Beam Shaping via Microscopic Meta-surface-wave

  • Xiangang LuoEmail author


In previous chapter, we discussed the theory, design principle, and application of phase modulation based on plasmonic nanoslits, nanoholes, and other nanoapertures. The coupling of SPPs at the interfaces forms catenary plasmons featured by catenary-liked intensity profile. This can be understood from two aspects: first, the analytic mathematical description of plasmonic modes in metal–insulator–metal layered waveguide takes the form of hyperbolic cosine and sine functions; second, the summation of evanescent tails of waveguide modes would form a catenary. In this chapter, we show a generalized concept of catenary optical fields. The interference fields of two subwavelength scatters would follow a catenary shape. For instance, the two sides of a subwavelength slit perforated in a thin metallic screen could generate strong localized fields featured by a catenary function. This effect can be also observed in periodic slits, i.e., 1D grating. Interestingly, the equivalent impedance of such grating is described by the catenary of equal strength, which is termed catenary dispersion. Based on these properties, we proposed the concept of microscopic meta-surface-wave, which forms one important basis to discuss the light–matter interaction in subwavelength structures.


Meta-surface-wave Wavefront shaping Beam steering Cloak Virtual shaping 


  1. 1.
    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
  2. 2.
    J.A. Polo, A. Lakhtakia, Surface electromagnetic waves: a review. Laser. Photonics. Rev. 5, 234–246 (2011)CrossRefGoogle Scholar
  3. 3.
    X. Luo, Principles of electromagnetic waves in metasurfaces. Sci. China-Phys. Mech. Astron. 58, 594201 (2015)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.
    P. Cheben, R. Halir, J.H. Schmid, H.A. Atwater, D.R. Smith, Subwavelength integrated photonics. Nature 560, 565–572 (2018)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    M. Khorasaninejad, F. Capasso, Metalenses: versatile multifunctional photonic components. Science 358, eaam8100 (2017)CrossRefGoogle Scholar
  8. 8.
    M. Pu, X. Ma, X. Li, Y. Guo, X. Luo, Merging plasmonics and metamaterials by two-dimensional subwavelength structures. J. Mater. Chem. C 5, 4361 (2017)CrossRefGoogle Scholar
  9. 9.
    X. Luo, Subwavelength optical engineering with metasurface waves. Adv. Opt. Mater. 6, 1701201 (2018)CrossRefGoogle Scholar
  10. 10.
    S.B. Glybovski, S.A. Tretyakov, P.A. Belov, Y.S. Kivshar, C.R. Simovski, Metasurfaces: from microwaves to visible. Phys. Rep. 634, 1–72 (2016)CrossRefGoogle Scholar
  11. 11.
    X. Luo, T. Ishihara, Surface plasmon resonant interference nanolithography technique. Appl. Phys. Lett. 84, 4780–4782 (2004)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    X. Luo, Engineering optics 2.0: a revolution in optical materials, devices, and systems. ACS Photonics 5, 4724-4738 (2018)CrossRefGoogle Scholar
  14. 14.
    X. Luo, T. Ishihara, in Sub 100 nm lithography based on plasmon polariton resonance. 2003 International Microprocesses and Nanotechnology Conference (IEEE, 2003), pp. 138–139Google Scholar
  15. 15.
    T. Xu, C. Wang, C. Du, X. Luo, Plasmonic beam deflector. Opt. Express 16, 4753–4759 (2008)CrossRefGoogle Scholar
  16. 16.
    M.G. Moharam, T.K. Gaylord, Rigorous coupled-wave analysis of metallic surface-relief gratings. J. Opt. Soc. Am. A 3, 1780–1787 (1986)CrossRefGoogle Scholar
  17. 17.
    M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, X. Luo, Investigation of Fano resonance in planar metamaterial with perturbed periodicity. Opt. Express 21, 992–1001 (2013)CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    Q. Feng, M. Pu, C. Hu, X. Luo, Engineering the dispersion of metamaterial surface for broadband infrared absorption. Opt. Lett. 37, 2133–2135 (2012)CrossRefGoogle Scholar
  20. 20.
