Three-dimensional Electromagnetic Band-Gap Structures: Theory and Applications

In this chapter, a Fourier Modal Method (FMM) for accurate and efficient characterization of threedimensional (3D) Electromagnetic Band-Gap (EBG) materials is presented. The full-wave theory is described in detail. The EBG has a finite thickness and it is considered as a superposition of doubly periodic gratings, infinitely extending only in two dimensions. We employ the FMM with the correct Fourier factorization rules for discontinuous functions, obtaining a much faster convergence than with the customary approach. For a numerically stable treatment of the evanescent waves at the boundaries between different gratings, we use the S-matrix algorithm in the solution of the boundary problem. The potentiality of the approach in the analysis of electromagnetic crystals is discussed. Some applications are presented: an EBG with a complete 3D band-gap; a spatial, frequency and polarization filtering cavity; a woodpile superstrate to be employed for directivity-enhancing of planar antennas.