TE-wave scattering from a shallow circular channel in a perfectly conducting plane

The problem of TE-wave scattering by a shallow circular channel in a perfectly conducting plane is considered and its rigorous series solution is also derived. By the region-matching technique, a semi-circular auxiliary boundary is introduced to divide the analyzed region into two subregions. The magnetic field of each subregion is represented in terms of an infinite series of wavefunctions with unknown coefficients. To include more practical applications, the wave source is assumed to be a Gaussian beam. The Kozaki's approximate expansion for Gaussian-beam incidence is adopted, which can convert into the plane-wave expansion with a special condition. With the enforcement of interface continuity conditions and the satisfaction of the channel surface boundary condition through the Graf's addition formula, the unknown expansion coefficients are determined. Comparisons for the semi-circular channel case with available data in the literature indicate excellent agreement. Pronounced effects of the depth-to-half-width ratio of the channel on backscattering width, far-field radiation pattern and equi-amplitude distribution of the magnetic field are illustrated by graphical results. The flexible and tunable features of the presented geometry make it easily applicable to the design and fabrication of multiple finite channels for optical devices.