Derivation and application of a class of generalized boundary conditions (electromagnetic scattering)

Boundary conditions involving higher order derivatives are presented for simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to nonplanar surfaces. As an illustration, a metal-backed uniform dielectric layer is simulated. It is shown that fourth-order conditions are capable of providing an accurate simulation for layers at least a quarter of a wavelength in thickness.<>