Skip to main content

Thank you for visiting 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.

Absolute extinction cross-section of individual magnetic split-ring resonators


Complete control of an electromagnetic wave requires access to its electric and magnetic vector components. Realizing this level of control with metamaterials has recently opened new avenues regarding negative refractive indices1,2 and invisibility cloaking3,4. The required microscopic building blocks are artificial electric and magnetic dipoles. Magnetic dipoles oscillating at optical frequencies have become available only recently in the form of man-made split-ring resonators5, essentially subwavelength resonant electromagnets. Previous experimental work has focused on arrays of electric and/or magnetic dipoles1,2,6,7. For further developments in this field, knowledge of the properties of the individual dipoles is highly desirable. In this paper, using a modulation technique8,9, we measure the absolute extinction cross-section of a single split-ring resonator for the first time. At the fundamental magnetic resonance, it is found to be about one-seventh of λ2 at a wavelength of λ = 1.4 µm, which is in excellent agreement with microscopic calculations.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


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

Figure 1: Determining the absolute extinction cross-section.
Figure 2: Measured absolute extinction cross-section spectra.
Figure 3: Calculated absolute cross-section spectra.


  1. Shalaev, V. M. Optical negative-index metamaterials. Nature Photon. 1, 41–48 (2007).

    Article  ADS  Google Scholar 

  2. Soukoulis, C. M., Linden, S. & Wegener, M. Negative refractive index at optical wavelengths. Science 315, 47–49 (2007).

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  5. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).

    Article  ADS  Google Scholar 

  6. Linden, S. et al. Magnetic response of metamaterials at 100 Terahertz. Science 306, 1351–1353 (2004).

    Article  ADS  Google Scholar 

  7. Enkrich, C. et al. Magnetic metamaterials at telecommunication and visible frequencies. Phys. Rev. Lett. 95, 203901-1 (2005).

    Article  ADS  Google Scholar 

  8. Arbouet, A. et al. Direct measurement of the single-metal-cluster optical absorption. Phys. Rev. Lett. 93, 127401-1 (2004).

    Article  ADS  Google Scholar 

  9. Muskens, O. L. et al. Single-metal nanoparticle absorption spectroscopy and optical characterization. Appl. Phys. Lett. 88, 063109-1 (2006).

    Article  ADS  Google Scholar 

  10. Shamonina, E. & Solymar, L. Properties of magnetically coupled metamaterial elements. J. Magn. Magn. Mater. 300, 38–43 (2006).

    Article  ADS  Google Scholar 

  11. Dolling, G., Wegener, M., Schädle, A., Burger, S. & Linden, S. Observation of magnetization waves in negative-index photonic metamaterials. Appl. Phys. Lett. 89, 231118–231120 (2006).

    Article  ADS  Google Scholar 

  12. Liu, N. et al. Three-dimensional photonic metamaterials at optical frequencies. Nature Mater. 7, 31–37 (2008).

    Article  ADS  Google Scholar 

  13. Sönnichsen, C., Franzl, T., Wilk, T., von Plessen, G. & Feldmann, J. Drastic reduction of plasmon damping in gold nanorods. Phys. Rev. Lett. 88, 077402-1 (2002).

    Article  ADS  Google Scholar 

  14. Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

    Google Scholar 

  15. Rockstuhl, C. et al. On the reinterpretation of resonances in split-ring-resonators at normal incidence. Opt. Express 14, 8827–8836 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Meyrath, T. P., Zentgraf, T. & Giessen, H. Lorentz model for metamaterials: optical frequency resonance circuits. Phys. Rev. B 75, 205102-1 (2007).

    Article  ADS  Google Scholar 

  18. Busch, K. et al. Periodic nanostructures for photonics. Phys. Rep. 444, 101–202 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Taflove, A. & Hagness, S. C. Computational Electrodynamics: The Finite-Difference Time-Domain Method 3rd edn (Artech House, Boston, 2005).

    MATH  Google Scholar 

Download references


We thank Costas M. Soukoulis for discussions. We acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN) within subprojects A1.2, A1.5, A5.2 and A5.3 as well as by the BMBF-Verbund METAMAT and by the European Union project PHOME. The research of S.L. is also supported through a Helmholtz-Hochschul-Nachwuchsgruppe (VH-NG-232). The PhD research of N.F., M.K. and J.N. is further supported by the Karlsruhe School of Optics and Photonics (KSOP).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Nils Feth.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Husnik, M., Klein, M., Feth, N. et al. Absolute extinction cross-section of individual magnetic split-ring resonators. Nature Photon 2, 614–617 (2008).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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