    T. Senior, Approximate boundary conditions. IEEE Trans. Antennas Propag. 29, 826–829 (1981)CrossRefGoogle Scholar
  21. 21.
    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
  22. 22.
    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
  23. 23.
    M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, X. Luo, Design principles for infrared wide-angle perfect absorber based on plasmonic structure. Opt. Express 19, 17413–17420 (2011)CrossRefGoogle Scholar
  24. 24.
    H.-T. Chen, Interference theory of metamaterial perfect absorbers. Opt. Express 20, 7165–7172 (2012)CrossRefGoogle Scholar
  25. 25.
    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
  26. 26.
    Z. Ma, S.M. Hanham, P. Albella, B. Ng, H.T. Lu, Y. Gong, S.A. Maier, M. Hong, Terahertz all-dielectric magnetic mirror metasurfaces. ACS Photonics 3, 1010–1018 (2016)CrossRefGoogle Scholar
  27. 27.
    R. Paniagua-Domínguez, Y.F. Yu, A.E. Miroshnichenko, L.A. Krivitsky, Y.H. Fu, V. Valuckas, L. Gonzaga, Y.T. Toh, A.Y.S. Kay, B.S. Luk’yanchuk, A.I. Kuznetsov, Generalized Brewster effect in dielectric metasurfaces. Nat. Commun. 7, 10362 (2016)Google Scholar
  28. 28.
    D. Van Labeke, D. Gerard, B. Guizal, F.I. Baida, L. Li, An angle-independent frequency selective surface in the optical range. Opt. Express 14, 11945–11951 (2006)CrossRefGoogle Scholar
  29. 29.
    M. Pu, X. Li, Y. Guo, X. Ma, X. Luo, Nanoapertures with ordered rotations: symmetry transformation and wide-angle flat lensing. Opt. Express 25, 31471–31477 (2017)CrossRefGoogle Scholar
  30. 30.
    X. Xie, X. Li, M. Pu, X. Ma, K. Liu, Y. Guo, X. Luo, Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion. Adv. Funct. Mater. 28, 1706673 (2018)CrossRefGoogle Scholar
  31. 31.
    M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, X. Luo, Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping. Sci. Rep. 5, 9822 (2015)CrossRefGoogle Scholar
  32. 32.
    S. Simms, V. Fusco, Chessboard reflector for RCS reduction. Electron. Lett. 44, 316–317 (2008)CrossRefGoogle Scholar
  33. 33.
    L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, S. Zhang, Three-dimensional optical holography using a plasmonic metasurface. Nat. Commun. 4, 2808 (2013)CrossRefGoogle Scholar
  34. 34.
    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
  35. 35.
    Y. Guo, J. Yan, M. Pu, X. Li, X. Ma, Z. Zhao, X. Luo, Ultra-wideband manipulation of electromagnetic waves by bilayer scattering engineered gradient metasurface. RSC Adv. 8, 13061–13066 (2018)CrossRefGoogle Scholar
  36. 36.
    Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, X. Luo, Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion. Sci. Rep. 5, 8434 (2015)CrossRefGoogle Scholar
  37. 37.
    G.G. Macfarlane, Quasi-stationary field theory and its application to diaphragms and junctions in transmission lines and wave guides. J. Inst. Electr. Eng. Part III A Radiolocation 93, 703–719 (1946)Google Scholar
  38. 38.
    J.R. Swandic, Bandwidth Limits and Other Considerations for Monostatic RCS Reduction by Virtual Shaping (Naval Surface Warfare Center, Carderock Div., 2004)Google Scholar
  39. 39.
    J.B. Pendry, D. Schurig, D.R. Smith, Controlling electromagnetic fields. Science 312, 1780–1782 (2006)CrossRefGoogle Scholar
  40. 40.
    X. Ni, Z.J. Wong, M. Mrejen, Y. Wang, X. Zhang, An ultrathin invisibility skin cloak for visible light. Science 349, 1310–1314 (2015)CrossRefGoogle Scholar
  41. 41.
    C. Huang, J. Yang, X. Wu, J. Song, M. Pu, C. Wang, X. Luo, Reconfigurable metasurface cloak for dynamical electromagnetic illusions. ACS Photonics 5, 1718–1725 (2018)CrossRefGoogle Scholar
  42. 42.
