Mathematical Analysis of Electromagnetic Guided Propagation and Scattering in Millimeter-Wave and Optical Fields

After the year 1960, mathematical analysis for electromagnetic scattering, diffraction and guided field with complicated boundaries have been developed, based on field analysis methods shown in the previous period around years of 1950. J. A. Kong, K. Hongo and we are belonging to such investigation generation. Millimeter wave and optical technologies have rapidly grown after the coherent millimeter wave devices and lasers have been investigated. Here, some typical studies are shown. Novel mathematical method of integral equation method with conformal mapping is discussed for asymptotic diffraction of electromagnetic field by complicated boundaries, such as an elliptic cylinder perturbed by the circular cylinder. Mode conversions of millimeter wave fields in the waveguide junction between over size circular waveguide and conical horn are investigated by the asymptotic diffraction theory. Field characteristics of the Fabry-Perot resonator with finite circular curved disks are analyzed by the vector integral equations. General scattering and transmission characteristics of beam waves in curved boundaries with wedges are analyzed by spectral function method.