Catenary Plasmons for Flat Lensing, Beam Deflecting, and Shaping

  • Xiangang LuoEmail author


As discussed in the Chap.  4, surface plasmons are collective excitations of free electrons and photons. The electric force line of surface plasmons at a metal–dielectric surface follows the function defined by a catenary of equal strength. When surface plasmons in adjacent interfaces are coupled together, the evanescent tails would lead to catenary optical fields described by hyperbolic cosine and sine functions. These catenary optical fields help to increase the focal depth of surface plasmon imaging and nanolithography. Here, we show that another unique property of the plasmonic catenary fields can be used to locally modulate the phase retardation. Based on the Young’s double slits interference with unequal widths, the plasmonic propagating phase shift is revealed, and various functional flat plasmonic devices are designed and experimentally demonstrated. Since the gradient phase shift could introduce an additional horizontal wavevector, the classic Snell’s law has also been generalized. Besides propagating phase shift, this chapter also describes the geometric phase induced by the rotated plasmonic nanoslits. Owing to the anisotropic field distribution and dispersion described by two catenary functions, the transmission of both metallic grating and rectangular nanoapertures depend on the polarization of incident light. Consequently, under circularly polarized illumination (with a spin angular momentum of \(\pm \hbar\) for each photon), a space-variant surface structure would generate a polarization-dependent phase retardation. This geometric phase has been investigated to realize both flat lens and spin-controlled beam shaping.


Catenary plasmon Flat lens Extraordinary Young’s interference Structural color Holography 


  1. 1.
    R.P Crease, The most beautiful experiment. Phys. World 15, 19 (2002)CrossRefGoogle Scholar
  2. 2.
    X. Luo, T. Ishihara, Surface plasmon resonant interference nanolithography technique. Appl. Phys. Lett. 84, 4780–4782 (2004)CrossRefGoogle Scholar
  3. 3.
    T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays. Nature 391, 667–669 (1998)CrossRefGoogle Scholar
  4. 4.
    W.L. Barnes, A. Dereux, T.W. Ebbesen, Surface plasmon subwavelength optics. Nature 424, 824–830 (2003)CrossRefGoogle Scholar
  5. 5.
    M. Pu, Y. Guo, X. Li, X. Ma, X. Luo, Revisitation of extraordinary Young’s interference: From catenary optical fields to spin-orbit interaction in metasurfaces. ACS Photonics 5, 3198–3204 (2018)CrossRefGoogle Scholar
  6. 6.
    H. Shi, X. Luo, C. Du, Young’s interference of double metallic nanoslit with different widths. Opt. Express 15, 11321–11327 (2007)CrossRefGoogle Scholar
  7. 7.
    T. Xu, Y. Zhao, D. Gan, C. Wang, C. Du, X. Luo, Directional excitation of surface plasmons with subwavelength slits. Appl. Phys. Lett. 92, 101501 (2008)CrossRefGoogle Scholar
  8. 8.
    W.E. Kock, Metal-lens antennas. Proc. IRE 34, 828–836 (1946)CrossRefGoogle Scholar
  9. 9.
    M. Pu, X. Ma, Y. Guo, X. Li, X. Luo, Theory of microscopic meta-surface waves based on catenary optical fields and dispersion. Opt. Express 26, 19555–19562 (2018)CrossRefGoogle Scholar
  10. 10.
    W.E. Kock, Metallic delay lenses. Bell Syst. Tech. J. 27, 58–82 (1948)CrossRefGoogle Scholar
  11. 11.
    J. Pendry, A. Holden, W. Stewart, I. Youngs, Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996)CrossRefGoogle Scholar
  12. 12.
    R. Shelby, D. Smith, S. Schultz, Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)CrossRefGoogle Scholar
  13. 13.
    V.G. Veselago, E.E. Narimanov, The left hand of brightness: Past, present and future of negative index materials. Nat. Mater. 5, 759–762 (2006)CrossRefGoogle Scholar
  14. 14.
    T. Xu, L. Fang, B. Zeng, Y. Liu, C. Wang, Q. Feng, X. Luo, Subwavelength nanolithography based on unidirectional excitation of surface plasmons. J. Opt. -Pure Appl. Opt. 11, 085003 (2009)CrossRefGoogle Scholar
  15. 15.
    G. Lerosey, D.F.P. Pile, P. Matheu, G. Bartal, X. Zhang, Controlling the phase and amplitude of plasmon sources at a subwavelength scale. Nano Lett. 9, 327–331 (2009)CrossRefGoogle Scholar
  16. 16.
    C. Lu, X. Hu, H. Yang, Q. Gong, Ultrawide-band unidirectional surface plasmon polariton launchers. Adv. Opt. Mater. 1, 792–797 (2013)CrossRefGoogle Scholar
  17. 17.
