An electromagnetic theory, an art of four small equations, can propose revolutionary solutions for the development of advanced passive and active devices, even for next generation communication services. The electromagnetic theory and related numerical algorithms enable us to continuously study and invent the novel field formulations toward technological breakthrough. In this talk, two new methods, overlapping T-block method (OTM) for metal-only reflectarrays and scattering theory of diffraction (STD) for periodic structures, will be presented to emphasize how to apply the electromagnetic theory to solve major engineering problems.

An overlapping T-block method (OTM) for the problems of electromagnetic scattering and dispersion relations was proposed to obtain analytic yet numerically efficient closed-form solutions by combining a mode-matching technique (MMT) and a Green’s function approach (GFA). The OTM allows us to systematically divide an original geometry into several overlapping T-blocks, thus obtaining the novel analysis schemes for fast CPU time, better accuracy, and wide versatility. A metal-only reflectarray (MOR) antenna with ultra high gain (more than 50 dBi) was analyzed and designed by the OTM. Owing to the fact that the MOR is made up of metal only without any dielectrics, the MOR antenna has wideband, extremely low loss, high aperture efficiency, and high power capability for millimeter- and submillimeter-wave bands.

Dielectric periodic structures with very small radius have recently been used for nano-structures such as biosensors, nano-antennas, polarization selective surface, and terahertz transmission lines. Therefore, it is of theoretical and practical interest to rigorously obtain the asymptotic diffraction formulations of semi-infinite number of magnetodielectric periodic structures based on an scattering theory of diffraction (STD). The STD can be further extended to large number of periodic arrays for nano-structures. Using the mixed coordinate systems and common-area concept, analytic and fast-convergent scattering and dispersion equations of periodic circular cylinders were obtained. The proposed STD can be generalized to magnetodielectric periodic arrays with truncated edges by extending a diffraction methodology developed for metallic rectangular grooves.