Asymptotic boundary condition for corrugated surfaces, and its application to scattering from circular cylinders with dielectric filled corrugations

A simple asymptotic solution for periodic corrugated surfaces when the corrugation period approaches zero is presented. The authors enforce an asymptotic boundary condition between the region inside the corrugations and the outer region, after a simple expansion of the fields in the corrugated region. This expansion is obtained by considering the corrugated region as a homogeneous region inside which the fields have no derivatives in the direction normal to the walls of the corrugations. The asymptotic corrugation boundary condition (ACBC) replaces the use of Floquet mode expansions (FME) of the field in the outer region, and it overcomes the known limitations of the surface impedance approach. The authors show how to apply the method to calculate the plane wave scattering from a circular cylinder with dielectric-filled corrugations. The series solution is obtained and verified with a solution based on Floquet mode expansions. Excellent agreement is obtained between the two solutions after introducing the ratio of the corrugation width (w) and the period (p) into the ACBC and with λ/p is about 10 or more