Vol. 107

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Resonant Modes and Resonant Transmission in Multi-Layer Structures

By Andrei I. Smolyakov, E. A. Fourkal, Sergei I. Krasheninnikov, and Natalia Sternberg
Progress In Electromagnetics Research, Vol. 107, 293-314, 2010


Resonant modes of multi-layer structures which contain the regions of negative epsilon material (such as a metal in the visible range) are analyzed. Existence of two separate classes of resonant modes is demonstrated. One is related to the excitation of the surface mode at the interface of the regions with opposite signs of the dielectric constant and involve energy transport by evanescent modes throughout the whole structure. The second class involves propagating modes (which form the resonant standing wave) in some regions and the evanescent waves in other layers with ε<0. It is shown that the resonant transmission is related to the existence of quasi-stationary leaky modes having a finite life-time and characterized by large wave amplitude in the trapping region. It is shown that both types of resonances can coexist in multi-layer structures. It is also shown that the interaction of the symmetric and anti-symmetric surface eigen-modes widens the resonant transmission region.


Andrei I. Smolyakov, E. A. Fourkal, Sergei I. Krasheninnikov, and Natalia Sternberg, "Resonant Modes and Resonant Transmission in Multi-Layer Structures," Progress In Electromagnetics Research, Vol. 107, 293-314, 2010.


    1. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 8, No. 18, 3966-3969, 2000.

    2. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Physical Review Letters, Vol. 84, No. 18, 4184-4187, 2000.

    3. Feng, S. M., J. M. Elson, and P. L. Overfelt, "Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes," Optics Express, Vol. 13, No. 11, 4113-4124, 2005.

    4. Feng, T. H., Y. H. Li, J. Y. Guo, L. He, H. Q. Li, Y. W. Zhang, Y. L. Shi, and H. Chen, "Highly localized mode in a pair structure made of epsilon-negative and mu-negative metamaterials," Journal of Applied Physics, Vol. 104, No. 1, 2008.

    5. Alu, A. and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 10, 2558-2571, 2003.

    6. Alu, A. and N. Engheta, "Evanescent growth and tunneling through stacks of frequency-selective surfaces," IEEE Antennas and Wireless Propagation Letters, Vol. 4, 417-420, 2005.

    7. Brodin, G., A. Marklund, L. Stenflo, and R. K. Shukla, "Anomalous reflection and excitation of surface waves in metamaterials," Physics Letters A, Vol. 367, No. 3, 233-236, 2007.

    8. Bliokh, K. Y. and Y. P. Bliokh, "What are the left-handed media and what is interesting about them?," Physics-Uspekhi, Vol. 47, No. 4, 393-400, 2004.

    9. Fang, N., H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science, Vol. 308, No. 5721, 534-537, 2005.

    10. Dragila, R., B. Lutherdavies, and S. Vukovic, "High transparency of classically opaque metallic-films," Physical Review Letters, Vol. 55, No. 10, 1117-1120, 1985.

    11. Hayashi, S., H. Kurokawa, and H. Oga, "Observation of resonant photon tunneling in photonic double barrier structures," Optical Review, Vol. 6, No. 3, 204-210, 1999.

    12. Wegener, M., G. Dolling, and S. Linden, "Plasmonics: Backward waves moving forward," Nature Materials, Vol. 6, No. 7, 475-476, 2007.

    13. Zhou, L., W. J. Wen, C. T. Chan, and P. Sheng, "Electromagneticwave tunneling through negative-permittivity media with high magnetic fields," Physical Review Letters, Vol. 94, No. 24, 2005.

    14. Hooper, I. R., T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Physical Review Letters, Vol. 97, No. 5, 2006.

    15. Tomita, S., T. Yokoyama, H. Yanagi, B. Wood, J. B. Pendry, M. Fujii, and S. Hayashi, "Resonant photon tunneling via surface plasmon polaritons through one-dimensional metal-dielectric metamaterials," Optics Express, Vol. 16, No. 13, 9942-9950, 2008.

