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.

  • Letter
  • Published:

Anisotropy-induced photonic bound states in the continuum

Nature Photonics volume 11, pages 232–236 (2017)Cite this article

Subjects

Abstract

Bound states in the continuum (BICs) are radiationless localized states embedded in the part of the parameter space that otherwise corresponds to radiative modes. Many decades after their original prediction1,2,3 and early observations in acoustic systems4, such states have been demonstrated recently in photonic structures with engineered geometries5,6,7,8,9,10,11,12,13,14,15,16,17,18. Here, we put forward a mechanism, based on waveguiding structures that contain anisotropic birefringent materials, that affords the existence of BICs with fundamentally new properties. In particular, anisotropy-induced BICs may exist in symmetric as well as in asymmetric geometries; they may form in tunable angular propagation directions; their polarization may be pure transverse electric, pure transverse magnetic or full vector with tunable polarization hybridity; and they may be the only possible bound states of properly designed structures, and thus appear as a discrete, isolated bound state embedded in a whole sea of radiative states.

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: Modal spectroscopy.
Figure 2: Type of anisotropy-induced BICs.
Figure 3: Polarization hybridity and angular locus of BICs.
Figure 4: Theoretical and experimental modal spectroscopy spectra for an antiguiding waveguide on a calcite substrate.

Similar content being viewed by others

References

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

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. Parker, R. Resonance effects in wake shedding from parallel plates: some experimental observations. J. Sound Vib. 4, 62–72 (1966).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Bulgakov, E. N. & Sadreev, A. F. Bound states in the continuum in photonic waveguides inspired by defects. Phys. Rev. B 78, 075105 (2008).

    Article  ADS  Google Scholar 

  7. Moiseyev, N. Suppression of Feshbach resonance widths in two-dimensional waveguides and quantum dots: a lower bound for the number of bound states in the continuum. Phys. Rev. Lett. 102, 1–4 (2009).

    Article  Google Scholar 

  8. Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 28–31 (2011).

    Article  Google Scholar 

  9. Hsu, C. W. et al. Observation of trapped light within the radiation continuum. Nature 499, 188–191 (2013).

    Article  ADS  Google Scholar 

  10. Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Topological nature of optical bound states in the continuum. Phys. Rev. Lett. 113, 257401 (2014).

    Article  ADS  Google Scholar 

  11. Yang, Y., Peng, C., Liang, Y., Li, Z. & Noda, S. Analytical perspective for bound states in the continuum in photonic crystal slabs. Phys. Rev. Lett. 113, 037401 (2014).

    Article  ADS  Google Scholar 

  12. Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 1, 16048 (2016).

    Article  ADS  Google Scholar 

  13. Monticone, F. & Alù, A. Embedded photonic eigenvalues in 3D nanostructures. Phys. Rev. Lett. 112, 213903 (2014).

    Article  ADS  Google Scholar 

  14. Gao, X. et al. Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs. Sci. Rep. 6, 31908 (2016).

    Article  ADS  Google Scholar 

  15. Rivera, N. et al. Controlling directionality and dimensionality of wave propagation through separable bound states in the continuum. Sci. Rep. 6, 33394 (2016).

    Article  ADS  Google Scholar 

  16. Kodigala, A. et al. Lasing action from photonic bound states in continuum. Nature 541, 196–199 (2017).

    Article  ADS  Google Scholar 

  17. Dreisow, F. et al. Adiabatic transfer of light via a continuum in optical waveguides. Opt. Lett. 34, 2405–2407 (2009).

    Article  ADS  Google Scholar 

  18. 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 

  19. 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 

  20. Corrielli, G., Della Valle, G., Crespi, A., Osellame, R. & Longhi, S. Observation of surface states with algebraic localization. Phys. Rev. Lett. 111, 220403 (2013).

    Article  ADS  Google Scholar 

  21. Weimann, S. et al. Compact surface Fano states embedded in the continuum of waveguide arrays. Phys. Rev. Lett. 111, 240403 (2013).

    Article  ADS  Google Scholar 

  22. Shipman, S. P. & Welters, A. T. Resonant electromagnetic scattering in anisotropic layered media. J. Math. Phys. 54, 103511 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  23. Krishnamoorthy, H. N. S., Jacob, Z., Narimanov, E., Kretzschmar, I. & Menon, V. M. Topological transitions in metamaterials. Science 336, 205–209 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  24. Jahani, S. & Jacob, Z. All-dielectric metamaterials. Nat. Nanotech. 11, 23–36 (2016).

    Article  ADS  Google Scholar 

  25. Poddubny, A., Iorsh, I., Belov, P. & Kivshar, Y. Hyperbolic metamaterials. Nat. Photon. 7, 948–957 (2013); corrigendum 8, 78 (2014).

    Article  ADS  Google Scholar 

  26. Monticone, F. & Alú, A. Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies. Proc. IEEE 103, 793–821 (2015).

    Article  Google Scholar 

  27. Knoesen, A., Gaylord, T. K. & Moharam, M. G. Hybrid guided modes in uniaxial dielectric planar waveguides. J. Light. Technol. 6, 1083–1104 (1988).

    Article  ADS  Google Scholar 

  28. Torner, L., Recolons, J. & Torres, J. P. Guided-to-leaky mode transition in uniaxial optical slab waveguides. J. Light. Technol. 11, 1592–1600 (1993).

    Article  ADS  Google Scholar 

  29. Marcuse, D. & Kaminow, I. Modes of a symmetric slab optical waveguide in birefringent media, part II: slab with coplanar optical axis. IEEE J. Quantum Electron. 15, 92–101 (1979).

    Article  ADS  Google Scholar 

  30. Hsu, C. W. et al. Bloch surface eigenstates within the radiation continuum. Light Sci. Appl. 2, e84 (2013).

    Article  Google Scholar 

  31. Li, J., Gauza, S. & Wu, S.-T. Temperature effect on liquid crystal refractive indices. J. Appl. Phys. 96, 19–24 (2004).

    Article  ADS  Google Scholar 

  32. Gomez-Diaz, J. S. & Alù, A. Flatland optics with hyperbolic metasurfaces. ACS Photon. 3, 2211–2224 (2016).

    Article  Google Scholar 

  33. Smalley, D. E., Smithwick, Q. Y. J., Bove, V. M., Barabas, J. & Jolly, S. Anisotropic leaky-mode modulator for holographic video displays. Nature 498, 313–317 (2013).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522) and grant FIS2015-71559-P, the Fundació privada Cellex, the Fundació privada Mir-Puig, and the Generalitat de Catalunya through the CERCA Programme. The authors also thank P. Mantilla for the spin coating of the calcite samples and R.J. Sewell for discussions in writing the paper.

Author information

Authors and Affiliations

  1. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avenue Carl Friedrich Gauss, 3, Castelldefels (Barcelona), 08860, Spain

    Jordi Gomis-Bresco, David Artigas & Lluis Torner

  2. Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Barcelona, 08034, Spain

    David Artigas & Lluis Torner

Authors
  1. Jordi Gomis-Bresco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Artigas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lluis Torner
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to the work.

Corresponding author

Correspondence to Lluis Torner.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 899 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gomis-Bresco, J., Artigas, D. & Torner, L. Anisotropy-induced photonic bound states in the continuum. Nature Photon 11, 232–236 (2017). https://doi.org/10.1038/nphoton.2017.31

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2017.31

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