A LOD-like method that characterizes the analytical solution is proposed to study the one-dimensional (1-D) chiral media. Through theoretical analysis and numerical simulation, it is found that the proposed scheme is unconditionally stable. This scheme employs the new mesh-dividing method for bi-isotropic media, in which the two sections on the right side of the rearranged curl equations are regarded as two directions and the LOD-like algorithm is used to deal with the equivalent two-dimensional (2-D) problem. In the first substep, the conventional LOD method is used in computation, while for the second substep, the analytical solution is employed instead. By simulating the polarization rotation of a mono-frequency linear polarized wave both in a 1-D homogeneous chiral media and through a chiral slab, the scheme is testified to be unconditionally stable.
2. Sun, C. and C. W. Trueman, "Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations," Electron. Lett., Vol. 39, No. 7, 595-597, 2003.
3. Shibayama, J., et al., "Efficient implicit FDTD algorithm based on locally one-dimensional scheme," Electron. Lett., Vol. 41, No. 19, 1046-1047, 2005.
4. Grande, A., et al., "FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 3, 773-784, 2004.
5. Grande, A., et al., "Two-dimensional extension of a novel FDTD technique for modeling dispersive lossy bi-isotropic media using the auxiliary differential equation method," IEEE Microw. Wireless Compon. Lett., Vol. 15, No. 5, 375-377, 2005.
6. Ji, F., K. N. Yung Edward, and X. Q. Sheng, "Three-dimensional FDTD analysis of chiral discontinuities in the waveguide," Int. J. Infrared Millimeter Waves, Vol. 23, No. 10, 1521-1528, 2002.
7. Demir, V., A. Elsherbeni, and E. Arvas, "FDTD formulations for scattering from three dimensional chiral objects," 20th Annual Review of Progress in Applied Computational Electromagnetics, Syracuse, NY, 2004.
8. Akyurtlu, A., "Modeling of bi-anisotropic media using the finite-difference time-domain method,", Ph.D. dissertation, Dept. of Electrical Engineering, Pennsylvania State Univ., University Park, 2001.
9. Akyurtlu, A. and D. H. Werner, "BI-FDTD: A novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media ," IEEE Trans. Antennas Propag., Vol. 52, No. 2, 416-425, 2004.
10. Alcantara, L. D. S., "An unconditionally stable FDTD method for electromagnetic wave propagation analysis in bi-isotropic media," IEEE MTT-S, 661-664, Brasilia, Brazil, 2006.
11. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media, Artech House, MA, 1994.
12. Sihvola, A. H., "Electromagnetic modeling of bi-isotropic media," Progress In Electromagnetics Research, Vol. 09, 45-86, 1994.
13. Kuzu, L., V. Demir, A. Z. Elsherbeni, and E. Arvas, "Electromagnetic scattering from arbitrarily shaped chiral objects using the finite difference frequency domain method," Progress In Electromagnetics Research, Vol. 67, 1-24, 2007.
14. Shi, Y. and C. H. Chan, "Solution to electromagnetic scattering by bi-isotropic media using multilevel Green's function interpolation method," Progress In Electromagnetics Research, Vol. 97, 259-274, 2009.
15. Topa, A. L., C. R. Paiva, and A. M. Barbosa, "Electromagnetic wave propagation in chiral H-guides," Progress In Electromagnetics Research, Vol. 103, 285-303, 2010.
16. Gomez, A., et al., "Full-wave hybrid technique for 3D isotropic-chiral-material discontinuities in rectangular waveguides: Theory and experiment," IEEE Trans. Microwave Theory Tech., Vol. 56, No. 12, 2815-2825, 2008.
17. Stefanski, T. and T. D. Drysdale, "Improved implementation of the Mur first-order absorbing boundary condition in the ADIFDTD method," Microwave Opt. Technol., Vol. 50, No. 7, 1757-1761, 2008.