FDTD Implementation and Application of High Order Impedance Boundary Condition Using Rational Functions

An algorithm is proposed for the implementation of the high-order surface impedance boundary condition using the finite-difference time-domain method. The surface impedance function of a lossy medium is approximated by a series of rational functions in the Laplace domain, whereas the dyadic differential operator is approximated by a second-order power series. By assuming that the fields are piecewise linear, the time-domain convolution integrals are computed using a recursive formula. The impedance function of a coating layer is approximated by a third-order power series. The algorithm can be applied to scattering problems of a three-dimensional coating for both vertically and horizontally polarized waves. The advantage of the proposed method is that the result can be applied to media of arbitrary conductivities, with a wide range of incident angles from zero to graze. Some numerical examples are given to substantiate the theory.