volume | PIER Journals

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Dr. Hector Kinto-Ramírez

Dr. Martha Alicia Palomino-Ovando

Dr. Felipe Ramos-Mendieta