An analysis of transverse electric scattering from a rectangular channel in a conducting plane

The problem of transverse electric plane wave scattering from a rectangular channel which is engraved in a perfect conducting plane is investigated. A Fourier transform technique is employed to express the scattered field in the spectral domain in terms of parallel‐plate waveguide modes. The boundary conditions are enforced on the conducting surface and the channel aperture to obtain simultaneous equations for the transmitted field inside the channel. The simultaneous equations are solved to represent the transmitted field in a series form. By using the stationary phase approximation, the exact expression for the far‐zone scattered field is obtained and the echo width behavior is numerically studied in terms of the scattering angle, frequency, and channel size. It is found that the behavior of the echo width versus the channel depth exibits resonance irrespective of the size of the channel width. An approximate series expression (Kirchhoff solution) for the echo width is valid for high‐frequency scattering regimes (a > 2 λ). We also present an approximate closed form solution for nadir backscattering which is valid when a > 0.2λ.