Studies of the band gap properties of one-dimensional superlattices with alternate layers of air and left-handed materials are carried out within the framework of Maxwell's equations. By left-handed material, we mean a material with dispersive negative electric and magnetic responses. Modeling them by Drude-type responses or by fabricated ones, we characterize the ⟨">">">>n(ω)⟩ = 0 gap, i.e., the zeroth order gap, which has been predicted and detected. The band structure and analytic equations for the band edges have been obtained in the long wavelength limit in case of periodic, Fibonacci, and Thue-Morse superlattices. Our studies reveal the nature of the width of the zeroth order band gap, whose edge equations are defined by null averages of the response functions. Oblique incidence is also investigated, yielding remarkable results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andre, A., Lukin, M.D.: Manipulating light pulses via dynamically controlled photonic band gap. Phys. Rev. Lett. 89(14), 143602 (2002).
Barnes, W.L., Dereux, A., Ebbesen, T.W.: Surface plasmon subwavelength optics. Nature 424(6950), 824 (2003).
Bria, D., Djafari-Rouhani, B., Akjouj, A., Dobrzynski, L., Vigneron, J.P., El Boudouti, E.H., Nougaoui, A.: Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials. Phys. Rev. E 69(6), 066613 (2004).
Bruno-Alfonso, A., Reyes-Gómez, E., Cavalcanti, S.B., Oliveira, L.E.: Band edge states of the ⟨n⟩ = 0 gap of Fibonacci photonic lattices. Phys. Rev. A 78(3), 035801 (2008a).
Bruno-Alfonso, A., Reyes-Gómez, E., Cavalcanti, S.B., Oliveira, L.E.: Band-edge states of the zeroth-order gap in quasi-periodic photonic superlattices. In Tománek, P., Senderáková, D., Hrabovsky, M. (eds.) Photonics, Devices, and Systems IV. Proc. of SPIE Vol. 7138, 71381A (2008b).
Busch, K., John, S.: Liquid-crystal photonic-band-gap materials: The tunable electromagnetic vacuum. Phys. Rev. Lett. 83(5), 967 (1999).
Cavalcanti, S.B., Dios-Leyva, M., Reyes-Gómez, E., Oliveira, L.E.: Band structure and band-gap control in photonic superlattices. Phys. Rev. B 74(15), 153102 (2006).
Cavalcanti, S.B., Dios-Leyva, M., Reyes-Gómez, E., Oliveira, L.E.: Photonic band structure and symmetry properties of electromagnetic modes in photonic crystals. Phys. Rev. E 75(2), 026607 (2007), and references therein.
Cubuku, E., Aydin, K., Ozbay, E., Foteinopolou, S., Soukoulis, C.M.: Subwavelength resolution in a two-dimensional photonic-crystal-based superlens. Phys. Rev. Lett. 91(20), 207401 (2003).
Daninthe, H., Foteinopoulou, S., Soukoulis, C.M.: Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials. Phot. Nanostruct. Fund. Appl. 4(3), 123 (2006).
Duque, CA., Porras-Montenegro, N., Cavalcanti, S.B., Oliveira, L.E.: Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field. J. Appl. Phys. 105(3), 034303 (2009).
Edwards, B., Alu, A., Young, M.E., Silveirinha, M., Engheta, N.: Multifrequency optical invisibility cloak with layered plasmonic shells. Phys. Rev. Lett. 100(11), 033903 (2008).
Eleftheriades, G.V., Iyer, A.K., Kremer, P.C.: Planar negative refractive index media using periodically L-C loaded transmission lines. IEEE Trans. Microwave Theory Tech. 50(12), 2702 (2002).
Fredkin, D.R., Ron, A.: Effectively left-handed (negative index) composite material. Appl. Phys. Lett. 81(10), 1753 (2002).
Grbic, A., Eleftheriades, G.V.: Experimental verification of backward-wave radiation from a negative refractive index metamaterial. J. Appl. Phys. 92(10), 5930 (2002).
Jiang, H., Chen, H., Li, H., Zhang, Y., Zhu, S.: Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials. Appl. Phys. Lett. 83(26), 5386 (2003).
