incidence. The dominant mode is the mode which propagates (reflection and/or transmission) along the specular direction (satisfying Snell's Law). Finding the reflection (or transmission) coefficient involves solving an integral equation via the Method of Moments, which transforms the integral equation into a matrix equation.;The work in this dissertation exposes several substantial contributions to the body of knowledge of electromagnetic scattering from periodic structures. The contributions include: (A) Analytical derivations of constraints on the values that the reflection coefficient can assume. The analysis also includes constraints on ohmic losses, grating lobes, and cross-polarization. (B) Showing the existence of infinite Q (zero bandwidth) resonances that can occur for infinite periodic structures when the excitation has an odd symmetry. (C) Exposing conditions where the problem can become ill-posed, due to instability. An ill-posed problem gives rise to a singular matrix (matrix determinant → 0), so care must be taken to ensure solution accuracy. (D) Effective implementation of a matrix interpolation scheme in order to reduce the total computer simulation time. Calculation of the matrix elements is the most time constraining task of the simulation, so significant speedup can result with matrix interpolation. (E) Explanation of the effect of tilting the periodic scatterers. The behavior of the resonance of a dipole array is investigated as a function of the tilt angle. (F) Analysis of very closely coupled arrays, which are shown to be good building blocks for bandgap structures (structures that reflect 100% of the energy for all angles of incidence within a certain frequency range). The close coupling gives rise to a capacitive effect.