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:

High quality factor phase gradient metasurfaces

Nature Nanotechnology volume 15, pages 956–961 (2020)Cite this article

Subjects

Abstract

Dielectric microcavities with quality factors (Q-factors) in the thousands to billions markedly enhance light–matter interactions, with applications spanning high-efficiency on-chip lasing, frequency comb generation and modulation and sensitive molecular detection. However, as the dimensions of dielectric cavities are reduced to subwavelength scales, their resonant modes begin to scatter light into many spatial channels. Such enhanced scattering is a powerful tool for light manipulation, but also leads to high radiative loss rates and commensurately low Q-factors, generally of order ten. Here, we describe and experimentally demonstrate a strategy for the generation of high Q-factor resonances in subwavelength-thick phase gradient metasurfaces. By including subtle structural perturbations in individual metasurface elements, resonances are created that weakly couple free-space light into otherwise bound and spatially localized modes. Our metasurface can achieve Q-factors >2,500 while beam steering light to particular directions. High-Q beam splitters are also demonstrated. With high-Q metasurfaces, the optical transfer function, near-field intensity and resonant line shape can all be rationally designed, providing a foundation for efficient, free-space-reconfigurable and nonlinear nanophotonics.

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

Fig. 1: Conceptual and numerical design of high-Q phase gradient metasurfaces.
Fig. 2: Experimental demonstration of high-Q phase gradient metasurface beam steering.
Fig. 3: Narrowband and slow-light beam steering.
Fig. 4: High-Q metasurface beam splitter.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors on reasonable request.

References

  1. Armani, D. K., Kippenberg, T. J., Spillane, S. M. & Vahala, K. J. Ultra-high-Q toroid microcavity on a chip. Nature 421, 925–928 (2003).

    CAS  Google Scholar 

  2. Gorodetsky, M. L., Savchenkov, A. A. & Ilchenko, V. S. Ultimate Q of optical microsphere resonators. Opt. Lett. 21, 453–455 (1996).

    CAS  Google Scholar 

  3. Vernooy, D. W., Ilchenko, V. S., Mabuchi, H., Streed, E. W. & Kimble, H. J. High-Q measurements of fused-silica microspheres in the near infrared. Opt Lett 23, 247–249 (1998).

    CAS  Google Scholar 

  4. Kippenberg, T. J., Spillane, S. M. & Vahala, K. J. Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity. Phys. Rev. Lett. 93, 083904 (2004).

  5. Lin, H.-B., Eversole, J. D. & Campillo, A. J. Continuous-wave stimulated Raman scattering in microdroplets. Opt. Lett. 17, 828–830 (1992).

    Google Scholar 

  6. Min, B., Kippenberg, T. J. & Vahala, K. J. Compact, fiber-compatible, cascaded Raman laser. Opt. Lett. 28, 1507–1509 (2003).

    Google Scholar 

  7. Treussart, F. et al. Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium. Eur. Phys. J. D 1, 235–238 (1998).

    CAS  Google Scholar 

  8. Akahane, Y., Asano, T., Song, B. S. & Noda, S. High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature 425, 944–947 (2003).

    CAS  Google Scholar 

  9. Lee, H. et al. Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photonics 6, 369–373 (2012).

    CAS  Google Scholar 

  10. Lin, G., Diallo, S., Henriet, R., Jacquot, M. & Chembo, Y. K. Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor. Opt. Lett. 39, 6009–6012 (2014).

    Google Scholar 

  11. Takahashi, Y. et al. A micrometre-scale Raman silicon laser with a microwatt threshold. Nature 498, 470–474 (2013).

    CAS  Google Scholar 

  12. Peng, B. et al. Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394–398 (2014).

    CAS  Google Scholar 

  13. Ellis, B. et al. Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser. Nat. Photonics 5, 297–300 (2011).

    CAS  Google Scholar 

  14. Stern, B., Ji, X., Okawachi, Y., Gaeta, A. L. & Lipson, M. Battery-operated integrated frequency comb generator. Nature 562, 401–405 (2018).

