Optical and Quantum Electronics

, Volume 47, Issue 2, pp 363–373 | Cite as

Investigation of nonlinear light optimum parameters to compensate loss in multilayer metamaterial waveguide with an active cladding layer



The active structures having nonlinear optic features, metamaterial waveguides are a material of interest for compensating loss effects and creating zero light group velocity. In this paper, the multilayer structure of metamaterial waveguide with five layers is investigated. The core is metamaterial having loss and the inner cladding layer is dielectric material composed with nonlinear active materials which through applying an external light having specific wavelength, represents nonlinear characteristics. The propagation and power relations is achieved and calculated in each layer and afterward, setting three nonlinear active material \(Au/ZnO, Au/SiO_{2}\), and \(Ag/SiO_{2}\), in the cladding layer and applying an external light pump with \(\lambda =532\,\hbox {nm}\), the amplitude of external light pump and critical thickness of the core for zero optic group velocity for each structure is measured. Then by drawing related diagrams, the measurements and results are compared, and the most appropriate structure will be selected.


Metamaterial waveguide Multilayer structure Nonlinear optic Slow optic 


  1. Alu, A., Engheta, N.: Guided modes in awaveguide filled with a pair of single-nagative (SNG), doublenegative(DNG), and/or double-positive (DPS) layers. IEEE Trans. Microw. Theory Technol. 52, 199–210 (2004)ADSCrossRefGoogle Scholar
  2. Berman, P.R.: Goos–Hanchen shift in negatively refractive media. Phys. Rev. E. 66, 067603–067605 (2002)ADSCrossRefGoogle Scholar
  3. Dolling, G., Enkrich, C., Wegener, M., Soukoulis, C.M., Linden, S.: Low-loss negative-index metamaterial at telecommunication wavelengths. Opt. Lett. 31, 1800–1802 (2006)ADSCrossRefGoogle Scholar
  4. Dolling, G., Enkrich, C., Wegener, M., Soukoulis, C.M., Linden, S.: Negative-index material at 780 nm wavelength. Opt. Lett. 32, 53–55 (2007)ADSCrossRefGoogle Scholar
  5. Erfaninia, H., Rostami, A.: Group velocity reduction in multilayer metamaterial waveguide. Optik 124, 1230–1233 (2013)ADSCrossRefGoogle Scholar
  6. Fang, A., Koschny, T., Soukoulis, C.M.: Self-consistent calculations of loss-compensated fishnet metamaterials. Phys. Rev. B. 82, 121102–121105 (2010)ADSCrossRefGoogle Scholar
  7. Ganeev, R.A., Ryasnyansky, A.I., Stepanov, A.L., Usmanov, T.: Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm. Opt. Quantum Electron. 36, 949–960 (2004)CrossRefGoogle Scholar
  8. Hao, Z., Martin, M.C., Harteneck, B., Cabrini, S., Anderson, E.H.: Negative index of refraction observed in asingle layer of closed ring magnetic dipole resonators. Appl. Phys. Lett. 91, 253119–253121 (2007)ADSCrossRefGoogle Scholar
  9. He, J., He, S.: Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate. IEEE Microw. Wirel. Compon. Lett. 16, 96–98 (2005)CrossRefGoogle Scholar
  10. Jiang, T., Zhao, J., Feng, Y.: Stopping light by an air waveguide with anisotropic metamaterial cladding. Opt. Express 17, 170–177 (2009)ADSCrossRefGoogle Scholar
  11. Kirby, E.I., Hamm, J.M., Pickering, T., Tsakmakidis, K.L., Hess, O.: Evanescent gain in “Trapped Rainbow” negative refractive index heterostructures. (2010). arXiv:1010.5468
