Propagation of surface waves at the interface between nonlinear MTMs and anisotropic materials

Abstract

Metamaterials (MTMs), which have both negative permeability and negative permittivity, have potential applications in optoelectronics and communications. These materials are fabricated in laboratories which is an added advantage. The focus of this work is on the propagation of surface waves at the interface between nonlinear MTMs and anisotropic materials in the optical range. The dispersion equation is derived from Maxwell’s equations. The dispersion equation is solved numerically to study the characteristics of the propagated wave. Only TE modes are considered. The results display the dependence of the propagating waves on the characteristics of the structure composite materials.

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References

  1. 1.

    C.L. Xu, w.P. Huang, J. Chrostowski, S.K. Chaudhuri, A full-vectorial beam propagation method for anisotropic waveguides. J. Lightwave Technol. 12, 1926–1931 (1994)

    ADS  Article  Google Scholar 

  2. 2.

    R.C. Alferness, Effective waveguide electro-optic TE+TM mode converter/waveguide filter. Appl. Phys. Lett. 36, 513–515 (1980)

    ADS  Article  Google Scholar 

  3. 3.

    R.H. Stolen, V. Ramaswamy, P. Kaiser, W. Pleibel, Linear polarization in birefringent single-mode fibers. Appl. Phys. Lett. 33, 699–701 (1978)

    ADS  Article  Google Scholar 

  4. 4.

    D.N. Payne, A.J. Barlow, J.J. Hansen, Development of low- and high-birefringence fibers. IEEE J. Quantum Electron. 18, 477487 (1982)

    Article  Google Scholar 

  5. 5.

    L. Thylen, D. Yevick, Beam propagation method in anisotropic media. Appl. Opt. 21, 2751–2754 (1982)

    ADS  Article  Google Scholar 

  6. 6.

    J.A. Fleck Jr., M.D. Feit, Beam propagation in uniaxial anisotropic media. J. Opt. Soc. Am. 73, 920–926 (1983)

    ADS  Article  Google Scholar 

  7. 7.

    J.M. Liu, L. Gomelsky, Vectorial beam propagation method. J. Opt. Soc. Am. 9, 1574–1585 (1992)

    ADS  Article  Google Scholar 

  8. 8.

    V.S. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp. 10, 509–514 (1968)

    ADS  Article  Google Scholar 

  9. 9.

    J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2083 (1999)

    ADS  Article  Google Scholar 

  10. 10.

    D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000)

    ADS  Article  Google Scholar 

  11. 11.

    H. El-Khozondar, R. El-Khozondar, M. Shabat, A. Koch, Metallic nonlinear magnetooptical nonreciprocal isolator. Optik 122, 256–258 (2011)

    ADS  Article  Google Scholar 

  12. 12.

    H. El-Khozondar, R. El-Khozondar, M. Shabat, Characteristics of magnetooptical integrated metamaterials isolator. Int. J. Mod. Phys. B 23, 4675–4683 (2009)

    ADS  Article  MATH  Google Scholar 

  13. 13.

    R. El-Khozondar, H. El-Khozondar, M. Shabat, Applications of metamaterials in optical waveguide isolator. J. Al-Aqsa Univ. 12, 35–50 (2008)

    Google Scholar 

  14. 14.

    H.J. El-Khozondar, R.J. El-Khozondar, M.M. Shabat, Double-negative metamaterial optical waveguide behavior subjected to stress. Islamic Univ. J. Natur. Sci. Eng. 16(1), 9–20 (2008)

    Google Scholar 

  15. 15.

    R. El-Khozondar, H. El-Khozondar, M. Shabat, A. Koch, TM waves propagation at magnetoplasma-MTMs. World J. Condens. Matter Phys. 2, 171–174 (2012)

    ADS  Article  Google Scholar 

  16. 16.

    H.J. El-Khozondar, R.J. El-Khozondar, S. Zouhdi, Surface waves at the interface between tunable LC-MTMs and nonlinear media. Appl. Phys. A, Mater. Sci. Process. 109, 865–867 (2012)

    ADS  Article  Google Scholar 

  17. 17.

    H. El-Khozondar, M. Müller, R. El-Khozondar, M. Shabat, A. Koch, Sensitivity of double-negative metamaterial optical sensor. Int. J. Pure Appl. Sci. Technol. 11, 29–35 (2012)

    Google Scholar 

  18. 18.

    H. El-Khozondar, M. Müller, R. El-Khozondar, A. Koch, Influence of magnetic field inhomogeneity on a magneto-optical current sensor. J. Sensor Technol. 2, 19–22 (2012)

    Article  Google Scholar 

  19. 19.

