Catenary Optical Fields and Dispersion for Perfect Absorption of Light

  • Xiangang LuoEmail author


Besides the localized manipulation of phase and polarization, catenary optical fields can be used to realize perfect absorption of light. First, the catenary coupling occurring at structured holes or gaps may help to couple light into the subwavelength structures. Second, the localized resonance strongly increases the localized intensity as well as the absorption probability of incident photons. Third, the catenary fields may change the dispersion of electromagnetic modes, thus broadband absorption becomes possible. We also noted that the counter-propagating waves in a thin lossy slab would form catenary-shaped intensity profile, which means that the catenary is a universal characteristic for the absorption of light in structured materials.


  1. 1.
    H.A. Atwater, A. Polman, Plasmonics for improved photovoltaic devices. Nat. Mater. 9, 205–213 (2010)CrossRefGoogle Scholar
  2. 2.
    X. Luo, Subwavelength artificial structures: opening a new era for engineering optics. Adv. Mater. 1804680 (2018)Google Scholar
  3. 3.
    R.W. Wood, On a remarkable case of uneven distribution of light in a diffraction grating spectrum. Proc. R. Soc. Lond. 18, 269 (1902)Google Scholar
  4. 4.
    D. Maystre, Theory of wood’s anomalies, ed. by S. Enoch, N. Bonod. Plasmonics (Springer Series in Optical Sciences No. 167, Springer, 2012)Google Scholar
  5. 5.
    M.C. Hutley, D. Maystre, The total absorption of light by a diffraction grating. Opt. Commun. 19, 431–436 (1976)CrossRefGoogle Scholar
  6. 6.
    C. Hu, Z. Zhao, X. Chen, X. Luo, Realizing near-perfect absorption at visible frequencies. Opt. Express 17, 11039–11044 (2009)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    H. Liu, P. Lalanne, Microscopic theory of the extraordinary optical transmission. Nature 452, 728–731 (2008)CrossRefGoogle Scholar
  9. 9.
    C. Hu, L. Liu, Z. Zhao, X. Chen, X. Luo, Mixed plasmons coupling for expanding the bandwidth of near-perfect absorption at visible frequencies. Opt. Express 17, 16745–16749 (2009)CrossRefGoogle Scholar
  10. 10.
    C. Wang, P. Gao, Z. Zhao, N. Yao, Y. Wang, L. Liu, K. Liu, X. Luo, Deep sub-wavelength imaging lithography by a reflective plasmonic slab. Opt. Express 21, 20683–20691 (2013)CrossRefGoogle Scholar
  11. 11.
    P. Gao, N. Yao, C. Wang, Z. Zhao, Y. Luo, Y. Wang, G. Gao, K. Liu, C. Zhao, X. Luo, Enhancing aspect profile of half-pitch 32 nm and 22 nm lithography with plasmonic cavity lens. Appl. Phys. Lett. 106, 093110 (2015)CrossRefGoogle Scholar
  12. 12.
    T.V. Teperik, F.J. García de Abajo, A.G. Borisov, M. Abdelsalam, P.N. Bartlett, Y. Sugawara, J.J. Baumberg, Omnidirectional absorption in nanostructured metal surfaces. Nat. Photonics 2, 299–301 (2008)CrossRefGoogle Scholar
  13. 13.
    S.A. Tretyakov, S.I. Maslovski, Thin absorbing structure for all incidence angles based on the use of a high-impedance surface. Microw. Opt. Technol. Lett. 38, 175–178 (2003)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    T.D. Dao, K. Chen, S. Ishii, A. Ohi, T. Nabatame, M. Kitajima, T. Nagao, Infrared perfect absorbers fabricated by colloidal mask etching of Al–Al2O3–Al trilayers. ACS Photonics 2, 964–970 (2015)CrossRefGoogle Scholar
  16. 16.
    E.D. Palik, Handbook of Optical Constants of Solids (Academic press, 1985)Google Scholar
  17. 17.
    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
  18. 18.
