An Unconditionally Stable 1-D FDTD Algorithm for Modeling Chiral Media Based on Similar LOD Method

Abstract

An unconditionally stable scheme, which employs a similar technique to the locally one-dimensional (LOD) method, is proposed to study the one-dimensional (1D) nondispersive chiral media. In the proposed scheme, the recent new mesh-dividing method for bi-isotropic media is used. The method regards the two terms on the right-hand side of the rearranged curl equations as two directions and uses the LOD algorithm to deal with the equivalent two-dimensional (2D) problem. Through Fourier stability analysis and numerical simulation, it is found that the time-step size is not restricted by the Courant-Friedrich-Levy (CFL) stability condition, hence the proposed scheme is unconditionally stable. Compared with the similar Alternating Direction Implicit (ADI) method, the proposed scheme has lighter calculation burden and higher accuracy.Index Terms-Chiral media, finite-difference time-domain method (FDTD), locally one-dimensional (LOD), unconditionally stable.

ADI-FDTD Modeling of Tellegen Media

“…The main advantage of the LOD-and the ADI-FDTD techniques is that these schemes are unconditionally stable, the Courant condition is removed, and the time-step size is only limited by accuracy considerations. However, the stability analysis performed in [11] shows that the proposed formulation is unstable for the case of Tellegen media. Moreover, for Tellegen media, the stability condition of the approach presented in [12] is more restrictive than that of the conventional FDTD method.…”

“…However, the stability of these approaches has seldom been addressed. Recently, two FDTDbased implicit schemes have been presented for the modeling of monochromatic wave propagation in BI media [11], [12]. These works are based on the locally one-dimensional (LOD)and the alternating-direction implicit (ADI)-FDTD schemes, respectively.…”