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.

Universal impedance matching and the perfect transmission of white light

A Publisher Correction to this article was published on 05 June 2018

This article has been updated


Light is reflected at the interface between heterogeneous media due to the mismatch of impedance1,2,3. Removing this mismatch using additional materials, a technique known as anti-reflection, has so far been restricted to specific frequencies and incidence angles3,4,5,6,7. The anti-reflection of white light, which requires the simultaneous matching of impedance over extremely wide angular and spectral ranges, has until now been considered impossible. Here, we develop a theory of universal impedance matching and introduce a matching layer that enables the perfect transmission of white light. The ability of a matching layer to assist in omnidirectional and frequency-independent anti-reflection has been confirmed analytically and numerically. We explain the feasibility of a universal matching layer using metamaterials, and demonstrate a transmission rate of over 99% for white light in the visible range with a double-layered dielectric metamaterial. This is confirmed experimentally by demonstrating the omnidirectional anti-reflection of microwaves in heterogeneous media.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Perfect transmission of white light with a universal impedance matching layer.
Fig. 2: Omnidirectional and frequency-independent anti-reflection and transmission.
Fig. 3: Metamaterial realization of the UIML.
Fig. 4: Microwave measurement of reflectance using a metamaterial UIML.

Change history

  • 05 June 2018

    In the version of this Letter originally published, there were errors in equations (2), (3)–(7) and (11), and in the equation in the right panel of Fig. 1b, and some artefacts appeared in Fig. 2b; the details are shown in the correction notice. These errors have now been corrected in the online versions.


  1. Born, M. & Wolf, E. Principles of Optics (Cambridge Univ. Press, Cambridge, 2003).

    Google Scholar 

  2. Brewster, D. On the laws which regulate the polarisation of light by reflection from transparent bodies. Phil. Trans. R. Soc. Lond. 105, 125–159 (1815).

    Article  Google Scholar 

  3. Rayleigh, L. On the intensity of light reflected from certain surfaces at nearly perpendicular incidence. Proc. R. Soc. Lond. 41, 275–294 (1886).

    Article  MATH  Google Scholar 

  4. Macleod, H. A. Thin-film Optical Filters (McGraw-Hill, New York, 1989).

    Google Scholar 

  5. Raut, H. K., Ganesh, V. A., Nair, A. S. & Ramakrishna, S. Anti-reflective coatings: a critical, in-depth review. Energ. Environ. Sci. 4, 3779–3804 (2011).

    Article  Google Scholar 

  6. Clapham, P. B. & Hutley, M. C. Reduction of lens reflection by the ‘moth eye’ principle. Nature 244, 281–282 (1973).

    ADS  Article  Google Scholar 

  7. Huang, Y. F. et al. Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures. Nat. Nanotech. 2, 770–774 (2007).

    ADS  Article  Google Scholar 

  8. Spinelli, P., Verschuuren, M. A. & Polman, A. Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonator. Nat. Commun. 3, 692 (2012).

    ADS  Article  Google Scholar 

  9. Berenger, J. P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185–200 (1994).

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. Kay, I. & Moses, H. E. Reflectionless transmission through dielectrics and scattering potentials. Appl. Phys. 27, 1503–1508 (1956).

    Article  MATH  Google Scholar 

  13. Ablowitz, M. J. & Clarkson, P. A. Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge Univ. Press, Cambridge, 1992).

    MATH  Google Scholar 

  14. Horsley, S. A. R., Artoni, M. & La Rocca, G. C. Spatial Kramers–Kronig relations and the reflection of waves. Nat. Photon. 9, 436–439 (2015).

    ADS  Article  Google Scholar 

  15. Taflove, A. & Hagness, S. C. Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, London, 2005).

    MATH  Google Scholar 

  16. Halevi, P. & Fuchs, R. Generalised additional boundary condition for non-local dielectrics. J. Phys. C 17, 3869–3888 (1984).

    ADS  Article  Google Scholar 

  17. Churchill, R. J. & Philbin, T. G. Electromagnetic reflection, transmission and energy density at boundaries of nonlocal media. Phys. Rev. B 94, 235422 (2016).

    ADS  Article  Google Scholar 

  18. Kim, K. H. & Park, Q. H. Perfect anti-reflection from first principles. Sci. Rep. 3, 1062 (2013).

    Article  Google Scholar 

  19. Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. Electrodynamics of Continuous Media (Pergamon, Oxford, 1960).

    MATH  Google Scholar 

  20. Yeh, P. Optical Waves in Layered Media (Wiley, Hoboken, NJ, 2005).

    Google Scholar 

  21. Belov, P. A. et al. Strong spatial dispersion in wire media in the very large wavelength limit. Phys. Rev. B 67, 113103 (2003).

    ADS  Article  Google Scholar 

  22. Chebykin, A. V., Orlov, A. A., Simovski, C. R., Kivshar, Y. S. & Belov, P. A. Nonlocal effective parameters of multilayered metal–dielectric metamaterials. Phys. Rev. B 86, 115420 (2012).

    ADS  Article  Google Scholar 

  23. Nicolson, A. M. & Ross, G. F. Measurement of the intrinsic properties of materials by time-domain techniques. IEEE Trans. Instrum. Meas. 19, 377–382 (1970).

    Article  Google Scholar 

  24. Weir, W. B. Automatic measurement of complex dielectric constant and permeability at microwave frequencies. Proc. IEEE 62, 33–36 (1974).

    Article  Google Scholar 

Download references


This work was supported by the Samsung Science and Technology Foundation under project no. SSTF- BA1401-05. Q.-H.P. thanks Y. Kivshar and W. Choi for comments and encouragement.

Author information

Authors and Affiliations



Q.-H.P. developed the theory with numerical tests and wrote the paper. K.I., J.-H.K. and Q.-H.P. conducted the microwave experiments and analysed the data.

Corresponding author

Correspondence to Q-Han Park.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary discussion, conditions and derivations; Supplementary Figures 1–6; Supplementary References 1–9.

Supplementary Video 1

Propagation of an optical pulse, moving to the right, incident onto a quarter-wave anti-reflection layer.

Supplementary Video 2

Propagation of an optical pulse, moving to the right, incident onto a universal impedance matching layer.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Im, K., Kang, JH. & Park, QH. Universal impedance matching and the perfect transmission of white light. Nature Photon 12, 143–149 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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