    R. Zia, M.L. Brongersma, Surface plasmon polariton analogue to Young’s double-slit experiment. Nat. Nanotechnol. 2, 426 (2007)CrossRefGoogle Scholar
  18. 18.
    X. Luo, M. Pu, X. Li, X. Ma, Broadband spin Hall effect of light in single nanoapertures. Light Sci. Appl. 6, e16276 (2017)CrossRefGoogle Scholar
  19. 19.
    B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, G. Bartal, Sub-100 nm focusing of short wavelength plasmons in homogeneous 2D space. Nano Lett. 14, 5598–5602 (2014)CrossRefGoogle Scholar
  20. 20.
    F.J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G.A. Wurtz, A.V. Zayats, Near-field interference for the unidirectional excitation of electromagnetic guided modes. Science 340, 328–330 (2013)CrossRefGoogle Scholar
  21. 21.
    T. Xu, C. Wang, C. Du, X. Luo, Plasmonic beam deflector. Opt. Express 16, 4753–4759 (2008)CrossRefGoogle Scholar
  22. 22.
    X. Luo, Principles of electromagnetic waves in metasurfaces. Sci. China-Phys. Mech. Astron. 58, 594201 (2015)CrossRefGoogle Scholar
  23. 23.
    Y. Xu, Y. Fu, H. Chen, Planar gradient metamaterials. Nat. Rev. Mater. 1, 16067 (2016)CrossRefGoogle Scholar
  24. 24.
    P. Lalanne, P. Chavel, Metalenses at visible wavelengths: Past, present, perspectives. Laser Photonics Rev. 11, 1600295 (2017)CrossRefGoogle Scholar
  25. 25.
    F. Capasso, The future and promise of flat optics: A personal perspective. Nanophotonics 7, 953 (2018)CrossRefGoogle Scholar
  26. 26.
    X. Luo, Subwavelength optical engineering with metasurface waves. Adv. Opt. Mater. 6, 1701201 (2018)CrossRefGoogle Scholar
  27. 27.
    N. Yu, P. Genevet, M.A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science 334, 333–337 (2011)CrossRefGoogle Scholar
  28. 28.
    X. Ni, N.K. Emani, A.V. Kildishev, A. Boltasseva, V.M. Shalaev, Broadband light bending with plasmonic nanoantennas. Science 335, 427–427 (2012)CrossRefGoogle Scholar
  29. 29.
    M. Khorasaninejad, W.T. Chen, R.C. Devlin, J. Oh, A.Y. Zhu, F. Capasso, Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging. Science 352, 1190–1194 (2016)CrossRefGoogle Scholar
  30. 30.
    S. Chen, Z. Li, Y. Zhang, H. Cheng, J. Tian, Phase manipulation of electromagnetic waves with metasurfaces and its applications in nanophotonics. Adv. Opt. Mater. 6, 1800104 (2018)CrossRefGoogle Scholar
  31. 31.
    P. Lalanne, S. Astilean, P. Chavel, E. Cambril, H. Launois, Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings. Opt. Lett. 23, 1081–1083 (1998)CrossRefGoogle Scholar
  32. 32.
    J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)Google Scholar
  33. 33.
    T. Xu, C. Du, C. Wang, X. Luo, Subwavelength imaging by metallic slab lens with nanoslits. Appl. Phys. Lett. 91, 201501 (2007)CrossRefGoogle Scholar
  34. 34.
    L. Verslegers, P.B. Catrysse, Z. Yu, J.S. White, E.S. Barnard, M.L. Brongersma, S. Fan, Planar lenses based on nanoscale slit arrays in a metallic film. Nano Lett. 9, 235–238 (2009)CrossRefGoogle Scholar
  35. 35.
    C. Min, P. Wang, X. Jiao, Y. Deng, H. Ming, Beam manipulating by metallic nano-optic lens containing nonlinear media. Opt. Express 15, 9541–9546 (2007)CrossRefGoogle Scholar
  36. 36.
    Y. Chen, X. Li, Y. Sonnefraud, A.I. Fernández-Domínguez, X. Luo, M. Hong, S.A. Maier, Engineering the phase front of light with phase-change material based planar lenses. Sci. Rep. 5, 8660 (2015)CrossRefGoogle Scholar
  37. 37.
    Y. Chen, C. Zhou, X. Luo, C. Du, Structured lens formed by a 2D square hole array in a metallic film. Opt. Lett. 33, 753–755 (2008)CrossRefGoogle Scholar
  38. 38.
    L. Lin, X.M. Goh, L.P. McGuinness, A. Roberts, Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing. Nano Lett. 10, 1936 (2010)CrossRefGoogle Scholar
  39. 39.
