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.

Scalable single-mode surface-emitting laser via open-Dirac singularities

Nature volume 608, pages 692–698 (2022)Cite this article

Subjects

Abstract

Single-aperture cavities are a key component of lasers that are instrumental for the amplification and emission of a single light mode. However, the appearance of high-order transverse modes as the size of the cavities increases has frustrated efforts to scale-up cavities while preserving single-mode operation since the invention of the laser six decades ago1,2,3,4,5,6,7,8. A suitable physical mechanism that allows single-mode lasing irrespective of the cavity size—a ‘scale invariant’ cavity or laser—has not been identified yet. Here we propose and demonstrate experimentally that open-Dirac electromagnetic cavities with linear dispersion—which in our devices are realized by a truncated photonic crystal arranged in a hexagonal pattern—exhibit unconventional scaling of losses in reciprocal space, leading to single-mode lasing that is maintained as the cavity is scaled up in size. The physical origin of this phenomenon lies in the convergence of the complex part of the free spectral range in open-Dirac cavities towards a constant governed by the loss rates of distinct Bloch bands, whereas for common cavities it converges to zero as the size grows, leading to inevitable multimode emission. An unconventional flat-envelope fundamental mode locks all unit cells in the cavity in phase, leading to single-mode lasing. We name such sources Berkeley surface-emitting lasers (BerkSELs) and demonstrate that their far-field corresponds to a topological singularity of charge two, in agreement with our theory. Open-Dirac cavities unlock avenues for light–matter interaction and cavity quantum electrodynamics.

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

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Fig. 1: Scalable open-Dirac electromagnetic cavity and the Berkeley surface-emitting laser.
Fig. 2: Quantization of the band structure in open-Dirac cavities forming higher-order modes and evidence for an unconventional fundamental mode with a flat envelope.
Fig. 3: Complex frequency scaling of open-Dirac electromagnetic cavities.
Fig. 4: Lasing characteristics of BerkSELs erasing higher-order modes around the open-Dirac singularity.
Fig. 5: Far-field scaling of BerkSELs and photon statistics.

Data availability

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

Code availability

The computer codes that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Schawlow, A. L. & Townes, C. H. Infrared and optical masers. Phys. Rev. 112, 1940–1949 (1958).

    Article  ADS  CAS  Google Scholar 

  2. Kogelnik, H. & Shank, C. V. Stimulated emission in a periodic structure. Appl. Phys. Lett. 18, 152–154 (1971).

    Article  ADS  CAS  Google Scholar 

  3. Soda, H., Iga, K., Kitahara, C. & Suematsu, Y. GaInAsP/InP surface emitting injection lasers. Jpn J. Appl. Phys. 18, 2329–2330 (1979).

    Article  ADS  CAS  Google Scholar 

  4. Meier, M. et al. Laser action from two-dimensional distributed feedback in photonic crystals. Appl. Phys. Lett. 74, 7–9 (1999).

    Article  ADS  CAS  Google Scholar 

  5. Imada, M. et al. Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure. Appl. Phys. Lett. 75, 316–318 (1999).

    Article  ADS  CAS  Google Scholar 

  6. Choquette, K. D., Hou, H. Q., Geib, K. M. & Hammons, B. E. Uniform and high power selectively oxidized 8x8 VCSEL array. In IEEE/LEOS Summer Topical Meetings 11–12 (IEEE, 1997).

  7. Francis, D., Chen, H.-L., Yuen, W., Li, G. & Chang-Hasnain, C. Monolithic 2D-VCSEL array with 2 W CW and 5 W pulsed output power. Electron. Lett. 34, 2132–2133 (1998).

    Article  ADS  Google Scholar 

  8. Yoshida, M. et al. Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams. Nat. Mater. 18, 121–128 (2019).

    Article  CAS  Google Scholar 

  9. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  ADS  CAS  Google Scholar 

  10. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988).

