Skip to main content
SpringerLink
Log in

Catenary Plasmons for Flat Lensing, Beam Deflecting, and Shaping

  • Chapter
  • First Online:
Catenary Optics

  • 691 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R.P Crease, The most beautiful experiment. Phys. World 15, 19 (2002)

    Article  Google Scholar 

  2. X. Luo, T. Ishihara, Surface plasmon resonant interference nanolithography technique. Appl. Phys. Lett. 84, 4780–4782 (2004)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  6. H. Shi, X. Luo, C. Du, Young’s interference of double metallic nanoslit with different widths. Opt. Express 15, 11321–11327 (2007)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. W.E. Kock, Metal-lens antennas. Proc. IRE 34, 828–836 (1946)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  10. W.E. Kock, Metallic delay lenses. Bell Syst. Tech. J. 27, 58–82 (1948)

    Article  Google Scholar 

  11. J. Pendry, A. Holden, W. Stewart, I. Youngs, Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996)

    Article  CAS  Google Scholar 

  12. R. Shelby, D. Smith, S. Schultz, Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  16. C. Lu, X. Hu, H. Yang, Q. Gong, Ultrawide-band unidirectional surface plasmon polariton launchers. Adv. Opt. Mater. 1, 792–797 (2013)

    Article  Google Scholar 

  17. R. Zia, M.L. Brongersma, Surface plasmon polariton analogue to Young’s double-slit experiment. Nat. Nanotechnol. 2, 426 (2007)

    Article  CAS  Google Scholar 

  18. X. Luo, M. Pu, X. Li, X. Ma, Broadband spin Hall effect of light in single nanoapertures. Light Sci. Appl. 6, e16276 (2017)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  21. T. Xu, C. Wang, C. Du, X. Luo, Plasmonic beam deflector. Opt. Express 16, 4753–4759 (2008)

    Article  Google Scholar 

  22. X. Luo, Principles of electromagnetic waves in metasurfaces. Sci. China-Phys. Mech. Astron. 58, 594201 (2015)

    Article  Google Scholar 

  23. Y. Xu, Y. Fu, H. Chen, Planar gradient metamaterials. Nat. Rev. Mater. 1, 16067 (2016)

    Article  CAS  Google Scholar 

  24. P. Lalanne, P. Chavel, Metalenses at visible wavelengths: Past, present, perspectives. Laser Photonics Rev. 11, 1600295 (2017)

    Article  Google Scholar 

  25. F. Capasso, The future and promise of flat optics: A personal perspective. Nanophotonics 7, 953 (2018)

    Article  Google Scholar 

  26. X. Luo, Subwavelength optical engineering with metasurface waves. Adv. Opt. Mater. 6, 1701201 (2018)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  32. J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)

    CAS  Google Scholar 

  33. T. Xu, C. Du, C. Wang, X. Luo, Subwavelength imaging by metallic slab lens with nanoslits. Appl. Phys. Lett. 91, 201501 (2007)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  39. M. Totzeck, W. Ulrich, A. Gohnermeier, W. Kaiser, Semiconductor fabrication: Pushing deep ultraviolet lithography to its limits. Nat. Photonics 1, 629–631 (2007)

    Article  CAS  Google Scholar 

  40. S. Ishii, V.M. Shalaev, A.V. Kildishev, Holey-metal lenses: Sieving single modes with proper phases. Nano Lett. 13, 159–163 (2013)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  43. F. Aieta, M.A. Kats, P. Genevet, F. Capasso, Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science 347, 1342–1345 (2015)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  47. O. Avayu, E. Almeida, Y. Prior, T. Ellenbogen, Composite functional metasurfaces for multispectral achromatic optics. Nat. Commun. 8, 14992 (2017)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  49. L. Rayleigh, XXXI. Investigations in optics, with special reference to the spectroscope. Philos. Mag. Ser. 5(8), 261–274 (1879)

    Article  Google Scholar 

  50. N.I. Zheludev, What diffraction limit? Nat. Mater. 7, 420–422 (2008)

    Article  CAS  Google Scholar 

  51. M. Pu, C. Wang, Y. Wang, X. Luo, Subwavelength electromagnetics below the diffraction limit. Acta Phys. Sin. 66, 144101 (2017)

    Google Scholar 

  52. F. Qin, M. Hong, Breaking the diffraction limit in far field by planar metalens. Sci. China Phys. Mech. Astron. 60, 044231 (2017)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  54. B. Huang, M. Bates, X. Zhuang, Super resolution fluorescence microscopy. Annu. Rev. Biochem. 78, 993 (2009)

    Article  CAS  Google Scholar 

  55. G.T. di Francia, Super-gain antennas and optical resolving power. G Suppl Nuovo Cim 9, 426–438 (1952)

    Article  Google Scholar 

  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. E.T.F. Rogers, N.I. Zheludev, Optical super-oscillations: Sub-wavelength light focusing and super-resolution imaging. J. Opt. 15, 094008 (2013)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  62. L.B. Whitbourn, R.C. Compton, Equivalent-circuit formulas for metal grid reflectors at a dielectric boundary. Appl. Opt. 24, 217–220 (1985)

    Article  CAS  Google Scholar 

  63. N. Engheta, Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials. Science 317, 1698–1702 (2007)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  65. C. Genet, T.W. Ebbesen, Light in tiny holes. Nature 445, 39–46 (2007)

    Article  CAS  Google Scholar 

  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. 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)

    Article  CAS  Google Scholar 

  68. P.B. Johnson, R.W. Christy, Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  71. T. Smith, J. Guild, The C.I.E. colorimetric standards and their use. Trans. Opt. Soc. 33, 73 (1931)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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. X. Ni, A.V. Kildishev, V.M. Shalaev, Metasurface holograms for visible light. Nat. Commun. 4, 2807 (2013)

    Article  Google Scholar 

  80. Z.-L. Deng, G. Li, Metasurface optical holography. Mater. Today Phys. 3, 16–32 (2017)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Optical Technologies on Nano-fabrication and Micro-engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan, China

    Xiangang Luo

Authors
  1. Xiangang Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiangang Luo .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Luo, X. (2019). Catenary Plasmons for Flat Lensing, Beam Deflecting, and Shaping. In: Catenary Optics. Springer, Singapore. https://doi.org/10.1007/978-981-13-4818-1_5

Download citation

Publish with us

Policies and ethics

Search

Navigation