1.1 Historical Perspective on the Research in Periodic Structures
The class of periodic structures has been a subject of continuing interest in the literature. The main effort in the past has been on the scattering and guiding of waves by one-dimensional (1D) periodic structures. In particular, the microwave field has employed periodic structures in many different applications, of which a few examples are linear accelerators, slow-wave structures in microwave tubes, filters, artificial dielectrics, slot arrays, phase-array antennas, frequency-selective structures, leaky-wave antennas, and so on. On the other hand, the 1D periodic structure also has its own applications in optical engineering; for example, in dielectric gratings used in integrated-optics applications (Tamir 1975, 1979) (diffraction gratings for beam splitting, grating couplers, and leaky-wave structures).
In recent years, considerable attention has been focused on the numerical and experimental studies of wave phenomena associated with two-dimensional (2D) and three-dimensional (3D) structures, and many applications have been demonstrated. Most of the potential applications were found and developed in the optics community, such as the photonic crystal. A photonic crystal contains dielectric or metallic inclusions periodically arranged in a 2D or 3D lattice pattern; these mimic a natural crystal with a small and basic building block of atoms or molecules repeated in space. The periodic nature ...