Kleckner, T.D., Modotto, D., Locatelli, A., Mondia, J.P., Linden, S., Morandotti, R., De Angelis, C., Stanley, C.R., van Driel, H.M., Aitchison, J.S.: Design, fabrication, and characterization of deep-etched waveguide gratings. J. Light. Tech. 23(12), 3832 (2005).
Konoplev, I.V., McGrane, P., Cross, A.W., Ronald, K., Phelps, A.D.R.: Wave interference and band gap control in multiconductor one-dimensional Bragg structures. J. of Appl. Phys. 97(7), 073101 (2005a).
Konoplev, I.V., McGrane, P., Phelps, A.D.R., Cross, A.W., Ronald, K.: Observation of photonic band-gap control in one-dimensional Bragg structures. Appl. Phys. Lett. 87(12), 121104 (2005b), and references therein.
Kosaka, H., Kawashima, T., Tomita, A., Notomi, N., Tamamura, T., Sato, T., Kawakami, S.: Superprism phenomena in photonic crystals. Phys. Rev. B 58(16), 10096 (1998).
Li, J., Zhou, L., Chan, C.T., Sheng, P.: Photonic band gap from a stack of positive and negative index materials. Phys. Rev. Lett. 90(8), 083901 (2003).
Liu, L., Caloz, C., Chang, C.C., Itoh, T.: Forward coupling phenomena between artificial left-handed transmission lines. J. Appl. Phys. 92(9), 5560 (2002).
Longhi, S., Janner, D.: Diffraction and localization in low-dimensional photonic bandgaps. Optics Lett. 29(22), 2653 (2004).
Lord Rayleigh: On the maintenance of vibrations by forces of double frequency and on the propagation of waves through a medium endowed with a periodic structure. Phil. Mag. XXIV, 145 (1887).
Maier, S.A., Atwater, H.A.: Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures. J. Appl. Phys. 98(1), 011101 (2005).
Mishra, S., Satpathy, S.: One-dimensional photonic crystal: The Kronig-Penney model. Phys. Rev. B 68(4), 045121 (2003).
Murzina, T.V., Sychev, F.Yu., Kim, E.M., Rau, E.I., Obydena, S.S., Aktsipetrov, O.A., Bader, M.A., Marowsky, G.: One-dimensional photonic crystals based on porous n-type silicon. J. Appl. Phys. 98(12), 123702 (2005).
Ozbay, E.: Plasmonics: Merging photonics and electronics at nanoscale dimensions. Science 311(5758), 189 (2006).
Pacheco, J.Jr., Grzegorczyk, T.M., Wu, B.-I., Zhang, Y., Kong, J.A.: Power propagation in homogeneous isotropic frequency-dispersive left-handed media. Phys. Rev. Lett. 89(25), 257402 (2002).
Parimi, P.V., Lu, W.T., Vodo, P., Sridhar, S.: Photonic crystals — Imaging by flat lens using negative refraction. Nature 426(6965), 404 (2003).
Shadrivov, I.V., Zharova, N.A., Kivshar, Y.S.: Defect modes and transmission properties of left-handed bandgap structures. Phys. Rev. E 70(4), 046615 (2004).
Veselago, V.G.: The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys.-Usp. 10(4), 509 (1968).
Wang, L., Chen, H., Zhu, S.-Y.: Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials. Phys. Rev. B 70(24), 245102 (2004).
Wu, L., He, S., Chen, L.: On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials. Opt. Exp. 11(11), 1283 (2003a).
Wu, L., He, S., Shen, L.: Band structure for a one-dimensional photonic crystal containing left-handed materials. Phys. Rev. B 67(23), 235103 (2003b).
Yariv, A., and Yeh, P.: Optical waves in crystals. John Wiley & Sons, New York (1984).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Cavalcanti, S.B., Reyes-Gómez, E., Bruno-Alfonso, A., Carvalho, C.A.A.d., Oliveira, L.E. (2010). On the Photonic Dispersion of Periodic Superlattices Made of Left-Handed Materials. In: Hall, T.J., Gaponenko, S.V., Paredes, S.A. (eds) Extreme Photonics & Applications. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3634-6_11
Download citation
DOI: https://doi.org/10.1007/978-90-481-3634-6_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3633-9
Online ISBN: 978-90-481-3634-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)