    CAS  Google Scholar 

  15. Wang, C. et al. Monolithic lithium niobate photonic circuits for Kerr frequency comb generation and modulation. Nat. Commun. 10, 978 (2019).

  16. Guo, X. et al. Parametric down-conversion photon-pair source on a nanophotonic chip. Light Sci. Appl. 6, e16249 (2017).

    CAS  Google Scholar 

  17. Sun, S., Kim, H., Luo, Z., Solomon, G. S. & Waks, E. A single-photon switch and transistor enabled by a solid-state quantum memory. Science 361, 57–60 (2018).

    CAS  Google Scholar 

  18. Scheucher, M., Hilico, A., Will, E., Volz, J. & Rauschenbeutel, A. Quantum optical circulator controlled by a single chirally coupled atom. Science 354, 1577–1580 (2016).

    CAS  Google Scholar 

  19. Vollmer, F., Arnold, S. & Keng, D. Single virus detection from the reactive shift of a whispering-gallery mode. Proc. Natl Acad. Sci. USA 105, 20701–20704 (2008).

    CAS  Google Scholar 

  20. Kuznetsov, A. I., Miroshnichenko, A. E., Brongersma, M. L., Kivshar, Y. S. & Luk’yanchuk, B. Optically resonant dielectric nanostructures. Science 354, aag2472 (2016).

    Google Scholar 

  21. Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).

    CAS  Google Scholar 

  22. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

    CAS  Google Scholar 

  23. Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).

    CAS  Google Scholar 

  24. Zheng, G. et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotechnol. 10, 308–312 (2015).

    CAS  Google Scholar 

  25. Liu, L. et al. Broadband metasurfaces with simultaneous control of phase and amplitude. Adv. Mater. 26, 5031–5036 (2014).

    CAS  Google Scholar 

  26. Balthasar Mueller, J. P., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).

    CAS  Google Scholar 

  27. Yin, X., Ye, Z., Rho, J., Wang, Y. & Zhang, X. Photonic spin hall effect at metasurfaces. Science 339, 1405–1407 (2013).

    CAS  Google Scholar 

  28. Li, G. et al. Continuous control of the nonlinearity phase for harmonic generations. Nat. Mater. 14, 607–612 (2015).

    CAS  Google Scholar 

  29. Almeida, E., Shalem, G. & Prior, Y. Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces. Nat. Commun. 7, 10367 (2016).

  30. Wang, L. et al. Nonlinear wavefront control with all-dielectric metasurfaces. Nano Lett. 18, 3978–3984 (2018).

    Google Scholar 

  31. Wu, P. C. et al. Dynamic beam steering with all-dielectric electro-optic III–V multiple-quantum-well metasurfaces. Nat. Commun. 10, 3654 (2019).

    Google Scholar 

  32. Li, S. Q. et al. Phase-only transmissive spatial light modulator based on tunable dielectric metasurface. Science 364, 1087–1090 (2019).

    CAS  Google Scholar 

  33. Decker, M. et al. High-efficiency dielectric Huygens’ surfaces. Adv. Opt. Mater. 3, 813–820 (2015).

    CAS  Google Scholar 

  34. Pfeiffer, C. et al. Efficient light bending with isotropic metamaterial Huygens’ surfaces. Nano Lett. 14, 2491–2497 (2014).

    CAS  Google Scholar 

  35. Estakhri, N. M. & Alù, A. Wave-front transformation with gradient metasurfaces. Phys. Rev. X 6, 041008 (2016).

    Google Scholar 

  36. Wang, S. S. & Magnusson, R. Theory and applications of guided-mode resonance filters. Appl. Opt. 32, 2606–2613 (1993).

    Google Scholar 

  37. Lawrence, M., Barton, D. R. & Dionne, J. A. Nonreciprocal flat optics with silicon metasurfaces. Nano Lett. 18, 1104–1109 (2018).

