volume | PIER Journals

Abstract

We analyze the transverse-electric wave propagation through lossless trilayer stacks containing single-negative (SNG) materials in which only one of the two material constants, permittivity (epsilon) or permeability (mu), is negative. We consider the following combinations: ENG/MNG/ENG, ENG/DPS/MNG, DPS/ENG/DPS, and ENG/DPS/ENG, where ENG refers to epsilon-negative, MNG to mu-negative, and DPS to double-positive media. The transfer matrix formalism is applied. Although the waves are evanescent in the SNG media, combining the SNG layers or the SNG and DPS layers, leads to some unusual features, such as the complete tunneling. Since the symmetrical trilayer is equivalent to a single homogeneous layer, the complete tunneling conditions are easily predicted analytically for the trilayer stacks, and we show that in most of cases, they are rather well applicable to the respective bilayer stacks. The field and the Poynting vector distributions are studied in different trilayers and, in some cases, in the respective bilayers. In particular, we show that the complete tunneling is facilitated theoretically in the electrically thin stacks. Similar results could be obtained for the transverse-magnetic waves and the respective dual combinations by using the duality principle.

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp., Vol. 10, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

2. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneous negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, 4184-4187, 2000.
doi:10.1103/PhysRevLett.84.4184

3. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

4. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002.
doi:10.2528/PIER01082101

5. Ran, L.-X., H.-F. Jiang Tao, H. Chen, X.-M. Zhang, K.-S. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," Progress In Electromagnetics Research, Vol. 51, 249-279, 2005.
doi:10.2528/PIER04040502

6. McCall, M. W., "What is negative refraction? Optics," Journal of Modern, Vol. 56, 1727-1740, 2009.

7. Alu, A. and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency," IEEE Trans. Antennas Propagation, Vol. 51, 2558-2571, 2003.
doi:10.1109/TAP.2003.817553

8. Dong, L., G. Du, H. Jiang, H. Chen, and Y. Shi, "Transmission properties of lossy single-negative materials," J. Opt. Soc. Am. B, Vol. 26, 1091-1096, 2009.
doi:10.1364/JOSAB.26.001091

9. Lin, W.-H., C.-J. Wu, and S.-J. Chang, "Angular dependence of wave reflection in a lossy single-negative bilayer," Progress In Electromagnetics Research, Vol. 107, 253-267, 2010.
doi:10.2528/PIER10061606

10. Ding, Y., Y. Li, H. Jiang, and H. Chen, "Electromagnetic tunneling in nonconjugated epsilon-negative and mu-negative metamaterial pair," PIERS Online, Vol. 6, No. 2, 109-112, 2010.
doi:10.2529/PIERS091004104845

11. Feng, T., Y. Li, H. Jiang, Y. Sun, L. He, H. Li, Y. Zhang, Y. Shi, and H. Chen, "Electromagnetic tunneling in a sandwich structure containing single negative media," Phys. Rev. E, Vol. 79, 026601, 2009.
doi:10.1103/PhysRevE.79.026601

12. Zhou, L., W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett., Vol. 94, 243905, 2005.
doi:10.1103/PhysRevLett.94.243905

13. Tai, G.-C., C.-H.Chen, and Y.-W. Kiang, "Plasma-dielectric sandwich structure used as a tunable bandpass microwave filter," IEEE Trans. Microwave Theory Tech., Vol. 32, 111-113, 1984.

14. Jiang, H., H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E, Vol. 69, 066607, 2004.
doi:10.1103/PhysRevE.69.066607

15. Wang, L. G., H. Chen, and S. Y. Zhou, "Omnidirectional gap and defect mode of one-dimensional photonic crystals with singlenegative materials ," Phys. Rev. B, Vol. 70, 245102, 2004.
doi:10.1103/PhysRevB.70.245102

16. Yeh, D.-W. and C.-J. Wu, "Analysis of photonic band structure in a one-dimensional photonic crystal containing single-negative material," Optics Express, Vol. 17, 16666-16680, 2009.
doi:10.1364/OE.17.016666

17. Yeh, D.-W. and C.-J. Wu, "Thickness-dependent photonic bandgap in a one-dimensional single-negative photonic crystal," J. Opt. Soc. Am. B, Vol. 26, 1506-1510, 2009.
doi:10.1364/JOSAB.26.001506

18. Rahimi, H., "Backward Tamm states in 1D single-negative metamaterial photonic crystals," Progress In Electromagnetics Research Letters, Vol. 13, 149-159, 2010.
doi:10.2528/PIERL09121305

19. Rahimi, H., A. Namdar, S. Roshan Entezar, and H. Tajalli, "Photonic transmission spectra in one-dimensional Fibonacci multilayer structures containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 102, 15-30, 2010.
doi:10.2528/PIER09122303

20. Orfanidis, S. J., Electromagnetic Waves and Antennas, Chapter 6 Rutger University, 2008, www.ece.rutgers.edu/»orfanidi/ewa.

21. Lakhtakia, A. and C. M. Krowne, "Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material)," Optik, Vol. 114, No. 7, 305-307, 2003.
doi:10.1078/0030-4026-00266

22. Feng, S., "Graphical retrieval method for orthorhombic anisotropic materials," Optics Express, Vol. 18, 17009-17019, 2010.
doi:10.1364/OE.18.017009

Dr. Eva Cojocaru