Table of Contents Author Guidelines Submit a Manuscript
International Journal of Antennas and Propagation
Volume 2012, Article ID 170963, 16 pages
Research Article

A Coupled-Field Expansion Method for Single-Layer and Multilayer Planar Periodic Structures

1Center for Electromagnetic and Antenna Engineering, Department of Electronic Engineering, Macquarie University, Sydney, NSW 2109, Australia
2China Aerospace Science and Technology Corporation, Number 5 Academy, Number 513 Institute, Yantai 264000, China

Received 10 July 2011; Accepted 28 December 2011

Academic Editor: Wei Hong

Copyright © 2012 Yading Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new, rigorous, field-based, seminumerical analysis method is presented to obtain the reflection and transmission coefficients of 2D planar periodic structures with arbitrarily shaped metallization patterns for both normal and oblique incidence conditions. It is useful for the analysis, design, and optimization of many single-layer and multilayer planar structures, such as frequency-selective surfaces (FSSs), artificial magnetic conductor (AMC) surfaces, electromagnetic bandgap (EBG) structures, some metamaterials and high-impedance surfaces. In this coupled-field expansion method (CFEM), the x- and y-components of the vector magnetic potential in each homogeneous region in a unit cell are expanded in terms of Bloch-Floquet modes and the solution to the coupled-field problem is formulated. The unique, analytical formulation presented here leads to a linear system with reasonably simple matrix elements. By cascading the matrices representing each interface, multilayer periodic structures are analyzed in a very flexible way. Being field based, CFEM does not require substrate Green's functions to analyze surfaces printed on dielectric substrates. The method was validated by analyzing one single-layer periodic surface (a printed AMC on a dielectric substrate) and one multilayer periodic surface (a circular polarizer) and comparing CFEM results with HFSS results.