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2008-07-16

Geometrical Analysis of Wave Propagation in Left-Handed Metamaterials.Part I

By Consuelo Bellver-Cebreros and Marcelo Rodriguez-Danta
Progress In Electromagnetics Research C, Vol. 4, 103-119, 2008

Abstract

Geometrical analyses of basic equations of electromagnetics waves propagation in anisotropic dielectric materials with magnetic isotropy are presented in two complementary papers (Part I and Part II). In the present one, analysis arises from quadrics associated with relative dielectric tensor (ε) compatible with conical surfaces that represent the general plane wave equation (relation of dispersion). This study systematizes rays propagation in left-handed materials (LHMs) exhibiting dielectric anisotropy and magnetic isotropy. In particular, indefinite dielectric media where dielectric permittivities are not all the same sign, have been investigated. Graphical alternative procedures for ray tracing in these media are presented.

Citation


Consuelo Bellver-Cebreros and Marcelo Rodriguez-Danta, "Geometrical Analysis of Wave Propagation in Left-Handed Metamaterials.Part I," Progress In Electromagnetics Research C, Vol. 4, 103-119, 2008.
http://jpier.org/PIERC/pier.php?paper=08061202

References


    1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp., Vol. 10, No. 4, 509-514, 1968.
    doi:10.1070/PU1968v010n04ABEH003699

    2. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966-3969, 2000.
    doi:10.1103/PhysRevLett.85.3966

    3. 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

    4. Woodley, J. and M. Mojahedi, "Backward wave propagation in left-handed media with isotropic and anisotropic permittivity tensors," J. Opt. Soc. Am. B, Vol. 23, No. 11, 2377-2382, 2006.
    doi:10.1364/JOSAB.23.002377

    5. Smith, D. R., P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B, Vol. 21, 1032-1042, 2004.
    doi:10.1364/JOSAB.21.001032

    6. Ding, W., L. Chen, and C. H. Liang, "Characteristics of electromagnetic wave propagation in biaxial anisotropic left-handed materials," Progress In Electromagnetics Reseach, Vol. 70, 37-52, 2007.
    doi:10.2528/PIER07011001

    7. Shen, L. F. and Z. H. Wang, "The propagation characteristics in a doubly clad optical fiber including left-handed materials," Journal of Electromagnetic Waves and Applications, Vol. 22, 895-904, 2008.
    doi:10.1163/156939308784150173

    8. Ran, L., J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," Progress In Electromagnetics Research, Vol. 51, 249, 2005.
    doi:10.2528/PIER04040502

    9. Grzegorczyk, T. M., X. Chen, J. Pacheco, J. Chen, B. I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, Vol. 51, 83, 2005.
    doi:10.2528/PIER04040901

    10. Wu, B. I., W.Wang, J. Pacheco, X. Chen, T. M. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhace gain," Progress In Electromagnetics Research, Vol. 51, 295-328, 2005.
    doi:10.2528/PIER04070701

    11. Chen, H., B. I. Wu, and J. A. Kong, "Review of electromagnetic theory in left-handed materials," J. of Electromagn. Waves and Appl., Vol. 20, No. 15, 2137-2151, 2006.
    doi:10.1163/156939306779322585

    12. Yang, R., Y. Xie, P. Wang, and T. Yang, "Conjugate left- and right-handed material bilayered substrates qualify the subwavelength cavity resonator microstrip antennas as sensors," J. of Electromagn. Waves and Appl., Vol. 20, No. 15, 2113-2122, 2006.
    doi:10.1163/156939306779322486

    13. Grzegorczyk, T. M. and J. A. Kong, "Review of left-handed metamaterials: Evolution from theoretical and numerical studies to potential applications," J. of Electromagn. Waves and Appl., Vol. 20, No. 14, 2053-2064, 2006.
    doi:10.1163/156939306779322620

    14. Yang, R., Y. Xie, P. Wang, and L. Li, "Microstrip antennas with left-handed materials substrates," J. of Electromagn. Waves and Appl., Vol. 20, No. 9, 1221-1233, 2006.
    doi:10.1163/156939306777442908

    15. Wang, M. Y. and J. Xu, "FDTD study on scattering of metallic column covered by double-negative metamaterial," J. of Electromagn. Waves and Appl., Vol. 21, No. 14, 1905-1914, 2007.
    doi:10.1163/156939307783152777

    16. Li, Z. and T. J. Cui, "Novel waveguide directional couplers using left-handed materials," J. of Electromagn. Waves and Appl., Vol. 21, No. 8, 1053-1062, 2007.

    17. Abdalla, M. A. and Z. Hu, "On the study of left-handed coplanar waveguide coupler on ferrite substrate," Progress In Electromagnetics Research Letters, Vol. 1, 69-75, 2008.
    doi:10.2528/PIERL07111808

    18. Lindell, I. V., S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media-media with negative parameters, capable of supporting backward waves," Microw. Opt. Tech. Lett., Vol. 31, 129-133, 2001.
    doi:10.1002/mop.1378

    19. Smith, D. R. and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett., Vol. 90, 077405, 2003.
    doi:10.1103/PhysRevLett.90.077405

    20. Boltasseva, A. and V. M. Shalaev, "Fabrication of optical negative-index metamaterials: Recent advances and outlook," Metamaterials, Vol. 2, 1-17, 2008.
    doi:10.1016/j.metmat.2008.03.004

    21. Bellver-Cebreros, C. and M. Rodriguez-Danta, "Fresnel equation revisited: Application to left-handed media with dielectric anisotropy," EOS Topical Meeting on Diffractive Optics 2007, 133-134, European Optical Society, 2007.

    22. Bellver-Cebreros, C. and M. Rodriguez-Danta, "Eikonal equation, alternative expression of Fresnel's equation and Mohr's construction in optical anisotropic media," Opt. Commun., Vol. 189, 193-209, 2001.
    doi:10.1016/S0030-4018(01)01028-8

    23. Bellver-Cebreros, C. and M. Rodriguez-Danta, "Geometrical analysis of wave propagation in left-handed metamaterials. Part II," Progress In Electromagnetics Research C, Vol. 4, 85-102, 2008.

    24. Fung, Y. C., Foundations of Solid Mechanics, Prentice Hall, Englewood Cliffs, New Jersey, 1965.

    25. Born, M. and E. Wolf, Principles of Optics, Pergamon Press, New York, 1999.

    26. Scharf, T., Polarized Light in Liquid Crystals and Polymers, John Wiley and Sons, Hoboken, New Jersey, 2007.

    27. Akhmanov, S. A. and S. Yu. Nikitin, Physical Optics, Clarendon Press, Oxford, 1999.

    28. Perez, J. H., Optique Geometrique et Ondulatoire, Masson, Paris, 1984.