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Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves

Nature Materials volume 11, pages 426–431 (2012)Cite this article

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Abstract

The arbitrary control of electromagnetic waves is a key aim of photonic research. Although, for example, the control of freely propagating waves (PWs; refs 1, 2, 3, 4, 5, 6) and surface waves (SWs; refs 7, 8, 9, 10) has separately become possible using transformation optics and metamaterials, a bridge linking both propagation types has not yet been found. Such a device has particular relevance given the many schemes of controlling electromagnetic waves at surfaces and interfaces, leading to trapped rainbows11,12, lensing13,14,15,16, beam bending17, deflection18,19,20, and even anomalous reflection/refraction21,22. Here, we demonstrate theoretically and experimentally that a specific gradient-index meta-surface can convert a PW to a SW with nearly 100% efficiency. Distinct from conventional devices such as prism23 or grating24,25,26 couplers, the momentum mismatch between PW and SW is compensated by the reflection-phase gradient of the meta-surface, and a nearly perfect PW–SW conversion can happen for any incidence angle larger than a critical value. Experiments in the microwave region, including both far-field and near-field characterizations, are in excellent agreement with full-wave simulations. Our findings may pave the way for many applications, including high-efficiency surface plasmon couplers, anti-reflection surfaces, light absorbers, and so on.

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Figure 1: Physical concept of the PW–SW conversion and mode-expansion calculations on model systems.
Figure 2: Sample design, fabrication, and far-field characterization.
Figure 3: Near-field characterizations on the meta-surfaces.
Figure 4: Verifications of the dispersion relation = ξ+k0sinθi.
Figure 5: Guiding the driven SWs outside the meta-surface.

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References

  1. Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006).

    Article  CAS  Google Scholar 

  2. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

    Article  CAS  Google Scholar 

  3. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).

    Article  CAS  Google Scholar 

  4. Cai, W. S., Chettiar, U. K., Kildishev, A. V. & Shalaev, V. M. Optical cloaking with metamaterials. Nature Photon. 1, 224–227 (2007).

    Article  CAS  Google Scholar 

  5. Chen, H. Y., Chan, C. T. & Sheng, P. Transformation optics and metamaterials. Nature Mater. 9, 387–396 (2010).

    Article  CAS  Google Scholar 

  6. Ma, H. F. & Cui, T. J. Three-dimensional broadband ground-plane cloak made of metamaterials. Nature Commun. 1, 21 (2010).

    CAS  Google Scholar 

  7. Liu, Y. M., Zentgraf, T., Bartal, G. & Zhang, X. Transformational plasmon optics. Nano Lett. 10, 1991–1997 (2010).

    Article  CAS  Google Scholar 

  8. Huidobro, P. A., Nesterov, M. L., Martin-Moreno, L. & Garcı´a-Vidal, F. J. Transformation optics for plasmonics. Nano Lett. 10, 1985–1990 (2010).

    Article  CAS  Google Scholar 

  9. Aubry, A. et al. Plasmonic light-harvesting devices over the whole visible spectrum. Nano Lett. 10, 2574–2579 (2010).

    Article  CAS  Google Scholar 

  10. Zentgraf, T., Liu, Y. M., Mikkelsen, M. H., Valentine, J. & Zhang, X. Plasmonic Luneburg and Eaton lenses. Nature Nanotech. 6, 151–155 (2011).

    Article  CAS  Google Scholar 

  11. Tsakmakidis, K. L., Boardman, A. D. & Hess, O. ‘Trapped rainbow’ storage of light in metamaterials. Nature 450, 397–401 (2007).

    Article  CAS  Google Scholar 

  12. Gan, Q. Q., Fu, Z., Ding, Y. J. & Bartoli, F. J. Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures. Phys. Rev. Lett. 100, 256803 (2008).

    Article  Google Scholar 

  13. Levy, U. et al. Inhomogenous dielectric metamaterials with space-variant polarizability. Phys. Rev. Lett. 98, 243901 (2007).

    Article  Google Scholar 

  14. Pinchuk, A. O. & Schatz, G. C. Metamaterials with gradient negative index of refraction. J. Opt. Soc. Am. A 24, A39–A44 (2007).

    Article  Google Scholar 

  15. Paul, O., Reinhard, B., Krolla, B., Beigang, R. & Rahm, M. Gradient index metamaterial based on slot elements. Appl. Phys. Lett. 96, 241110 (2010).

