Periodic dielectric or metallic structures have been a subject of continuing interest for applications to frequency selective or polarization selective devices in microwaves and optical waves. Various analytical or numerical techniques have been developed to formulate electromagnetic scattering from periodic scatterers. Recently, photonic bandgap structures in discrete periodic systems have received a growing attention, because they have many potential applications to narrow-band fiiters, high-quality resonant cavities, strongly guiding devices, and substrates for antennas. A one-dimensional periodic array of infinitely long cylindrical objects is typical of discrete periodic structures. The frequency response of the array is characterized by the scattering properties of individual cylinders and the multiple scattering due to the periodic arrangement of scatterers. When the array is layered, it constitutes a two-dimensional photonic bandgap structure. In the layered system, the multiple interaction of space-harmonics scattered from each of array layers pronounces the frequency response and the photonic bandgaps are formed in which any electromagnetic wave propagation is forbidden within a fairly large frequency range.
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