Optical Review

, Volume 24, Issue 2, pp 97–104 | Cite as

Probing surface plasmons by bare V-shaped tips: modeling by geometrical optics and rigorous diffraction theory

  • Gaurav BoseEmail author
  • Heikki J. Hyvärinen
  • Jani Tervo
  • Jari Turunen
Regular Paper


We consider probing inhomogeneous waves in the near fields of metallic nanostructures with the aid of a dielectric V-shaped wedge connected to a waveguide. A geometrical model based on the local plane interface approach is proposed to describe the interaction of the wedge with the inhomogeneous field. The fundamental ideas behind the geometrical model are validated by comparison with the results given by rigorous diffraction analysis, and applied to probing plasmonic interference patterns generated by metallic gratings with very narrow slits. The model explains intuitively why a bare wedge with a large apex angle is capable of subwavelength resolution in the spirit of scanning near-field microscopy.


Nanophotonics Diffractive optics Geometrical optics Plasmonics 



The work was supported by the Academy of Finland (Project 285880). J. Tervo is presently with Microsoft HoloLens, Keilalahdentie 2–4, 02150 Espoo, Finland.

Supplementary material

Supplementary material 1 (AVI 4643 KB)


  1. 1.
    Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill, New York (1968)Google Scholar
  2. 2.
    Petit, R. (ed.): Electromagnetic Theory of Gratings. Springer, Berlin (1980)Google Scholar
  3. 3.
    Neviére, M., Popov, E.: Light Propagation in Periodic Media. Differential Theory and Design. Marcel Dekker, New York (2003)Google Scholar
  4. 4.
    Kim, H., Park, J., Lee, B.: Fourier Modal Method and Its Applications in Computational Nanophotonics. Taylor & Francis, CRC Press (2012)Google Scholar
  5. 5.
    Pfeil, A., Wyrowski, F., Drauschke, A., Aagedal, H.: Analysis of optical elements with the local plane-interface approximation. Appl. Opt. 39, 3304–3313 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    Lajunen, H., Tervo, J., Turunen, J., Vallius, T., Wyrowski, F.: Simulation of light propagation by local spherical interface approximation. Appl. Opt. 42, 6804–6810 (2003)ADSCrossRefGoogle Scholar
  7. 7.
    Wyrowski, F., Kuhn, M.: Introduction to field tracing. J. Mod. Opt. 58, 449–466 (2011)ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Swanson, G.J.: Binary optics technology: theoretical limits of the diffraction efficiency of multilevel diffractive optical elements. MIT Tech. Rep. 914, MIT (1991)Google Scholar
  9. 9.
    Hessler, T., Rossi, M., Kunz, R.E., Gale, M.T.: Analysis and optimization of fabrication of continuous-relief diffractive optical elements. Appl. Opt. 37, 4069–4079 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    Sandfuchs, O., Brunner, R., Pätz, D., Sinzinger, S., Ruoff, J.: Rigorous analysis of shadowing effects in blazed transmission gratings. Opt. Lett. 31, 3638–3640 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    Sandfuchs, O., Pätz, D., Sinzinger, S., Pesch, A., Brunner, R.: Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime. J. Opt. Soc. Am. A 25, 1885–1893 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Noponen, E., Turunen, J., Vasara, A.: Electromagnetic theory and design of diffractive-lens arrays. J. Opt. Soc. Am. A 10, 434–443 (1993)ADSCrossRefGoogle Scholar
  13. 13.
    Wang, H., Kuang, D., Fang, Z.: Diffraction analysis of blazed transmission gratings with a modified extended scalar theory. J. Opt. Soc. Am. A 25, 1253–1259 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    Moulin, G., Goudail, F., Chavel, P., Kuang, D.: Heuristic models for diffracting by some simple mirror-objects. J. Opt. Soc. Am. A 26, 767–775 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    Bose, G., Hyvärinen, H.J., Tervo, J., Turunen, J.: Geometrical optics in the near field: local plane-interface approach with evanescent waves. Opt. Express 23, 330–339 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    Saleh, B.E.A., Teich, M.C.: Fundamentals of Photonics. Wiley, New York (1991)CrossRefGoogle Scholar
  17. 17.
    Stamnes, J.J.: Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves. Taylor & Francis, CRC Press (1986)Google Scholar
  18. 18.
    Keller, J.B.: Geometrical theory of diffraction. J. Opt. Soc. Am. 52, 116–130 (1962)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Hyvärinen, H.J., Turunen, J., Vahimaa, P.: Elementary-field modeling of surface-plasmon excitation with partially coherent light. Appl. Phys. B 101, 273–282 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    Porto, J.A., Garcia-Vidal, F.J., Pendry, J.B.: Transmission resonances on metallic gratings with very narrow slits. Phys. Rev. Lett. 83, 2845–2848 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    Weiner, J.: The electromagnetics of light transmission through subwavelength slits in metallic films. Opt. Express. 19, 16139–16153 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    Wuenschell, J., Kim, H.K.: Surface plasmon dynamics in an isolated metallic nanoslit. Opt. Express. 14, 10000–10013 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Garcia-Vidal, F.J., Martin-Moreno, L., Ebbesen, T.W., Kuipers, L.: Light passing through subwavelength apertures. Rev. Mod. Phys. 82, 729–787 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Bose, G.: Diffractive optics based on V-shaped structures and its applications. Ph.D dissertation 245, University of Eastern Finland (2016)Google Scholar
  25. 25.
    Silberstein, E., Lalanne, P., Hugonin, J.P., Cao, Q.: Use of grating theories in integrated optics. J. Opt. Soc. Am. A 18, 2865–2875 (2001)ADSCrossRefGoogle Scholar

Copyright information

© The Optical Society of Japan 2017

Authors and Affiliations

  1. 1.Institute of PhotonicsUniversity of Eastern FinlandJoensuuFinland
  2. 2.Microsoft HololensEspooFinland

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