  12. Maghamianzadeh, E., Erfaninia, H.: Novel adiabatic structure for stopping light in lossy metamaterial waveguide with active cladding ZnO/Au. Opt. Quantum Electron. (2014). doi: 10.1007/s11082-013-9852-4
  13. Mokhtari, B., Eddeqaqi, N.C., Atangana, J., Essama, B.G.O., Kofane, T.C.: Nonlinear dispersion equation and guided modes in a slab waveguide composed of a negative-index medium. Opt. Quantum Electron 46, 155–163 (2013)Google Scholar
  14. Ning, T., Zhou, Y., Shen, H., Lu, H., Sun, Z., Cao, L., Guan, D., Zhang, D., Yang, G.: Nonlinear optical properties of Au/ZnO nanoparticle arrays. Appl. Surf. Sci. 254, 1900–1903 (2008)ADSCrossRefGoogle Scholar
  15. Novitsky, A.V., Barkovsky, L.M.: Guided modes in negative-refractive-index fibres. J. Opt. A Pure Appl. Opt. 7, S51–S56 (2005)ADSCrossRefGoogle Scholar
  16. Pendry, J.B.: Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)ADSCrossRefGoogle Scholar
  17. Saleh, B.E.A., Teich, M.C.: Fundamentals of Photonics, pp. 877–879. Wiley, Hoboken, New Jersey (2007)Google Scholar
  18. Shadrivov, I.V., Zharov, A.A., Kivshar, Y.S.: Giant Goos–Hanchen effect at the reflection from left-handed metamaterials. Appl. Phys. Lett. 83, 2713–2715 (2003)ADSCrossRefGoogle Scholar
  19. Shelby, R.A., Smith, D.R., Schultz, S.A.: Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)ADSCrossRefGoogle Scholar
  20. Torres, C.T., Khomenko, A.V., Wong, J.C.C., Fernandez, L.R., Sosa, A.C., Oliver, A.: Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica. Opt. Express 15, 9248–9253 (2007)ADSCrossRefGoogle Scholar
  21. Tsakmakidis, K.L., Boardman, A.D., Hess, O.: Trapped rainbow storage of light in metamaterials. Nature 450, 397–401 (2007)ADSCrossRefGoogle Scholar
  22. Veselago, V.G.: The electrodynamics of substances with simultaneosly negativevalues of \(\varepsilon \) and \(\mu \). Sov. Phys. Usp. 10, 509–514 (1968)ADSCrossRefGoogle Scholar
  23. Wang, Z.H., Xiao, Z.Y., Li, S.P.: Guided modes in slab waveguides with a left handed material cover or substrate. Opt. Commun. 281, 607–613 (2008)ADSCrossRefGoogle Scholar
  24. Wuestner, S., Pusch, A., Tsakmakidis, K.L., Hamm, J.M., Hess, O.: Overcoming losses with gain in a negative refractive index metamaterial. Phys. Rev. Lett. 105, 127401–127404 (2010)ADSCrossRefGoogle Scholar
  25. Xiao, S., Drachev, V.P., Kildishev, A.V., Ni, X., Chettiar, U.K., Yuan, H.K., Shalaev, V.M.: Loss-free and active optical negative-index metamaterials. Nature 466, 735–738 (2010)ADSCrossRefGoogle Scholar
  26. Yamamoto, K., Nomura, S.: Energy compensated mode in a waveguide composed of lossy left-handed metamaterial. Opt. Commun. 276, 191–195 (2007)ADSCrossRefGoogle Scholar
  27. Zhang, S., Fan, W., Panoiu, N.C., Malloy, K.J., Osgood, R.M., Brueck, S.R.J.: Experimental demonstration of near-infrared negative-index metamaterials. Phys. Rev. Lett. 95, 137404–137407 (2005)ADSCrossRefGoogle Scholar
  28. Zhou, L., Chan, C.: Vortex-like surfacewave and its role on the transient phe-nomena of metamaterial focusing. Appl. Phys. Lett. 86, 101104–101106 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Electrical and Electronics Engineering, Dezful BranchIslamic Azad UniversityDezfulIran

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