2011-10-16
Photonic Modes in Dispersive and Lossy Superlattices Containing Negative-Index Materials
By
Progress In Electromagnetics Research B, Vol. 35, 133-149, 2011
Abstract
We have calculated the photonic bands of a dispersive and lossy periodic array of left-handed metamaterial layers in air. Depending on the behavior of the fields inside the metamaterial component, two categories of modes for oblique propagation are identified: the oscillatory and the tunneling modes. In order to characterize these two types of solutions, we calculate the complex photonic bands; a criterion of penetration-limit is introduced to quantify the absorption effects. Our results show that oscillatory TE and TM waves can be excited by light incident from air at low frequencies (within the metamaterial regime). In the region of high frequencies only TE tunneling modes are available. To complement the description of the absorption effects, we present transmission spectra and field profiles for TE waves in finite layered systems the two types of modes here studied.
Citation
Hector Kinto-Ramírez, Martha Alicia Palomino-Ovando, and Felipe Ramos-Mendieta, "Photonic Modes in Dispersive and Lossy Superlattices Containing Negative-Index Materials," Progress In Electromagnetics Research B, Vol. 35, 133-149, 2011.
doi:10.2528/PIERB11062911
References

1. Veselago, V. G., "Electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp., Vol. 10, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699        Google Scholar

2. Agranovich, V. M. and Y. N. Garstein, "Spatial dispersion and negative refraction of light," Physics-Uspekhi, Vol. 49, 1029-1044, 2006.
doi:10.1070/PU2006v049n10ABEH006067        Google Scholar

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

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

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

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

7. Pandey, G. N., K. B. Thapa, S. K. Srivastava, and S. P. Ojha, "Band structures and abnormal behavior of one dimensional photonic crystal containing negative index materials," Progress In Electromagnetic Research M, Vol. 2, 15-36, 2008.
doi:10.2528/PIERM08021501        Google Scholar

8. Srivastava, S. K. and S. P. Ojha, "Enhancement of omnidirectional reflection bands in one-dimensional photonic crystals with left-handed materials," Progress In Electromagnetic Research, Vol. 68, 91-111, 2007.
doi:10.2528/PIER06061602        Google Scholar

9. Wang, Z.-Y., X.-M. Chen, X.-Q. He, S.-L. Fan, and W.-Z. Chan, "Photonic crystal narrow filters with negative refractive index structural defects," Progress In Electromagnetic Research, Vol. 80, 421-430, 2008.
doi:10.2528/PIER07121002        Google Scholar

10. Zhang, Z. M. and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett., Vol. 80, 1097-1099, 2002.
doi:10.1063/1.1448172        Google Scholar

11. Kim, K. Y., "Photon tunneling in composite layers of negative-and positive-index media," Phys. Rev. E, Vol. 70, 047603, 2004.
doi:10.1103/PhysRevE.70.047603        Google Scholar

12. Li, J. S., L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett., Vol. 90, 083901, 2003.
doi:10.1103/PhysRevLett.90.083901        Google Scholar

13. Yuan, Y., L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Optics Express, Vol. 14, 2220-2227, 2006.
doi:10.1364/OE.14.002220        Google Scholar

14. Wu, L., S. He, and L. Shen, "Band structure for a one-dimensional photonic crystal containing left-handed materials," Phys. Rev. B, Vol. 67, 235103, 2003.
doi:10.1103/PhysRevB.67.235103        Google Scholar

15. García, N. and M. Nieto-Vesperinas, "Left-handed materials do not make a perfect lens," Phys. Rev. Lett., Vol. 88, 207403, 2002.
doi:10.1103/PhysRevLett.88.207403        Google Scholar

16. Rao, X. S. and C. K. Ong, "Amplifications of evanescent waves in a lossy left-handed material slab," Phys. Rev. B, Vol. 68, 113103, 2003.
doi:10.1103/PhysRevB.68.113103        Google Scholar

17. De Dios-Leyva, M. and J. A. Leyva-Galano, "Influence of absorption on the zero-n gap in one dimensional photonic crystals with left-handed materials," Phys. Rev. B, Vol. 78, 115106, 2008.
doi:10.1103/PhysRevB.78.115106        Google Scholar

18. Zhou, X. and G. Hu, "Total transmission condition for photon tunneling in a layered structure with metamaterials," J. Opt. A: Pure Appl. Opt., Vol. 9, 60-65, 2007.
doi:10.1088/1464-4258/9/1/011        Google Scholar

19. Markos, P. and C. M. Soukoulis, "Transmission studies of left-handed material," Phys. Rev. B, Vol. 65, 033401, 2001.
doi:10.1103/PhysRevB.65.033401        Google Scholar

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

21. Pacheco, Jr., J., T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, and J. A. Kong, "Power propagation in homogeneous isotropic frequency-dispersive left-handed media," Phys. Rev. Lett., Vol. 89, 257401, 2002.
doi:10.1103/PhysRevLett.89.257401        Google Scholar

22. Koschny, T., M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett., Vol. 93, 107402, 2004.
doi:10.1103/PhysRevLett.93.107402        Google Scholar

23. Caloz, C. and T. Itoh, Electromagnetic Metamaterial: Transmission Line Theory and Microwave Applications, John Wiley & Sons, Inc., 2006.

24. Gupta, S. D., R. Arun, and G. S. Agarwal, "Subluminal to superluminal propagation in a left-handed medium," Phys. Rev. B, Vol. 69, 113104, 2000.
doi:10.1103/PhysRevB.69.113104        Google Scholar

25. Villa-Villa, F., J. A. Gaspar-Armenta, and A. Mendoza-Suárez, "Surface modes in one dimensional photonic crystals that include left handed materials," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 4, 485-499, 2007.
doi:10.1163/156939307779367323        Google Scholar