    M. Choi, S.H. Lee, Y. Kim, S.B. Kang, J. Shin, M.H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, B. Min, A terahertz metamaterial with unnaturally high refractive index. Nature 470, 369–373 (2011)CrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    G. Dolling, C. Enkrich, M. Wegener, J.F. Zhou, C.M. Soukoulis, S. Linden, Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials. Opt. Lett. 30, 3198–3200 (2005)CrossRefGoogle Scholar
  21. 21.
    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
  22. 22.
    N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, H. Giessen, Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit. Nat. Mater. 8, 758–762 (2009)CrossRefGoogle Scholar
  23. 23.
    A. Epstein, G.V. Eleftheriades, Huygens’ metasurfaces via the equivalence principle: design and applications. J. Opt. Soc. Am. B 33, A31–A50 (2016)CrossRefGoogle Scholar
  24. 24.
    V.A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D.P. Tsai, N.I. Zheludev, Spectral collapse in ensembles of metamolecules. Phys. Rev. Lett. 104, 223901 (2010)CrossRefGoogle Scholar
  25. 25.
    J. Grant, Y. Ma, S. Saha, A. Khalid, D.R.S. Cumming, Polarization insensitive, broadband terahertz metamaterial absorber. Opt. Lett. 36, 3476–3478 (2011)CrossRefGoogle Scholar
  26. 26.
    C. Long, S. Yin, W. Wang, W. Li, J. Zhu, J. Guan, Broadening the absorption bandwidth of metamaterial absorbers by transverse magnetic harmonics of 210 mode. Sci. Rep. 6, 21431 (2016)CrossRefGoogle Scholar
  27. 27.
    Y. Guo, L. Yan, W. Pan, B. Luo, X. Luo, Ultra-broadband terahertz absorbers based on 4 × 4 cascaded metal-dielectric pairs. Plasmonics 9, 951–957 (2014)CrossRefGoogle Scholar
  28. 28.
    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
  29. 29.
    X. Luo, Principles of electromagnetic waves in metasurfaces. Sci. China-Phys. Mech. Astron. 58, 594201 (2015)CrossRefGoogle Scholar
  30. 30.
    G. Biener, A. Niv, V. Kleiner, E. Hasman, Metallic subwavelength structures for a broadband infrared absorption control. Opt. Lett. 32, 994–996 (2007)CrossRefGoogle Scholar
  31. 31.
    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
  32. 32.
    Y. Huang, J. Luo, M. Pu, Y. Guo, Z. Zhao, X. Ma, X. Li, X. Luo, Catenary electromagnetics for ultrabroadband lightweight absorbers and large-scale flat antennas. Adv. Sci. 1801691 (2019)Google Scholar
  33. 33.
    R.J. Langley, E.A. Parker, Equivalent circuit model for arrays of square loops. Electron. Lett. 18, 294–296 (1982)CrossRefGoogle Scholar
  34. 34.
    Y. Wang, X. Ma, X. Li, M. Pu, X. Luo. Perfect electromagnetic and sound absorption via subwavelength holes array. Opto-Electron. Adv. 1, 180013 (2018)CrossRefGoogle Scholar
  35. 35.
    K.N. Rozanov, Ultimate thickness to bandwidth ratio of radar absorbers. IEEE Trans. Antennas Propag. 48, 1230–1234 (2000)CrossRefGoogle Scholar
  36. 36.
    M. Zhang, F. Zhang, Y. Ou, J. Cai, H. Yu, Broadband terahertz absorber based on dispersion-engineered catenary coupling in dual metasurface. Nanophotonics 8, 117–125 (2019)CrossRefGoogle Scholar
  37. 37.
    M. Pu, P. Chen, Y. Wang, Z. Zhao, C. Huang, C. Wang, X. Ma, X. Luo, Anisotropic meta-mirror for achromatic electromagnetic polarization manipulation. Appl. Phys. Lett. 102, 131906 (2013)CrossRefGoogle Scholar
  38. 38.
    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
  39. 39.
