Electromagnetic plane-wave scattering from a sectorial groove in a perfectly conducting plane

Scattering characteristics of plane waves by a sectorial groove in a perfectly conducting plane are investigated. Both the transverse magnetic (TM) and transverse electric (TE) polarizations of the incident wave are considered. Judicious use of the region-matching technique provides a rigorous series solution to the problem. The analyzed region is separated into two sub-regions by choosing a semi-circular auxiliary boundary. The field in each sub-region is expanded as a summation of proper wave functions with unknown coefficients. Enforcing the matching of conditions on the auxiliary boundary and of boundary condition on the circular-arc surface of the groove leads to a linear set of equations and the unknown coefficients are then determined. Numerical results demonstrate the influence of central angles of the sectorial groove on echo width, far-field pattern and near-field distribution. The presented geometry is easily applicable to the design and fabrication of a grating structure for optical switches and tunable filters.