TO-FDTD Method for Arbitrary Skewed Periodic Structures at Oblique Incidence

Abstract

For accurately modeling general periodic structures with arbitrary skewed grids at oblique incidence, a novel finite-difference time-domain (FDTD) method based on the transformation optics theory (TO-FDTD) is proposed in this article. First, by choosing the appropriate transformation of coordinate and applying the transformation optics theory, the original space of the skewed grid is mapped to the virtual space of the Cartesian grid, and the electromagnetic parameter tensors in the virtual space are known accordingly. Then, based on the covariance of Maxwell’s equations, both the basic difference equations and the boundary conditions of FDTD for the virtual space are derived. After that, the phase delay of the periodic boundary condition caused by the oblique incidence is eliminated by adopting the technique of field transformation, and the final explicit-iterative equations of the TO-FDTD method are obtained as well. At last, some examples are analyzed to verify the numerical properties of the proposed method. The idea of modeling based on the transformation optics theory is not only suitable for skewed periodic structures but also applicable for some ultrathin or (and) curved-surface structures after further expansion.