In this paper, an efficient Transmission Line Matrix (TLM) algorithm for modeling chiral media is presented. The formulation is based on auxiliary differential equations (ADE) of electric and magnetic current densities. Permittivity and permeability are assumed to follow the Lorentz model while chirality is assumed to follow the Condon model. The proposed method models the dispersive nature of permittivity, permeability, and chirality by adding both voltage and current sources in supplementary stubs to the conventional symmetrical condensed node (SCN) of the TLM method. The electromagnetic coupling appears explicitly in the update equations of the voltage and current sources. The algorithm is developed to simulate electromagnetic wave propagation in a chiral medium. The co-polarized and cross-polarized transmitted and reflected waves from a chiral slab due to a normal incident plane wave are calculated. Validation is performed by comparing the results obtained from the proposed method with those obtained analytically.
2. Zebiri, C. and F. Benabdelaziz, "Asymptotic approach for rectangular microstrip patch antenna with magnetic anisotropy and chiral substrate," World Academy of Science, Engineering and Technology, Vol. 2, 316-322, 2008.
3. Guven, K., et al., "Electromagnetic cloaking with canonical spiral inclusions," New J. Phys., Vol. 10, No. 11, 2008.
4. Li, M., L. Guo, J. Dong, and H. Yang, "An ultra-thin chiral metamaterial absorber with high selectivity for LCP and RCP waves," Journal of Physics D: Applied Physics, Vol. 47, 2014.
5. Tretyakov, S. A. and A. A. Sochava, "Proposed composite material for nonreflecting shields and antenna radomes," Electronics Letters, Vol. 29, No. 12, 1048-1049, 1993.
6. Prosvirnin, S. L. and N. I. Zheludev, "Analysis of polarization transformations by a planar chiral array of complex-shaped particles," Journal of Optics A: Pure and Applied Optics, Vol. 11, 2009.
7. Varadan, V. K., A. Lkhtakia, and V. V. Varadan, "Propagation in a parallel-plate waveguide wholly filled with a chiral medium," Journal of Wave-material Interaction, Vol. 3, No. 3, 267-272, 1988.
8. Grande, A., I. Barba, A. C. L. Cabeceira, J. Represa, P. P. M. So, and W. J. R. Hoefer, "FDTD modeling of transient microwave signals in dispersive and lossy bi-isotropic media," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 3, 773-783, 2004.
9. Akyurtlu, A., D. H. Werner, and K. Aydin, "Bi-FDTD: A new technique for modeling electromagnetic wave interaction with Bi-isotropic media," Microwave and Optical Technology Letters, Vol. 26, No. 4, 239-242, 2000.
10. Akyurtlu, A., D. H. Werner, and K. Aydin, "A novel FDTD technique for modeling chiral media," IEEE Antennas Propagation Society Int. Symp., Vol. 3, 1332-1335, Salt Lake City, UT, 2000.
11. Akyurtlu, A. and D. H. Werner, "Modeling chiral media using a new dispersive FDTD technique," IEEE Antennas Propagation Society Int. Symp., Vol. 1, 44-47, Boston, MA, 2001.
12. Akyurtlu, A. and D. H. Werner, "Analysis of double negative media with magneto-electric coupling using a novel dispersive FDTD formulation," IEEE Int. Symp. Antennas Propagation USNC/URSI Nat. Radio Science Meeting, Vol. 3, 371-374, Columbus, 2003.
13. Akyurtlu, A. and D. H. Werner, "BI-FDTD: A novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 416-425, 2004.
14. Akyurtlu, A. and D. H. Werner, "A Novel dispersive FDTD formulation for modeling transient propagation in chiral metamaterials," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 9, 2267-2276, 2004.
15. Demir, V., A. Z. Elsherbeni, and E. Arvas, "FDTD formulation for dispersive chiral media using the z transform method," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 10, 3374-3384, 2005.
16. Attiya, A. M., "Shift-operator finite difference time domain analysis of chiral medium," Progress In Electromagnetics Research M, Vol. 13, 29-40, 2010.
17. Grande, A., I. Barba, A. C. L. Cabeceira, J. Represa, K. Karkkainen, and A. H. Sihvola, "Two-Dimensional Extension of a Novel FDTD technique for modeling dispersive lossy bi-isotropic media using the auxiliary differential equation method," IEEE Microwave and Wireless Components Letters, Vol. 15, No. 5, 375-377, 2005.
18. Wang, M. Y., H. F. Mu, W. Chen, L. Zhao, and J. Xu, "FDTD analysis of chiral metamaterials slab by using the auxiliary differential equation algorithm," Frequenz, Vol. 67, No. 5-6, 155-161, DE Gruyter, 2013.
19. Pereda, J. A., A. Grande, O. Gonzalez, and A. Vegas, "FDTD modeling of chiral media by using the mobius transformation technique," IEEE Antennas and Wireless Propagation Letters, Vol. 5, 327-330, 2006.
20. Paul, J., C. Christopoulos, and D. W. P. Thomas, "Time-domain modeling of electromagnetic wave propagation in complex materials," Electromagnetics, Vol. 19, No. 6, 527-546, 1999.
21. Yaich, M. I., M. Khalladi, and M. Essaaidi, "Efficient modeling of chiral media using SCN-TLM method," Serbian Journal of Electrical Engineering, 249-254, 2004.
22. Cabeceira, C. L., A. Grande, I. Barba, and J. Represa, "A 2D-TLM model for electromagnetic wave propagation in chiral media," Antennas & Propagation Society International Symposium, Vol. 2, No. 5, 1487-1490, 2004.
23. Sihvola, A. H., "Electromagnetic modeling of bi-isotropic media," Progress In Electromagnetic Research, Vol. 9, 45-86, 1994.
24. Solymar, L., Electrical Properties of Materials, Oxford University Press Inc., New York, 2010.
25. Christopoulos, C., "The Transmission-Line Modeling (TLM) method in electromagnetics," Synthesis Lectures on Computational Electromagnetics, Morgan & Claypool, 2006.
26. Jin, H. and R. Vahldieck, "Direct derivation of the TLM symmetrical condensed node and hybrid symmetrical condensed node from Maxwell’s equations using centered differencing and averaging," IEEE Transactions on Microwave Theory and Techniques, Vol. 42, 2554-2561, Dec. 1994.
27. Zhao, R., T. Koschny, and C. M. Soukoulis, "Chiral metamaterials: Retrieval of the effective parameters with and without substrate," Optics Express, Vol. 18, No. 14, 14553-14567, Jul. 2010.