Wave Equation Solution for Electromagnetic Field Incident on Planar Conducting Arrays

摘要

A new wave equation solution is presented for analyzing planar periodic patch or aperture arrays having complex conductivity with an arbitrary distribution. The approach extends prior developments in photonic band-gap theory by including the conductivity mechanism. The wave equation is written in the form Schrodinger's equation. Solutions are obtained in the spectral domain for the radiated field in terms of a summation of plane waves. The method provides valuable physical insights not readily obtainable using conventional solutions for periodic arrays. Incident and radiated fields are related in a single mathematical expression. This expression shows how each radiated field mode is coupled to the others via mutual capacitive and inductive terms. The theory may be readily extended to multiple layers.