Exact calculations of surface impedance for periodic rough surfaces

The concept of surface impedance has been widely used in electromagnetic theory of scattering. For a 2D scattering problem the impedance Z(x) on a surface ∑ can be defined as (1) where E║ and H║ represent the components of the electric and magnetic fields tangential to surface ∑, x is a coordinate on the surface and n^ the unit vector normal to it. If Z(x) is known, eq. (1) can be used as a boundary condition exactly equivalent to Maxwell’s, but since it is defined in terms of the fields this knowledge requires the complete solution of the scattering problem.