Skip to main content
Log in

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

  • Regular Paper
  • Published:
Optical Review Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill, New York (1968)

    Google Scholar 

  2. Petit, R. (ed.): Electromagnetic Theory of Gratings. Springer, Berlin (1980)

    Google Scholar 

  3. Neviére, M., Popov, E.: Light Propagation in Periodic Media. Differential Theory and Design. Marcel Dekker, New York (2003)

    Google Scholar 

  4. Kim, H., Park, J., Lee, B.: Fourier Modal Method and Its Applications in Computational Nanophotonics. Taylor & Francis, CRC Press (2012)

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  7. Wyrowski, F., Kuhn, M.: Introduction to field tracing. J. Mod. Opt. 58, 449–466 (2011)

    Article  ADS  MATH  Google Scholar 

  8. Swanson, G.J.: Binary optics technology: theoretical limits of the diffraction efficiency of multilevel diffractive optical elements. MIT Tech. Rep. 914, MIT (1991)

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  12. Noponen, E., Turunen, J., Vasara, A.: Electromagnetic theory and design of diffractive-lens arrays. J. Opt. Soc. Am. A 10, 434–443 (1993)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  16. Saleh, B.E.A., Teich, M.C.: Fundamentals of Photonics. Wiley, New York (1991)

    Book  Google Scholar 

  17. Stamnes, J.J.: Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves. Taylor & Francis, CRC Press (1986)

  18. Keller, J.B.: Geometrical theory of diffraction. J. Opt. Soc. Am. 52, 116–130 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  21. Weiner, J.: The electromagnetics of light transmission through subwavelength slits in metallic films. Opt. Express. 19, 16139–16153 (2011)

    Article  ADS  Google Scholar 

  22. Wuenschell, J., Kim, H.K.: Surface plasmon dynamics in an isolated metallic nanoslit. Opt. Express. 14, 10000–10013 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  24. Bose, G.: Diffractive optics based on V-shaped structures and its applications. Ph.D dissertation 245, University of Eastern Finland (2016)

  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)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gaurav Bose.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (AVI 4643 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bose, G., Hyvärinen, H.J., Tervo, J. et al. Probing surface plasmons by bare V-shaped tips: modeling by geometrical optics and rigorous diffraction theory. Opt Rev 24, 97–104 (2017). https://doi.org/10.1007/s10043-016-0301-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10043-016-0301-z

Keywords

Navigation