Improvement of accuracy and stability of FDTD algorithm regarding metamaterials

Abstract

For the last decade, metamaterials have received tremendous amount of interest. Metamaterials refract electromagnetic waves in desired directions. This unique property drew researcher’s attention in many fields such as physics, acoustics, astronomy, and military applications, etc. Increasing interest about metamaterials requires developments of accurate numerical algorithms regarding metamaterials. The Finite-Difference Time-Domain (FDTD) algorithm can analyze electromagnetic fields in the time domain and provide transient responses that cannot be provided by other frequency-domain algorithms such as the Finite-Element Method (FEM). However, the FDTD has some inherent problems such as stability, averaging between dislocated field nodes, stair-casing error that comes from different material parameters to the background. The problems were dealt with conventional materials many times before, on the other hand, the problems were less dealt with the metamaterials. However, these problems must be analyzed and resolved first for accurate FDTD simulations regarding metamaterials. In this study, we discuss limitations of conventional stability analysis schemes of FDTD and provide a new perspective of stability analysis regarding metamaterials. A new FDTD update equation with interpolation operations was proposed in the body region of metamaterial structures. The proposed algorithm was proved to be stable according to the new stability analysis scheme. At boundaries of metamaterials, the material parameters were matched to the background by using high-order polynomial functions in order to reduce stair-casing error. The proposed metamaterials were less sensitive to boundary abrasion compared to conventional metamaterials.