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.

  • Letter
  • Published:

Observation of trapped light within the radiation continuum


The ability to confine light is important both scientifically and technologically. Many light confinement methods exist, but they all achieve confinement with materials or systems that forbid outgoing waves. These systems can be implemented by metallic mirrors, by photonic band-gap materials1, by highly disordered media (Anderson localization2) and, for a subset of outgoing waves, by translational symmetry (total internal reflection1) or by rotational or reflection symmetry3,4. Exceptions to these examples exist only in theoretical proposals5,6,7,8. Here we predict and show experimentally that light can be perfectly confined in a patterned dielectric slab, even though outgoing waves are allowed in the surrounding medium. Technically, this is an observation of an ‘embedded eigenvalue’9—namely, a bound state in a continuum of radiation modes—that is not due to symmetry incompatibility5,6,7,8,10,11,12,13,14,15,16. Such a bound state can exist stably in a general class of geometries in which all of its radiation amplitudes vanish simultaneously as a result of destructive interference. This method to trap electromagnetic waves is also applicable to electronic12 and mechanical waves14,15.

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

Access options

Buy this article

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

Figure 1: Predictions of the theory.
Figure 2: Fabricated PhC slab and the measurement setup.
Figure 3: Detection of resonances from reflectivity data.
Figure 4: Quantitative evidence on the disappearance of leakage.

Similar content being viewed by others


  1. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light 2nd edn (Princeton Univ. Press, 2008)

    MATH  Google Scholar 

  2. Lagendijk, A., van Tiggelen, B. & Wiersma, D. S. Fifty years of Anderson localization. Phys. Today 62, 24–29 (2009)

    Article  CAS  Google Scholar 

  3. Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 183901 (2011)

    Article  ADS  Google Scholar 

  4. Lee, J. et al. Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs. Phys. Rev. Lett. 109, 067401 (2012)

    Article  ADS  Google Scholar 

  5. Watts, M. R., Johnson, S. G., Haus, H. A. & Joannopoulos, J. D. Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap. Opt. Lett. 27, 1785–1787 (2002)

    Article  CAS  ADS  Google Scholar 

  6. Marinica, D. C., Borisov, A. G. & Shabanov, S. V. Bound states in the continuum in photonics. Phys. Rev. Lett. 100, 183902 (2008)

    Article  CAS  ADS  Google Scholar 

  7. Molina, M. I., Miroshnichenko, A. E. & Kivshar, Y. S. Surface bound states in the continuum. Phys. Rev. Lett. 108, 070401 (2012)

    Article  ADS  Google Scholar 

  8. Hsu, C. W. et al. Bloch surface eigenstates within the radiation continuum. Light Sci. Applics 2, e84 (in the press)

    Article  Google Scholar 

  9. Hislop, P. D. & Sigal, I. M. Introduction to Spectral Theory: with Applications to Schrödinger Operators (Springer, 1996)

    Book  Google Scholar 

  10. von Neumann, J. & Wigner, E. Über merkwürdige diskrete Eigenwerte. Phys. Z. 30, 465–467 (1929)

    MATH  Google Scholar 

  11. Stillinger, F. H. & Herrick, D. R. Bound states in the continuum. Phys. Rev. A 11, 446–454 (1975)

    Article  CAS  ADS  Google Scholar 

  12. Friedrich, H. & Wintgen, D. Interfering resonances and bound states in the continuum. Phys. Rev. A 32, 3231–3242 (1985)

    Article  CAS  ADS  Google Scholar 

  13. Zhang, J. M., Braak, D. & Kollar, M. Bound states in the continuum realized in the one-dimensional two-particle hubbard model with an impurity. Phys. Rev. Lett. 109, 116405 (2012)

    Article  CAS  ADS  Google Scholar 

  14. Porter, R. & Evans, D. Embedded Rayleigh–Bloch surface waves along periodic rectangular arrays. Wave Motion 43, 29–50 (2005)

    Article  MathSciNet  Google Scholar 

  15. Linton, C. M. & McIver, P. Embedded trapped modes in water waves and acoustics. Wave Motion 45, 16–29 (2007)

    Article  MathSciNet  Google Scholar 

  16. Krüger, H. On the existence of embedded eigenvalues. J. Math. Anal. Appl. 395, 776–787 (2012)

    Article  MathSciNet  Google Scholar 

  17. Taflove, A. & Hagness, S. C. Computational Electrodynamics: the Finite-difference Time-domain Method 3rd edn (Artech House, 2005)

  18. Johnson, S. G. & Joannopoulos, J. D. Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 8, 173–190 (2001)

    Article  CAS  ADS  Google Scholar 

  19. Fan, S. & Joannopoulos, J. D. Analysis of guided resonances in photonic crystal slabs. Phys. Rev. B 65, 235112 (2002)

    Article  ADS  Google Scholar 

  20. Liu, V. & Fan, S. S4: a free electromagnetic solver for layered periodic structures. Comput. Phys. Commun. 183, 2233–2244 (2012)

    Article  CAS  ADS  MathSciNet  Google Scholar 

Download references


We thank L. Lu, O. Shapira and Y. Shen for discussions. This work was partly supported by the Army Research Office through the Institute for Soldier Nanotechnologies under contract no. W911NF-07-D0004. B.Z., J.L. (fabrication) and M.S. were partly supported by S3TEC, an Energy Frontier Research Center funded by the US Department of Energy under grant no. DE-SC0001299. S.-L.C. and J.L. were also partly supported by the Materials Research Science and Engineering Centers of the National Science Foundation under grant no. DMR-0819762.

Author information

Authors and Affiliations



C.W.H., B.Z., S.-L.C., J.D.J. and M.S. conceived the idea of this study. C.W.H. performed numerical simulations. C.W.H. and B.Z. conducted the measurement and analysis. J.L. fabricated the sample. S.G.J. proposed the Fourier-coefficient explanation. M.S. and J.D.J. supervised the project. C.W.H. wrote the paper with input from all authors.

Corresponding author

Correspondence to Chia Wei Hsu.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Equations, Supplementary Discussion, additional references and Supplementary Figures 1 and 2. (PDF 172 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hsu, C., Zhen, B., Lee, J. et al. Observation of trapped light within the radiation continuum. Nature 499, 188–191 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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