    H. El-Khozondar, R. El-Khozondar, M. Müller, A. Koch, Sensitivity of TM nonlinear magnetooptical integrated optical sensor. Multidiscip. Model. Mat. Struct. (MMMS) 8, 32–42 (2011)

    Google Scholar 

  20. 20.

    R. El-Khozondar, H. El-Khozondar, M. Shabat, Surface wave propagation in Ferroelectric/MTMS interface. Integr. Ferroelectr. 130, 50–57 (2011)

    Article  Google Scholar 

  21. 21.

    J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)

    ADS  Article  Google Scholar 

  22. 22.

    R.A. Shelby, D.R. Smith, S. Schultz, Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)

    ADS  Article  Google Scholar 

  23. 23.

    D.R. Smith, N. Kroll, Negative refraction index in left-handed materials. Phys. Rev. Lett. 85, 2933–2936 (2000)

    ADS  Article  Google Scholar 

  24. 24.

    I.V. Lindell, S.A. Tretyakov, K.I. Nikoskinen, S. Ilvonen, Bw media-media with negative parameters capable of supporting backward waves. Microw. Opt. Technol. Lett. 31, 129–133 (2001)

    Article  Google Scholar 

  25. 25.

    A.J. Hoffman, L. Alekseyev, S.S. Howard, K.J. Franz, D. Wasserman, V.A. Podolskiy, E.E. Narimanov, D.L. Sivco, C. Gmachl, Negative refraction in semiconductor metamaterials. Nat. Mater. 6, 946–950 (2007)

    ADS  Article  Google Scholar 

  26. 26.

    X.H. Hu, C.T. Chan, X.H. Hu, C.T. Chan, Photonic crystals with silver nanowires as a near-infrared superlens. Appl. Phys. Lett. 85, 1520–1522 (2004)

    ADS  Article  Google Scholar 

  27. 27.

    D.R. Smith, D. Schurig, Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors. Phys. Rev. Lett. 90, 077405 (2003)

    ADS  Article  Google Scholar 

  28. 28.

    D.R. Smith, D. Schurig, J.J. Mock, P. Kolinko, P. Rye, Partial focusing of radiation by a slab of indefinite media. Appl. Phys. Lett. 84, 2244 (2004)

    ADS  Article  Google Scholar 

  29. 29.

    A.A. Zharov, I.V. Shadrivov, Y.S. Kivshar, Nonlinear properties of left-handed meta-materials. Phys. Rev. Lett. 91, 037401 (2003)

    ADS  Article  Google Scholar 

  30. 30.

    M. Lapine, M. Gorkunov, K.H. Ringhofer, Nonlinearity of metamaterial arising fromdiode insertions into resonant conductive elements. Phys. Rev. E 67, 065601 (2003)

    ADS  Article  Google Scholar 

  31. 31.

    S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, D. Fan, Modulation instability in nonlinear negative-index material. Phys. Rev. E 73, 0366171–0366176 (2006). Copyright @ 2006, Optical Society of America, March 24, 2006

    Article  Google Scholar 

  32. 32.

    S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, D. Fan, Role of the anomalous self-steepening effect in modulation instability in negative-index material. Opt. Express 14, 1568–1575 (2006). Copyright @ 2006, Optical Society of America, February 22, 2006

    ADS  Article  Google Scholar 

  33. 33.

    S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, D. Fan, Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials. Phys. Rev. A 75, 033815 (2007)

    ADS  Article  Google Scholar 

  34. 34.

    N. Lazarides, G.P. Tsironis, Coupled nonlinear Schrödinger field equations for electro-magnetic wave propagation in nonlinear left-handed materials. Phys. Rev. E 71, 036614 (2005)

    ADS  Article  Google Scholar 

  35. 35.

    U.K. Chettiar, A.V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V.P. Drachev, V.M. Shalaev, Double negative index metamaterial: simultaneous negative permeability and permittivity at 812 nm, in Proc. Photonic Metamaterials: from Random to Periodic, Jackson Hole, WY, June 4–7 (2007)

    Google Scholar 

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Acknowledgements

The first and third authors would like to acknowledge the French government for funding the work through the Al-Maqdisi program grant.

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Correspondence to Hala J. El-Khozondar.

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El-Khozondar, H.J., El-Khozondar, R.J. & Zouhdi, S. Propagation of surface waves at the interface between nonlinear MTMs and anisotropic materials. Appl. Phys. A 115, 439–442 (2014). https://doi.org/10.1007/s00339-013-8041-4

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Keywords

  • Surface Wave
  • Dispersion Equation
  • Anisotropic Material
  • Anisotropic Medium
  • Effective Permeability