    Article  Google Scholar 

  16. Kundtz, N. & Smith, D. R. Extreme-angle broadband metamaterial lens. Nature Mater. 9, 129–132 (2010).

    Article  CAS  Google Scholar 

  17. Vasić, B., Isić, G., Gajić, R. & Hingerl, K. Controlling electromagnetic fields with graded photonic crystals in metamaterial regime. Opt. Express 18, 20321–20333 (2010).

    Article  Google Scholar 

  18. Smith, D. R., Mock, J. J., Starr, A. F. & Schurig, D. Gradient index metamaterials. Phys. Rev. E 71, 036609 (2005).

    Article  CAS  Google Scholar 

  19. Lin, X. Q. et al. Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens. Appl. Phys. Lett. 92, 131904 (2008).

    Article  Google Scholar 

  20. Liu, R. et al. Broadband gradient index microwave quasi optical elements based on non-resonant metamaterials. Opt. Express 17, 21030–21041 (2009).

    Article  CAS  Google Scholar 

  21. Yu, N. et al. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science 334, 333–337 (2011).

    Article  CAS  Google Scholar 

  22. Ni, X., Emani, N. K., Kildishev, A., V., Boltasseva, A. & Shalaev, V. M. Broadband light bending with plasmonic nanoantennas. Science 335, 427 (2012).

    Article  CAS  Google Scholar 

  23. Kretschmann, E. & Raether, H. Radiative decay of nonradiative surface plasmons excited by light. Z. Naturforsch. 23A, 2135–2136 (1968).

    Google Scholar 

  24. Raether, H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

    Book  Google Scholar 

  25. Neviere, M., Petit, R. & Cadilhac, M. About the theory of optical crating coupler-waveguide systems. Opt. Commun. 8, 113–117 (1973).

    Article  Google Scholar 

  26. Tang, Y. B., Wang, Z. C., Wosinski, L., Westergren, U. & He, S. L. Highly efficient nonuniform grating coupler for silicon-on-insulator nanophotonic circuits. Opt. Lett. 35, 1290–1292 (2010).

    Article  Google Scholar 

  27. Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003).

    Article  CAS  Google Scholar 

  28. Born, M. & Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, 1999).

    Book  Google Scholar 

  29. Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).

    Article  Google Scholar 

  30. Landau, L. D., Liftshitz, E. M. & Pitaevskii, L. P. Electrodynamics of Continuous Media 2nd edn (Pergamon, 1984).

    Google Scholar 

  31. Sheng, P., Stepleman, R. S. & Sanda, P. N. Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations. Phys. Rev. B 26, 2907–2917 (1982).

    Article  CAS  Google Scholar 

  32. Garcia-Vidal, F. J., Martín-Moreno, L. & Pendry, J. B. Surfaces with holes in them: New plasmonic metamaterials. J. Opt. A Pure Appl. Opt. 7, S97–S101 (2005).

    Article  Google Scholar 

  33. Bansal, R. Bending Snell’s laws. IEEE Antenn. Propag. Mag. 53, 146–147 (2011).

    Google Scholar 

  34. Hao, J. M., Zhou, L. & Chan, C. T. An effective-medium model for high-impedance surfaces. Appl. Phys. A 87, 281–284 (2007).

    Article  Google Scholar 

  35. Lockyear, M. J., Hibbins, A. P. & Sambles, J. R. Microwave surface-plasmon-like modes on thin metamaterials. Phys. Rev. Lett. 102, 073901 (2009).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (60990321, 11174055, 60725417) and the Ministry of Education of China (B06011). S.S. was supported by the National Science Council and National Center for Theoretical Sciences of Taiwan. We thank Y. R. Shen and C. T. Chan for helpful discussions.

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  1. Shulin Sun, Qiong He and Shiyi Xiao: These authors contributed equally to this work

Authors and Affiliations

  1. Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education) and Physics Department, State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China

    Shulin Sun, Qiong He, Shiyi Xiao, Qin Xu, Xin Li & Lei Zhou

  2. National Center of Theoretical Sciences at Taipei (Physics Division) and Department of Physics, National Taiwan University, Taipei 10617, Taiwan

    Shulin Sun

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Contributions

S.S. did the theoretical calculations and designed the samples. Q.H. and S.X. made the samples and did the measurements. Q.X. helped in theoretical calculations. X.L. helped in experimental measurements. L.Z. conceived the idea, developed the mode-expansion theory and wrote the manuscript.

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Correspondence to Lei Zhou.

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Sun, S., He, Q., Xiao, S. et al. Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves. Nature Mater 11, 426–431 (2012). https://doi.org/10.1038/nmat3292

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