The Unconditionally Stable Associated Hermite FDTD Method for 3-D Periodic Structure Analysis

Abstract

In this letter, the unconditionally stable associated hermite (AH) finite-difference time-domain (FDTD) method is extended to analyze three-dimensional (3-D) periodic structure. By combining the 3-D AH FDTD method and split-field technique, a 13-points coefficient matrix equation to eliminate phase shift is obtained with the corrected nonzero elements. To deal with the overflow at the periodic boundaries, the coefficient matrix is updated by the Floquet theory as long as the treatment of the angular points at the periodic boundary. The updating equation of the source term is derived by the total-field/scattered-field formula. The proposed method is verified by calculating the reflection coefficients of the infinite dielectric slab and the Jerusalem Cross FSS structure, respectively. The former shows a higher accuracy compared with the analytical solution with the average relative difference below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> 60 dB, and reflects less sensitive to the angle of incidence. And the later represents 7 times efficiency than that of the split-field FDTD method while keeping a sound accuracy.