Realizable design of field taper via coordinate transformation

Complex electromagnetic structures can be designed by exploiting the concept of spatial coordinate transformations. In this paper, we define a coordinate transformation scheme that enables one to taper the electric field between two waveguides of different cross-sections. The electromagnetic field launched from the wide input waveguide is compressed in the proposed field tapering device and guided into the narrow output waveguide. In closed rectangular waveguide configurations, the taper can further play the role of a mode selector due to the output waveguide's cut-off frequency. Realizable permittivity and permeability values that can be achieved with common existing metamaterials are determined from the transformation equations and simplified by a proposed parameter reduction method. Both a 2D continuous design model and a potential 3D discretized realization model are presented at microwave frequencies and the performances of the tapering devices are verified by full-wave finite element numerical simulations. Finally, near-field distributions are shown to demonstrate the field tapering functionality.