volume | PIER Journals

Abstract

In the framework of the Green function method, we theoretically study the photonic band structure of one-dimensional superlattice composed of alternating layers of right-handed and left-handed materials (RHM and LHM). The dispersion curves are studied by assuming that the dielectric permittivity and magnetic permeability are frequency dependent in each layer. It is shown that such structures can exhibit new types of electromagnetic modes and dispersion curves that do not exist in usual superlattices composed only of RHM. With an appropriate choice of the parameters, we show that it is possible to realize an absolute (or omnidirectional) band gap for either transverse electric (TE) or transverse magnetic (TM) polarizations of the electromagnetic waves. A combination of two multilayer structures composed of RHM and LHM is proposed to realize, in a certain range of frequency, an omnidirectional reflector of light for both polarizations.

1. Pendry, J. B., "Photonic crystals and light localization in the 21th century," NATO Science, Vol. 563, 329, C. M. Soukoulis (ed.), Series C, Kluwer, Dordrecht, 2002.

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

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

4. Marqués, R., J. Martel, F. Mesa, and F. Medina, "Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides," Phys. Rev. Lett., Vol. 89, 138901, 2002.

5. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Steweat, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Transactions on Microwaves and Techniques, Vol. 47, 2075, 2000.
doi:10.1109/22.798002

6. Foteinoupoulou, S., E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett., Vol. 90, 107402, 2003.
doi:10.1103/PhysRevLett.90.107402

7. Houck, A. A., J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett., Vol. 90, 137401, 2003.
doi:10.1103/PhysRevLett.90.137401

8. Parazzoli, C. G., R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett., Vol. 90, 107401, 2003.
doi:10.1103/PhysRevLett.90.107401

9. Ziolkowski, R. W. and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E, Vol. 64, 056625, 2001.
doi:10.1103/PhysRevE.64.056625

10. Smith, D. R., D. Schurig, and J. B. Pendry, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Appl. Phys. Lett., Vol. 81, 2713, 2002.
doi:10.1063/1.1512828

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

12. Feise, M. W., P. J. Bevelacqua, and J. B. Schneider, "Effects of surface waves on the behaviour of perfect lenses," Phys. Rev. B, Vol. 66, 035113, 2002.
doi:10.1103/PhysRevB.66.035113

13. Fang, N. and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett., Vol. 82, No. 161, 2003.

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

15. Enoch, S., G. Tayeb, P. Sabourous, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett., Vol. 89, 213902, 2002.
doi:10.1103/PhysRevLett.89.213902

16. Nefedov, I. S. and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E, Vol. 66, 036611, 2002.
doi:10.1103/PhysRevE.66.036611

17. Li, J., 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

18. Bria, D., B. Djafari-Rouhani, A. Akjouj, L. Dobrzynski, J. P. Vigneron, E. H. ElBoudouti, and A. Nougaoui, "Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials," Phys. Rev. E, Vol. 69, 066613, 2004.
doi:10.1103/PhysRevE.69.066613

19. 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

20. Xiang, Y., X. Dai, and S. Wen, "Omnodirectional gaps of one-dimensional potonic crystals containing indefinite metamaterials," J. Opt. Soc. Am. B, Vol. 24, 2033, 2010.

21. Zhang, F., D. P. Gaillot, C. Croënne, E. Lheurette, X. Mélique, and D. Lippens, "Low-loss left-anded metamaterials at millimeter waves," Appl. Phys. Let., Vol. 93, 083104, 2008.
doi:10.1063/1.2975187

22. Xinag, Y., X. Dai, S. Wen, and D. Fan, "Properties of omnidirectional gap and defect mode of one-dimensionla photonic crystal containing indefinite metamaterials with hyperbolic dispersion," J. Appl. Phys., Vol. 102, 093107, 2007.
doi:10.1063/1.2809446

23. Sun, W.-H., Y. Lu, R.-W. Peng, L.-S. Cao, D. Li, X. Wu, and M. Wang, "Omnidirectional transparency induced by matched impedance disordered metamaterials," J. Appl. Phys., Vol. 106, 013104, 2009.
doi:10.1063/1.3159018

24. De Dios-Leyva, M. and J. C. Drake-Pérez, "Zero-width band gap associated with the n = 0 condition in photonic crystals containing left-handed materials," Phys. Rev. E, Vol. 79, 036608, 2009.
doi:10.1103/PhysRevE.79.036608

25. Fink, J. N., S. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "Dielectric omnidirectional reflector," Science, Vol. 282, 1679, 1998.
doi:10.1126/science.282.5394.1679

26. Dowling, J. P., "Mirror on the wall: You're omnidirectional after all?," Science, Vol. 282, 1841, 1998.
doi:10.1126/science.282.5395.1841

27. Bria, D., B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, "Omnidirectional optical mirror in a cladded-superlattice structure," J. Appl. Phys., Vol. 91, 2569, 2002.
doi:10.1063/1.1433188

28. Bria, D. and B. Djafari-Rouhani, "Omnidirectional elastic band gap infinite lamellar structures," Phys. Rev. E, Vol. 66, 056609, 2002.
doi:10.1103/PhysRevE.66.056609

29. Xiang, Y., L. Ran, J. T. Huangfu, H. S. Chen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express, Vol. 14, 2223, 2006.

30. Aylo, R., P. P. Banerjee, and G. Nehmetallah, "Perturbed multilayered structures of positive and negative index materials," J. Opt. Soc. Am. B, Vol. 27, 599, 2010.
doi:10.1364/JOSAB.27.000599

31. Dobrzynski, L., "Interface response theory of continuous composite materials," Surf. Sci., Vol. 180, 489, 1987.
doi:10.1016/0039-6028(87)90222-6

32. Ouchani, N., D. Bria, B. Djafari-Rouhani, and A. Nougaoui, "Transverse-electric/Transversemagnetic polarization converter using 1D finite biaxial photonic crystal," J. Opt. Soc. Am. A, Vol. 24, No. 9, 2710, 2007.
doi:10.1364/JOSAA.24.002710

33. Ruppin, R., "Surface polaritons of a left-handed material slab," J. Phys. Condens. Matter, Vol. 13, 1811, 2001.
doi:10.1088/0953-8984/13/9/304

34. Shadrivov, I. V., N. A. Zharova, A. A. Zharov, and Y. S. Kivshar, "Defect modes and transmission properties of left-handed bandgaps structures," Phys. Rev. E, Vol. 70, 046615, 2004.
doi:10.1103/PhysRevE.70.046615

35. Cocoletzi, G. H., L. Dobrzynski, B. Djafari-Rouhani, H. AlWahsh, and D. Bria, "Electromagnetic wave propagation in quasi-one-dimensional comb-like structures made up of dissipative negative-phase-velocity materials," J. Phys.: Condens. Matter, Vol. 18, 3683, 2006.
doi:10.1088/0953-8984/18/15/014

Dr. Abdelmajid Essadqui

Dr. Jawad Ben-Ali

Dr. Driss Bria

Prof. Bahram Djafari-Rouhani

Dr. Abdelkrim Nougaoui