    M. Totzeck, W. Ulrich, A. Gohnermeier, W. Kaiser, Semiconductor fabrication: Pushing deep ultraviolet lithography to its limits. Nat. Photonics 1, 629–631 (2007)CrossRefGoogle Scholar
  40. 40.
    S. Ishii, V.M. Shalaev, A.V. Kildishev, Holey-metal lenses: Sieving single modes with proper phases. Nano Lett. 13, 159–163 (2013)CrossRefGoogle Scholar
  41. 41.
    J. Sun, X. Wang, T. Xu, Z.A. Kudyshev, A.N. Cartwright, N.M. Litchinitser, Spinning light on the nanoscale. Nano Lett. 14, 2726–2729 (2014)CrossRefGoogle Scholar
  42. 42.
    M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, X. Luo, Catenary optics for achromatic generation of perfect optical angular momentum. Sci. Adv. 1, e1500396 (2015)CrossRefGoogle Scholar
  43. 43.
    F. Aieta, M.A. Kats, P. Genevet, F. Capasso, Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science 347, 1342–1345 (2015)CrossRefGoogle Scholar
  44. 44.
    Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, X. Luo, Multispectral optical metasurfaces enabled by achromatic phase transition. Sci. Rep. 5, 15781 (2015)CrossRefGoogle Scholar
  45. 45.
    W.T. Chen, A.Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, F. Capasso, A broadband achromatic metalens for focusing and imaging in the visible. Nat. Nanotechnol. 13, 220–226 (2018)CrossRefGoogle Scholar
  46. 46.
    S. Wang, P.C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H.Y. Kuo, B.H. Chen, Y.H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, D.P. Tsai, A broadband achromatic metalens in the visible. Nat. Nanotechnol. 13, 227–232 (2018)CrossRefGoogle Scholar
  47. 47.
    O. Avayu, E. Almeida, Y. Prior, T. Ellenbogen, Composite functional metasurfaces for multispectral achromatic optics. Nat. Commun. 8, 14992 (2017)CrossRefGoogle Scholar
  48. 48.
    Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, X. Luo, Achromatic flat optical components via compensation between structure and material dispersions. Sci. Rep. 6, 19885 (2016)CrossRefGoogle Scholar
  49. 49.
    L. Rayleigh, XXXI. Investigations in optics, with special reference to the spectroscope. Philos. Mag. Ser. 5(8), 261–274 (1879)CrossRefGoogle Scholar
  50. 50.
    N.I. Zheludev, What diffraction limit? Nat. Mater. 7, 420–422 (2008)CrossRefGoogle Scholar
  51. 51.
    M. Pu, C. Wang, Y. Wang, X. Luo, Subwavelength electromagnetics below the diffraction limit. Acta Phys. Sin. 66, 144101 (2017)Google Scholar
  52. 52.
    F. Qin, M. Hong, Breaking the diffraction limit in far field by planar metalens. Sci. China Phys. Mech. Astron. 60, 044231 (2017)CrossRefGoogle Scholar
  53. 53.
    S.W. Hell, J. Wichmann, Breaking the diffraction resolution limit by stimulated emission: Stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 19, 780–782 (1994)CrossRefGoogle Scholar
  54. 54.
    B. Huang, M. Bates, X. Zhuang, Super resolution fluorescence microscopy. Annu. Rev. Biochem. 78, 993 (2009)CrossRefGoogle Scholar
  55. 55.
    G.T. di Francia, Super-gain antennas and optical resolving power. G Suppl Nuovo Cim 9, 426–438 (1952)CrossRefGoogle Scholar
  56. 56.
    M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999)Google Scholar
  57. 57.
    E.T.F. Rogers, N.I. Zheludev, Optical super-oscillations: Sub-wavelength light focusing and super-resolution imaging. J. Opt. 15, 094008 (2013)CrossRefGoogle Scholar
  58. 58.
    E.T.F. Rogers, S. Savo, J. Lindberg, T. Roy, M.R. Dennis, N. Zheludev, Super-oscillatory optical needle. Appl. Phys. Lett. 102, 031108 (2013)CrossRefGoogle Scholar
  59. 59.
    F. Qin, K. Huang, J. Wu, J. Teng, C. Qiu, M. Hong, A supercritical lens optical label-free microscopy: Sub-diffraction resolution and ultra-long working distance. Adv. Mater. 29, 1602721 (2017)CrossRefGoogle Scholar
  60. 60.
    C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, X. Luo, Super-resolution optical telescopes with local light diffraction shrinkage. Sci. Rep. 5, 18485 (2015)Google Scholar
  61. 61.
    D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, X. Luo, Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing. Laser Photonics Rev. 9, 713–719 (2015)CrossRefGoogle Scholar
  62. 62.