    16. Lin, L., R. J. Reeves, and R. J. Blaikie, "Surface-plasmon-enhanced light transmission through planar metallic films," Physical Review B, Vol. 74, No. 15, 2006.

    17. Mattiucci, N., G. D'Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, "Transmission function properties for multilayered structures: Application to super-resolution," Optics Express, Vol. 17, No. 20, 17517-17529, 2009.

    18. Prosvirnin, S. L., S. A. Tretyakov, T. D. Vasilyeva, A. Fourrier-Lamer, and S. Zouhdi, "Analysis of reflection and transmission of electromagnetic waves in complex layered arrays," Journal of Electromagnetic Waves and Applications, Vol. 14, No. 6, 807-826, 2000.

    19. Suyama, T., Y. Okino, and T. Matsuda, "Surface plasmon resonance absorption in a multilayered thin-film grating," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 13, 1773-1783, 2009.

    20. Lu, J., B. I. Wu, J. A. Kong, and M. Chen, "Guided modes with a linearly varying transverse field inside a left-handed dielectric slab," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 5, 689-697, 2006.

    21. Ramazashvili, R. R., "Total transmission of electromagneticwaves through slabs of plasmas and plasma-like media upon the excitation of surface-waves," Jetp Letters, Vol. 43, No. 5, 298-301, 1986.

    22. Fourkal, E., I. Velchev, C. M. Ma, and A. Smolyakov, "Evanescent wave interference and the total transparency of a warm highdensity plasma slab," Physics of Plasmas, Vol. 13, No. 9, 2006.

    23. Fourkal, E., I. Velchev, C. M. Ma, and A. Smolyakov, "Resonant transparency of materials with negative permittivity," Physics Letters A, Vol. 361, No. 4-5, 277-282, 2007.

    24. Chiao, R. Y., P. G. Kwiat, and A. M. Steinberg, "Analogies between electron and photon tunneling --- A proposed experiment to measure photon tunneling times," Physica B, Vol. 175, No. 1-3, 257-262, 1991.

    25. Winful, H. G., "Tunneling time, the hartman effect, and superluminality: A proposed resolution of an old paradox," Physics Reports-Review Section of Physics Letters, Vol. 436, No. 1-2, 1-69, 2006.

    26. Chang, L. L., L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Applied Physics Letters, Vol. 24, No. 12, 593-595, 1974.

    27. Chang, L. L. and L. Esaki, "Semiconductor quantum heterostructures," Physics Today, Vol. 45, No. 10, 36-43, 1992.

    28. Gradov, O. M. and L. Stenflo, "Linear-theory of a cold bounded plasma," Physics Reports-Review Section of Physics Letters, Vol. 94, No. 3, 111-137, 1983.

    29. Raether, H., Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer Verlag, Berlin, 1988.

    30. Ramakrishna, S. A., "Physics of negative refractive index materials," Reports on Progress in Physics, Vol. 68, No. 2, 449-521, 2005.

    31. Leontovich, M. A. and L. I. Mandelstam, "To the theory of schrodinger equation," Ztschr. Phys., Vol. 47, 131-136, 1928.

    32. Pollard, R. J., A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, "Optical nonlocalities and additional waves in epsilon-near-zero metamaterials," Physical Review Letters, Vol. 102, No. 12, 2009.

    33. Daninthe, H., S. Foteinopoulou, and C. M. Soukoulis, "Omnire-flectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photonics and Nanostructures --- Fundamentals and Applications, Vol. 4, No. 3, 123-131, 2006.

    34. Darmanyan, S. A. and A. V. Zayats, "Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: An analytical study," Physical Review B, Vol. 67, No. 3, 035424, 2003.

    35. Winful, H. G., "Apparent superluminality and the generalized hartman effect in double-barrier tunneling (Vol. 72, P. 046608, 2005)," Physical Review E, Vol. 73, No. 3, 2006.