Within the framework of the finite-difference time-domain (FDTD) and the weighted Laguerre polynomials (WLPs), we derive an effective update equation of the electromagnetic in the dispersive media by introducing the factorization-splitting (FS) schemes and auxiliary differential equation (ADE). As two examples, we employ a 2-D parallel plate waveguide loaded with two dispersive medium columns and a thin grapheme sheet to calculate the plane wave propagation by using the FS-ADE-WLP-FDTD method. Compared with the ADE-FDTD and the ADE-WLP-FDTD methods, the results from our proposed method show its accuracy and efficiency for dispersive media simulation.
2. Namiki, T., "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microw. Theory Tech., Vol. 7, No. 10, 2003-2007, Oct. 1999.
3. Kantartzis, N. V., T. T. Zygiridis, and T. D. Tsiboukis, "An unconditionally stable higher order ADI-FDTD technique for the dispersionless analysis of generalized 3-D EMC structures," IEEE Trans. Magn., Vol. 40, No. 3, 1436-1439, Mar. 2004.
4. Kantartzis, N. V., D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn., Vol. 43, No. 4, 1329-1332, Apr. 2007.
5. Shibayama, J., M. Muraki, J. Yamauchi, and H. Nakano, "Efficient implicit FDTD algorithm based on locally one-dimensional scheme," Electron. Lett., Vol. 41, No. 19, 1046-1047, Sep. 2005.
6. Rana, M. and A. Mohan, "Segmented-LOD-FDTD for electromagnetic propagation inside large complex tunnels," IEEE Trans. Magn., Vol. 48, No. 2, 223-226, Feb. 2012.
7. Kantartzis, N. V., T. Ohtani, and Y. Kanai, "Accuracy-adjustable nonstandard LOD-FDTD schemes for the design of carbon nanotube interconnects and nanocomposite EMC shields," IEEE Trans. Magn., Vol. 49, No. 5, 1821-1824, May 2013.
8. Chung, Y. S., T. K. Sarkar, B. H. Jung, and M. Salazar-Palma, "An unconditionally stable scheme for the finite-difference time-domain method," IEEE Trans. Microw. Theory Tech., Vol. 51, No. 3, 697-704, Mar. 2003.
9. Chen, W.-J., W. Shao, and B.-Z. Wang, "ADE-Laguerre-FDTD method for wave propagation in general dispersive materials," IEEE Microw. Wireless Compon. Lett., Vol. 23, No. 5, 228-230, May 2013.
10. Chen, Z., Y. T. Duan, Y. R. Zhang, and Y. Yi, "A new efficient algorithm for the unconditionally stable 2-D WLP-FDTD method," IEEE Trans. Antennas Propag., Vol. 61, No. 7, 3712-3720, Jul. 2013.
11. Gandhi, O. P., B. Q. Gao, and J. Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 4, 703-708, Apr. 2007.
12. Ha, M. and M. Swaminathan, "A Laguerre-FDTD formulation for frequency-dependent dispersive materials," IEEE Microw. Wireless Compon. Lett., Vol. 21, No. 5, 225-227, May 2011.
13. Hanson, G. W., "Dyadic Greens functions and guided surface waves for a surface conductivity model of graphene," J. Appl. Phys., Vol. 103, No. 6, 064302, Mar. 2008.