    L.B. Whitbourn, R.C. Compton, Equivalent-circuit formulas for metal grid reflectors at a dielectric boundary. Appl. Opt. 24, 217–220 (1985)CrossRefGoogle Scholar
  63. 63.
    N. Engheta, Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials. Science 317, 1698–1702 (2007)CrossRefGoogle Scholar
  64. 64.
    Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, X. Luo, Achromatic broadband super-resolution imaging by super-oscillatory metasurface. Laser Photonics Rev. 12, 1800064 (2018)CrossRefGoogle Scholar
  65. 65.
    C. Genet, T.W. Ebbesen, Light in tiny holes. Nature 445, 39–46 (2007)CrossRefGoogle Scholar
  66. 66.
    T. Xu, Y.-K. Wu, X. Luo, L.J. Guo, Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging. Nat. Commun. 1, 59 (2010)Google Scholar
  67. 67.
    T. Xu, E.C. Walter, A. Agrawal, C. Bohn, J. Velmurugan, W. Zhu, H.J. Lezec, A.A. Talin, High-contrast and fast electrochromic switching enabled by plasmonics. Nat. Commun. 7, 10479 (2016)CrossRefGoogle Scholar
  68. 68.
    P.B. Johnson, R.W. Christy, Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972)CrossRefGoogle Scholar
  69. 69.
    M. Song, X. Li, M. Pu, Y. Guo, K. Liu, H. Yu, X. Ma, X. Luo, Color display and encryption with a plasmonic polarizing metamirror. Nanophotonics 7, 323–331 (2018)CrossRefGoogle Scholar
  70. 70.
    X. Zhu, Y. Zhang, J. Zhang, J. Xu, Y. Ma, Z. Li, D. Yu, Ultrafine and smooth full metal nanostructures for plasmonics. Adv. Mater. 22, 4345–4349 (2010)CrossRefGoogle Scholar
  71. 71.
    T. Smith, J. Guild, The C.I.E. colorimetric standards and their use. Trans. Opt. Soc. 33, 73 (1931)CrossRefGoogle Scholar
  72. 72.
    V.R. Shrestha, S.-S. Lee, E.-S. Kim, D.-Y. Choi, Aluminum plasmonics based highly transmissive polarization-independent subtractive color Filters exploiting a nanopatch array. Nano Lett. 14, 6672–6678 (2014)CrossRefGoogle Scholar
  73. 73.
    Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J.D. Joannopoulos, M. Soljačić, Structural colors from Fano resonances. ACS Photonics 2, 27–32 (2015)CrossRefGoogle Scholar
  74. 74.
    A.F. Kaplan, T. Xu, L.J. Guo, High efficiency resonance-based spectrum filters with tunable transmission bandwidth fabricated using nanoimprint lithography. Appl. Phys. Lett. 99, 143111 (2011)CrossRefGoogle Scholar
  75. 75.
    L.J. Sherry, S. Chang, G.C. Schatz, R.P. Van Duyne, B.J. Wiley, Y. Xia, Localized surface plasmon resonance spectroscopy of single silver nanocubes. Nano Lett. 5, 2034–2038 (2005)CrossRefGoogle Scholar
  76. 76.
    Y.-W. Huang, W.T. Chen, W.-Y. Tsai, P.C. Wu, C.-M. Wang, G. Sun, D.P. Tsai, Aluminum plasmonic multicolor meta-hologram. Nano Lett. 15, 3122–3127 (2015)CrossRefGoogle Scholar
  77. 77.
    X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, X. Luo, Multicolor 3D meta-holography by broadband plasmonic modulation. Sci. Adv. 2, e1601102 (2016)CrossRefGoogle Scholar
  78. 78.
    R.W. Gerchberg, W.O. Saxton, A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237–250 (1972)Google Scholar
  79. 79.
    X. Ni, A.V. Kildishev, V.M. Shalaev, Metasurface holograms for visible light. Nat. Commun. 4, 2807 (2013)CrossRefGoogle Scholar
  80. 80.
    Z.-L. Deng, G. Li, Metasurface optical holography. Mater. Today Phys. 3, 16–32 (2017)CrossRefGoogle Scholar
  81. 81.
    S. Wang, X. Ouyang, Z. Feng, Y. Cao, M. Gu, X. Li, Diffractive photonic applications mediated by laser reduced graphene oxides. Opto-Electron. Adv. 1, 170002 (2018)Google Scholar
  82. 82.
    X. Zhang, M. Pu, J. Jin, X. Li, P. Gao, X. Ma, C. Wang, X. Luo, Helicity multiplexed spin-orbit interaction in metasurface for colorized and encrypted. Ann. Phys. 529, 1700248 (2017)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Optical Technologies on Nano-fabrication and Micro-engineering, Institute of Optics and ElectronicsChinese Academy of SciencesChengduChina

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