    Y.D. Chong, L. Ge, H. Cao, A.D. Stone, Coherent perfect absorbers: time-reversed lasers. Phys. Rev. Lett. 105, 053901 (2010)CrossRefGoogle Scholar
  40. 40.
    W. Wan, Y. Chong, L. Ge, H. Noh, A.D. Stone, H. Cao, Time-reversed lasing and interferometric control of absorption. Science 331, 889–892 (2011)CrossRefGoogle Scholar
  41. 41.
    D.G. Baranov, A.E. Krasnok, T. Shegai, A. Alù, Y.D. Chong, Coherent perfect absorbers: linear control of light with light. Nat. Rev. Mater. 2, 17064 (2017)CrossRefGoogle Scholar
  42. 42.
    C. Yan, M. Pu, J. Luo, Y. Huang, X. Li, X. Ma, X. Luo, Coherent perfect absorption of electromagnetic wave in subwavelength structures. Opt. Laser Technol. 101, 499–506 (2018)CrossRefGoogle Scholar
  43. 43.
    B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, 2 edn. (Wiley, 2007)Google Scholar
  44. 44.
    M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, X. Luo, Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination. Opt. Express 20, 2246–2254 (2012)CrossRefGoogle Scholar
  45. 45.
    M. Pu, Q. Feng, C. Hu, X. Luo, Perfect absorption of light by coherently induced plasmon hybridization in ultrathin metamaterial film. Plasmonics 7, 733–738 (2012)CrossRefGoogle Scholar
  46. 46.
    W. Woltersdorff, Über die optischen Konstanten dünner Metallschichten im langwelligen Ultrarot. Z. Für Phys. Hadrons Nucl. 91, 230–252 (1934)CrossRefGoogle Scholar
  47. 47.
    S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z.H. Hang, Y. Lai, B. Hou, M. Shen, C. Wang, Broadband perfect absorption of ultrathin conductive films with coherent illumination: superabsorption of microwave radiation. Phys. Rev. B 91, 220301(R) (2015)CrossRefGoogle Scholar
  48. 48.
    S. Li, Q. Duan, S. Li, Q. Yin, W. Lu, L. Li, B. Gu, B. Hou, W. Wen, Perfect electromagnetic absorption at one-atom-thick scale. Appl. Phys. Lett. 107, 181112 (2015)CrossRefGoogle Scholar
  49. 49.
    M.-G. Kang, T. Xu, H.J. Park, X. Luo, L.J. Guo, Efficiency enhancement of organic solar cells using transparent plasmonic Ag nanowire electrodes. Adv. Mater. 22, 4378 (2010)CrossRefGoogle Scholar
  50. 50.
    T. Kawawaki, Y. Takahashi, T. Tatsuma, Enhancement of dye-sensitized photocurrents by gold nanoparticles: effects of plasmon coupling. J. Phys. Chem. C 117, 5901–5907 (2013)CrossRefGoogle Scholar
  51. 51.
    X. Ma, Y. Guo, M. Pu, X. Li, X. Luo, Refined model for plasmon ruler based on catenary shaped optical fields. Plasmonics (2019)Google Scholar
  52. 52.
    J. Khurgin, W.-Y. Tsai, D.P. Tsai, G. Sun, Landau damping and limit to field confinement and enhancement in plasmonic dimers. ACS Photonics 4, 2871–2880 (2017)CrossRefGoogle Scholar
  53. 53.
    S.S. Aćimović, M.P. Kreuzer, M.U. González, R. Quidant, Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing. ACS Nano 3, 1231–1237 (2009)CrossRefGoogle Scholar
  54. 54.
    H. Aouani, M. Rahmani, M. Navarro-Cia, S.A. Maier, Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna. Nat. Nanotechnol. 9, 290–294 (2014)CrossRefGoogle Scholar
  55. 55.
    A.E. Miroshnichenko, S. Flach, Y.S. Kivshar, Fano resonances in nanoscale structures. Rev. Mod. Phys. 82, 2257–2298 (2010)CrossRefGoogle Scholar
  56. 56.
    M. Fleischhauer, A. Imamoglu, J.P. Marangos, Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005)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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