Surface distribution and field dependency upon the radius of curvature at smoothed corners of a scatterer

Previous numerical studies [1], [6] have demonstrated that, under E-polarized illumination, the maximum difference in the farfield patterns of an infinite cylindrical structure scatterer with a right-angle corner, and its rounded counterpart, is proportional to (kρ)^4/3, where ρ denotes the radius of curvature in the vicinity of the rounded corner point, as kρ → 0. A theoretical basis for these numerical results is derived by solving an approximate integral equation for the difference in the surface currents on a test structure, the lemniscate, and its rounded counterpart.