Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Capturing photons with transformation optics

Nature Physics volume 9, pages 518–522 (2013)Cite this article

Subjects

Abstract

Metallic objects in close contact and illuminated by light show spectacular enhancements of electromagnetic fields due to excitation of surface plasmons, which have the potential for exploitation in ultra sensitive spectroscopy and in nonlinear phenomena. They also play a role in van der Waals forces, heat transfer and non contact friction. The extremes of lengthscales, varying from the micrometre to the subnanometre, challenge direct computational attack. Here we show that transformation optics enables an analytic approach that offers both physical insight and easy access to quantitative analysis. For two metal spheres at various separations we present details of the technique and discuss the optical absorption spectrum, spatial distribution of the modes and the van der Waals forces.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: The geometry of the transformation.
Figure 2: Modes of two 5 nm radius spheres for various separations.
Figure 3: The potential distribution shown in real space and in the transformed space for two spheres each 10 nm in diameter, separated by 0.4 nm.
Figure 4: The absorption cross section for 10 nm diameter silver spheres separated by 0.1 nm compared with the physical cross section.
Figure 5: The van der Waals force acting between a small metallic sphere and a metallic surface as a function of distance.

Similar content being viewed by others

References

  1. Ward, A. J. & Pendry, J. B. Refraction and geometry in Maxwell’s equations. J. Mod. Opt. 43, 773–793 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  2. Shyroki, D. M. Note on transformation to general curvilinear coordinates for Maxwell’s curl equations. Preprint at http://arxiv.org/abs/physics/0307029v1 (2003).

  3. Schurig, D., Pendry, J. B. & Smith, D.R. Calculation of material properties and ray tracing in transformation media. Opt. Express 14, 9794–9804 (2006).

    Article  ADS  Google Scholar 

  4. Leonhardt, U. Transformation optics and the geometry of light. Prog. Opt. 53, 69–152 (2009).

    Article  ADS  Google Scholar 

  5. Kundtz, N. B., Smith, D. R. & Pendry, J. B. Electromagnetic design with transformation optics. Proc. IEEE 99, 1622–1633 (2011).

    Article  Google Scholar 

  6. Pendry, J. B., Aubry, A., Smith, D. R. & Maier, S. A. Transformation optics and subwavelength control of light. Science 337, 549–552 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  7. Pendry, J. B. Perfect Cylindrical lenses. Opt. Express 11, 755–760 (2003).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  10. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  11. McPhedran, R. C. & McKenzie, D. R. Electrostatic and optical resonances of arrays of cylinders. Appl. Phys. A 23, 223–235 (1980).

    Article  ADS  Google Scholar 

  12. McPhedran, R. C. & Perrins, W. T. Electrostatic and optical resonances of cylinder pairs. Appl. Phys. A 24, 311–318 (1981).

    Article  ADS  Google Scholar 

  13. McPhedran, R. C. & Milton, G. W. Transport properties of touching cylinder pairs and of the square array of touching cylinders. Proc. R. Soc. A 411, 313–326 (1987).

    Article  ADS  Google Scholar 

  14. Poladian, L. General theory of electrical images in sphere pairs. Q. J. Mech. Appl. Math. 41, 395–417 (1988).

    Article  MathSciNet  Google Scholar 

  15. Garcı´aVidal, F. J. & Pendry, J. B. A collective theory for surface enhanced Raman scattering. Phys. Rev. Lett. 77, 1163–1166 (1996).

    Article  ADS  Google Scholar 

  16. Stockman, M. I. Nanofocusing of optical energy in tapered plasmonic waveguides. Phys. Rev. Lett. 93, 137404 (2004).

    Article  ADS  Google Scholar 

  17. Talley, C. E. et al. Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates. Nano Lett. 5, 1569–1574 (2005).

    Article  ADS  Google Scholar 

  18. Sweatlock, L. A., Maier, S. A., Atwater, H. A., Penninkhof, J. J. & Polman, A. Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles. Phys. Rev. B 71, 235408 (2005).

    Article  ADS  Google Scholar 

  19. Romero, I., Aizpurua, J., Bryant, G. W. & Garcıa de Abajo, F. J. Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers. Opt. Express 14, 9988–9999 (2006).

    Article  ADS  Google Scholar 

  20. Hill, R. T. et al. Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light. Nano Lett. 10, 4150–4154 (2010).

    Article  ADS  Google Scholar 

  21. Schuller, J. A. et al. Plasmonics for extreme light concentration and manipulation. Nature Mater. 9, 193–204 (2010).

    Article  ADS  Google Scholar 

  22. Nordlander, P., Oubre, C., Prodan, E., Li, K. & Stockman, M. I. Plasmon hybridization in nanoparticle dimers. Nano Lett. 4, 899–903 (2004).

    Article  ADS  Google Scholar 

  23. Garcı´a deAbajo, F. J. Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides. J. Phys. Chem. C 112, 17983–17987 (2008).

    Article  Google Scholar 

  24. Aizpurua, J. & Rivacoba, S. Nonlocal effects in the plasmons of nanowires and nanocavities excited by fast electron beams. Phys. Rev. B 78, 035404 (2008).

    Article  ADS  Google Scholar 

  25. Esteban, R., Borisov, A. G., Nordlander, P. & Aizpurua, J. Bridging quantum and classical plasmonics with a quantum-corrected model. Nature Commun. 3, 825 (2012).

    ADS  Google Scholar 

  26. Savage, K. J. et al. Revealing the quantum regime in tunnelling plasmonics. Nature 491, 574–577 (2012).

    Article  ADS  Google Scholar 

  27. Landau, L. D. & Lifshitz, E. M. Electrodynamics of Continuous Media (Pergamon, 1963).

    Google Scholar 

  28. Palik, E. D. Handbook of Optical Constants of Solids (Academic, 1985).

    Google Scholar 

  29. Bimonte, G. & Emig, T. Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere–sphere and sphere-plane geometry. Phys. Rev. Lett. 109, 160403 (2012).

    Article  ADS  Google Scholar 

  30. Israelachvili, J. N. Intermolecular and Surface Forces (Academic, 1998).

    Google Scholar 

Download references

Acknowledgements

For our support we thank the following: the Gordon and Betty Moore Foundation (A.I.F-D. and J.B.P.), AFOSR (J.B.P.), the Royal Commission for the Exhibition of 1851 (R.Z), and the Leverhulme Trust (Y.L. and J.B.P.).

Author information

Authors and Affiliations

  1. Department of Physics, The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK

    J. B. Pendry, A. I. Fernández-Domínguez, Yu Luo & Rongkuo Zhao

Authors
  1. J. B. Pendry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Fernández-Domínguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rongkuo Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors are deemed to have contributed equally.

Corresponding author

Correspondence to J. B. Pendry.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pendry, J., Fernández-Domínguez, A., Luo, Y. et al. Capturing photons with transformation optics. Nature Phys 9, 518–522 (2013). https://doi.org/10.1038/nphys2667

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys2667

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing