EM scattering from the edge of a semi-infinite planar strip grating using approximate boundary conditions

Electromagnetic scattering by the edge of a semi-infinite, dense planar grating of free-standing metallic strips is analyzed. The grating is illuminated by an arbitrarily polarized plane wave impinging on its edge at oblique incidence. The strips can be arbitrarily oriented with respect to the edge. An equivalent canonical problem is defined by adopting for the strip grating well-known approximate boundary conditions derived in the framework of homogenization techniques. The exact spectral solution for the above canonical problem is deduced by the application of the Sommerfeld-Maliuzhinets method, and explicitly depends on the grating parameters. The spectral solution is defined along the Sommerfeld integration contour and can be evaluated asymptotically to derive high-frequency expressions for the diffracted field. Some numerical results are presented to show that the above solution predicts a non vanishing diffracted field for any incident field polarization, and smoothly converges to the known solutions for both the perfectly conducting half-plane and the unidirectionally conducting half-plane, which are contained in the adopted strip-grating model as limit cases.