    Y. Huang, M. Pu, F. Zhang, J. Luo, X. Li, X. Ma, X. Luo, Broadband functional metasurface: Achieving non-linear phase generation towards achromatic surface cloaking and lensing. Adv. Opt. Mater. 1801480 (2019)Google Scholar
  43. 43.
    F. Gires, P. Tournois, Interferometre utilisable pour la compression d’ impulsions lumineuses modulees en frequence. C. R. Acad. Sci. Paris 258, 6112–6115 (1964)Google Scholar
  44. 44.
    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
  45. 45.
    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
  46. 46.
    Y. Guo, X. Ma, M. Pu, X. Li, Z. Zhao, X. Luo, High-efficiency and wide-angle beam steering based on catenary optical fields in ultrathin metalens. Adv. Opt. Mater. 6, 1800592 (2018)CrossRefGoogle Scholar
  47. 47.
    R.K. Luneburg, Mathematical Theory of Optics (Brown University, 1944)Google Scholar
  48. 48.
    H. Ma, T. Cui, Three-dimensional broadband and broad-angle transformation-optics lens. Nat. Commun. 1, 124 (2010)CrossRefGoogle Scholar
  49. 49.
    N. Kundtz, D.R. Smith, Extreme-angle broadband metamaterial lens. Nat. Mater. 9, 129–132 (2010)CrossRefGoogle Scholar
  50. 50.
    Y.-Y. Zhao, Y.-L. Zhang, M.-L. Zheng, X.-Z. Dong, X.-M. Duan, Z.-S. Zhao, Three-dimensional Luneburg lens at optical frequencies. Laser Photonics Rev. 10, 665–672 (2016)CrossRefGoogle Scholar
  51. 51.
    D. Wu, J.-N. Wang, L.-G. Niu, X.-L. Zhang, S.Z. Wu, Q.-D. Chen, L.P. Lee, H.B. Sun, Bioinspired fabrication of high-quality 3D artificial compound eyes by voxel-modulation femtosecond laser writing for distortion-free wide-field-of-view imaging. Adv. Opt. Mater. 2, 751–758 (2014)CrossRefGoogle Scholar
  52. 52.
    K. Liu, Y. Guo, M. Pu, X. Ma, X. Li, X. Luo, Wide field-of-view and broadband terahertz beam steering based on gap plasmon geodesic antennas. Sci. Rep. 7, 41642 (2017)CrossRefGoogle Scholar
  53. 53.
    J. L. McFarland, Catenary geodesic lens antenna. U.S. patent 3,383,691 (1968)Google Scholar
  54. 54.
    A. Arbabi, E. Arbabi, S.M. Kamali, Y. Horie, S. Han, A. Faraon, Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations. Nat. Commun. 7, 13682 (2016)CrossRefGoogle Scholar
  55. 55.
    B. Groever, W.T. Chen, F. Capasso, Meta-lens doublet in the visible region. Nano Lett. 17, 4902–4907 (2017)CrossRefGoogle Scholar
  56. 56.
    T. Gissibl, S. Thiele, A. Herkommer, H. Giessen, Two-photon direct laser writing of ultracompact multi-lens objectives. Nat. Photon 10, 554–560 (2016)CrossRefGoogle Scholar
  57. 57.
    M. Pu, X. Li, Y. Guo, X. Ma, X. Luo, Nanoapertures with ordered rotations: symmetry transformation and wide-angle flat lensing. Opt. Express 25, 31471–31477 (2017)CrossRefGoogle Scholar
  58. 58.
    W. Liu, Z. Li, H. Cheng, C. Tang, J. Li, S. Zhang, S. Chen, J. Tian, Metasurface enabled wide-angle fourier lens. Adv. Mater. 30, 1706368 (2018)CrossRefGoogle Scholar
  59. 59.
    Y. Wang, M. Pu, Z. Zhang, X. Li, X. Ma, Z. Zhao, X. Luo, Quasi-continuous metasurface for ultra-broadband and polarization-controlled electromagnetic beam deflection. Sci. Rep. 5, 17733 (2015)CrossRefGoogle Scholar
  60. 60.