    CAS  Google Scholar 

  38. Jiang, X. et al. Chaos-assisted broadband momentum transformation in optical microresonators. Science 358, 344–347 (2017).

    CAS  Google Scholar 

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

    Google Scholar 

  40. Wu, C. et al. Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances. Nat. Commun. 5, 3892 (2014).

    CAS  Google Scholar 

  41. Yang, Y., Kravchenko, I. I., Briggs, D. P. & Valentine, J. All-dielectric metasurface analogue of electromagnetically induced transparency. Nat. Commun. 5, 5753 (2014).

    CAS  Google Scholar 

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

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

    CAS  Google Scholar 

  44. Ha, S. T. et al. Directional lasing in resonant semiconductor nanoantenna arrays. Nat. Nanotechnol. 13, 1042–1047 (2018).

    CAS  Google Scholar 

  45. Yang, Y. et al. Nonlinear fano-resonant dielectric metasurfaces. Nano Lett. 15, 7388–7393 (2015).

    CAS  Google Scholar 

  46. Limonov, M. F., Rybin, M. V., Poddubny, A. N. & Kivshar, Y. S. Fano resonances in photonics. Nat. Photonics 11, 543–554 (2017).

    CAS  Google Scholar 

  47. Klopfer, E., Lawrence, M., Barton, D. R., Dixon, J. & Dionne, J. A. Dynamic focusing with high-quality-factor metalenses. Nano Lett. 20, 5127–5132 (2020).

Download references

Acknowledgements

We thank R. Tiberio and U. Raghuram for helpful discussions regarding fabrication. This work was supported by PECASE (grant no. FA9550-15-10006) and NSF EFRI (grant no. 1641109). The device fabrication, performed in part by J.D., was supported by the DOE ‘Photonics at Thermodynamic Limits’ Energy Frontier Research Center under grant no. DE-SC0019140. J.v.d.G, J.-H.S. and M.L.B. acknowledge funding from an individual investigator grant from AFOSR (no. FA9550-18-1-0323). Part of this work was performed at the Stanford Nano Shared Facilities and Stanford Nanofabrication Facilities, which are supported by the National Science Foundation and National Nanotechnology Coordinated Infrastructure under award no. ECCS-1542152.

Author information

Author notes

  1. Jorik van de Groep

    Present address: Van der Waals-Zeeman Institute for Experimental Physics, Institute of Physics, University of Amsterdam, Amsterdam, Netherlands

  2. These authors contributed equally: Mark Lawrence, David R. Barton III.

Authors and Affiliations

  1. Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA

    Mark Lawrence, David R. Barton III & Jennifer A. Dionne

  2. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Jefferson Dixon

  3. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA

    Jung-Hwan Song, Jorik van de Groep & Mark L. Brongersma

  4. Department of Radiology, Stanford University, Stanford, CA, USA

    Jennifer A. Dionne

Authors
  1. Mark Lawrence
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David R. Barton III
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jefferson Dixon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jung-Hwan Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jorik van de Groep
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mark L. Brongersma
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jennifer A. Dionne
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.L., D.R.B. and J.D. conceived the idea. M.L. performed full-field simulations. D.R.B., J.D. and J.v.d.G. fabricated the devices. M.L. and J.-H.S. conducted optical characterization. D.R.B. and M.L. wrote the manuscript. J.A.D. supervised the project, along with M.L.B. on the relevant portions of the research. All authors contributed to preparation of the manuscript.

Corresponding authors

Correspondence to Mark Lawrence, David R. Barton III or Jennifer A. Dionne.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Nanotechnology thanks Lan Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–19 and discussion.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lawrence, M., Barton, D.R., Dixon, J. et al. High quality factor phase gradient metasurfaces. Nat. Nanotechnol. 15, 956–961 (2020). https://doi.org/10.1038/s41565-020-0754-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-020-0754-x

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