volume | PIER Journals

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

Dr. Kuisong Zheng

Dr. Wai-Yip Tam

Dr. De-Biao Ge

Professor Jia-Dong Xu