    W. Luo, S. Sun, H.-X. Xu, Q. He, L. Zhou, Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency. Phys. Rev. Appl. 7, 044033 (2017)CrossRefGoogle Scholar
  61. 61.
    Y. Guo, M. Pu, Z. Zhao, Y. Wang, J. Jin, P. Gao, X. Li, X. Ma, X. Luo, Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation. ACS Photonics 3, 2022–2029 (2016)CrossRefGoogle Scholar
  62. 62.
    F. Zhang, M. Pu, X. Li, P. Gao, X. Ma, J. Luo, H. Yu, X. Luo, All-dielectric metasurfaces for simultaneous giant circular asymmetric transmission and wavefront shaping based on asymmetric photonic spin–orbit interactions. Adv. Funct. Mater. 27, 1704295 (2017)CrossRefGoogle Scholar
  63. 63.
    F. Zhang, M. Pu, J. Luo, H. Yu, X. Luo, Symmetry breaking of photonic spin-orbit interactions in metasurfaces. Opto-Electron. Eng. 44, 319–325 (2017)Google Scholar
  64. 64.
    J.P. Balthasar Mueller, N.A. Rubin, R.C. Devlin, B. Groever, F. Capasso, Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017)Google Scholar
  65. 65.
    P. Zhang, S. Gong, R. Mittra, Beam-shaping technique based on generalized laws of refraction and reflection. IEEE Trans. Antennas Propag. 66, 771–779 (2018)CrossRefGoogle Scholar
  66. 66.
    C. Huang, W. Pan, X. Ma, B. Zhao, J. Cui, X. Luo, Using reconfigurable transmit array to achieve beam-steering and polarization manipulation applications. IEEE Trans. Antennas Propag. 63, 4801–4810 (2015)CrossRefGoogle Scholar
  67. 67.
    J.Y. Lau, S.V. Hum, Reconfigurable transmit array design approaches for beamforming applications. IEEE Trans. Antennas Propag. 60, 5679–5689 (2012)CrossRefGoogle Scholar
  68. 68.
    W. Pan, C. Huang, P. Chen, M. Pu, X. Ma, X. Luo, A beam steering horn antenna using active frequency selective surface. IEEE Trans. Antennas Propag. 61, 6218–6223 (2013)CrossRefGoogle Scholar
  69. 69.
    Q. Wang, E.T.F. Rogers, B. Gholipour, C.-M. Wang, G. Yuan, J. Teng, N.I. Zheludev, Optically reconfigurable metasurfaces and photonic devices based on phase change materials. Nat. Photonics 10, 60–65 (2016)CrossRefGoogle Scholar
  70. 70.
    Y. Qu, Q. Li, K. Du, L. Cai, J. Lu, M. Qiu, Dynamic thermal emission control based on ultrathin plasmonic metamaterials including phase-changing material GST. Laser Photonics Rev. 11, 1700091 (2017)CrossRefGoogle Scholar
  71. 71.
    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
  72. 72.
    P. Hosseini, C.D. Wright, H. Bhaskaran, An optoelectronic framework enabled by low-dimensional phase change films. Nature 511, 206–211 (2014)CrossRefGoogle Scholar
  73. 73.
    C.H. Chu, M.L. Tseng, J. Chen, P.C. Wu, Y.-H. Chen, H.-C. Wang, T.-Y. Chen, W.T. Hsieh, H.J. Wu, G. Sun, D.P. Tsai, Active dielectric metasurface based on phase-change medium. Laser Photonics Rev. 10, 986–994 (2016)CrossRefGoogle Scholar
  74. 74.
    M. Zhang, M. Pu, F. Zhang, Y. Guo, Q. He, X. Ma, Y. Huang, X. Li, H. Yu, X. Luo, Plasmonic metasurfaces for switchable photonic spin-orbit interactions based on phase change materials. Adv. Sci. 5, 1800835 (2018)CrossRefGoogle Scholar
  75. 75.
    A. Shaltout, J. Liu, A. Kildishev, V. Shalaev, Photonic spin Hall effect in gap–plasmon metasurfaces for on-chip chiroptical spectroscopy. Optica 2, 860–863 (2015)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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