2009-05-25
Uniaxial PML Absorbing Boundary Condition for Truncating the Boundary of DNG Metamaterials
By
Progress In Electromagnetics Research Letters, Vol. 8, 125-134, 2009
Abstract
The conventional perfectly matched layer (PML) absorbing boundary condition is shown to be unstable when it is extended to truncate the boundary of the double negative (DNG) medium. It is a consequence of the reverse directions of the Poynting and phase-velocity vectors of plane waves propagating in such material. In this paper, a modified uniaxial PML (UPML), which is stable for the DNG medium, is derived. The auxiliary differential equation technique is introduced to derive the discrete field-update equations of DNG-UPML. Numerical results demonstrate the effectiveness and stability of the new UPML for the DNG medium.
Citation
Kuisong Zheng, Wai-Yip Tam, De-Biao Ge, and Jia-Dong Xu, "Uniaxial PML Absorbing Boundary Condition for Truncating the Boundary of DNG Metamaterials," Progress In Electromagnetics Research Letters, Vol. 8, 125-134, 2009.
doi:10.2528/PIERL09030901
References

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp., Vol. 10, No. 4, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699        Google Scholar

2. Shelby, R. A., D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission though a two-dimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett., Vol. 78, 489-491, 2001.
doi:10.1063/1.1343489        Google Scholar

3. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
doi:10.1126/science.1058847        Google Scholar

4. Smith, D. R. and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett., Vol. 85, 2933-2936, 2000.
doi:10.1103/PhysRevLett.85.2933        Google Scholar

5. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letter, Vol. 85, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966        Google Scholar

6. Wittwer, D. C. and R. W. Ziolkowski, "Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media," IEEE Trans. Antennas Propag., Vol. 48, No. 2, 192-199, 2000.
doi:10.1109/8.833068        Google Scholar

7. Wittwer, D. C. and R.W. Ziolkowski, "Maxwellian material based absorbing boundary conditions fro lossy media in 3D," IEEE Trans. Antennas Propag., Vol. 48, 200-213, 2000.
doi:10.1109/8.833069        Google Scholar

8. Berenger, J. P., "A perfectly matched layer for the absorbing EM waves," J. Computat. Phys., Vol. 114, 185-200, 1994.
doi:10.1006/jcph.1994.1159        Google Scholar

9. Dong, X. T., X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly matched layer-absorbing boundary condition for left-handed materials," IEEE Microwave Wireless Compon. Lett., Vol. 14, 301-303, 2004.
doi:10.1109/LMWC.2004.827104        Google Scholar

10. Cummer, S. A., "Perfectly matched layer behavior in negative refractive index materials," IEEE Antennas Wireless Propagat. Lett., Vol. 3, 172-175, 2004.
doi:10.1109/LAWP.2004.833710        Google Scholar

11. Shi, Y., Y. Li, and C. H. Liang, "Perfectly matched layer absorbing boundary condition for truncating the boundary of the left-handed medium," Microwave Opt. Technol. Lett., Vol. 48, No. 1, 57-62, 2006.
doi:10.1002/mop.21260        Google Scholar

12. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd Ed., Artech House, 2005.

13. Ziolkowski, R. W. and A. D. Kipple, "Causality and double-negative metamaterials," Physical Review E, Vol. 68, 026615, 2003.
doi:10.1103/PhysRevE.68.026615        Google Scholar

14. Gedney, S. D., "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat., Vol. 44, 1630-1639, 1996.
doi:10.1109/8.546249        Google Scholar