    Article  ADS  CAS  Google Scholar 

  11. Yablonovitch, E. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58, 2059–2062 (1987).

    Article  ADS  CAS  Google Scholar 

  12. John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    Article  ADS  CAS  Google Scholar 

  13. Sakoda, K. Universality of mode symmetries in creating photonic Dirac cones. J. Opt. Soc. Am. B 29, 2770 (2012).

    Article  ADS  CAS  Google Scholar 

  14. Sakoda, K. Proof of the universality of mode symmetries in creating photonic Dirac cones. Opt. Express 20, 25181 (2012).

    Article  ADS  Google Scholar 

  15. Enoch, S., Tayeb, G., Sabouroux, P., Guérin, N. & Vincent, P. A metamaterial for directive emission. Phys. Rev. Lett. 89, 213902 (2002).

    Article  ADS  Google Scholar 

  16. Huang, X., Lai, Y., Hang, Z. H., Zheng, H. & Chan, C. T. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10, 582–586 (2011).

    Article  ADS  CAS  Google Scholar 

  17. Moitra, P. et al. Realization of an all-dielectric zero-index optical metamaterial. Nat. Photon. 7, 791–795 (2013).

    Article  ADS  CAS  Google Scholar 

  18. Li, Y. et al. On-chip zero-index metamaterials. Nat. Photon. 9, 738–742 (2015).

    Article  ADS  CAS  Google Scholar 

  19. Liberal, I. & Engheta, N. Near-zero refractive index photonics. Nat. Photon. 11, 149–158 (2017).

    Article  ADS  CAS  Google Scholar 

  20. Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).

    Article  ADS  CAS  Google Scholar 

  21. Bravo-Abad, J., Joannopoulos, J. D. & Soljacic, M. Enabling single-mode behavior over large areas with photonic Dirac cones. Proc. Natl Acad. Sci. USA 109, 9761–9765 (2012).

    Article  ADS  CAS  Google Scholar 

  22. Chua, S.-L., Lu, L., Bravo-Abad, J., Joannopoulos, J. D. & Soljačić, M. Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point. Opt. Lett. 39, 2072–2075 (2014).

    Article  ADS  CAS  Google Scholar 

  23. Gao, X. et al. Dirac-vortex topological cavities. Nat. Nanotechnol. 15, 1012–1018 (2020).

    Article  ADS  CAS  Google Scholar 

  24. Siegman, A. E. Lasers 466–472 (Univ. Science Book, 1986).

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

    Article  ADS  CAS  Google Scholar 

  26. Loudon, R. The Quantum Theory of Light 3rd edn (Oxford Univ. Press, 2000).

  27. Pan, S. H., Gu, Q., El Amili, A., Vallini, F. & Fainman, Y. Dynamic hysteresis in a coherent high-β nanolaser. Optica 3, 1260–1265 (2016).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This research was mostly supported by the Office of Naval Research (ONR) Young Investigator Award (N00014-19-1-2737), the ONR JTO MRI Award (N00014-20-1-2752), the ONR grant N00014-20-1-2723 and the National Science Foundation (NSF) Career Award (ECCS-1929659). It was partially supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory (LBNL) under US Department of Energy contract no. DE-AC02-05CH11231, the NSF QLCI programme through grant number OMA-2016245, the Moore Inventor Fellows programme and the Bakar Fellowship at UC Berkeley. The work was partially performed at the UC Berkeley Marvel Nanofabrication Laboratory, the Molecular Foundry at LBNL and the San Diego Nanotechnology Infrastructure, a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the National Science Foundation (ECCS-1542148). We thank M. Montero for technical assistance regarding fabrication.

Author information

Author notes

  1. These authors contributed equally: Rushin Contractor, Wanwoo Noh, Walid Redjem

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, CA, USA

    Rushin Contractor, Wanwoo Noh, Walid Redjem, Emma Martin & Boubacar Kanté

  2. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Wayesh Qarony & Boubacar Kanté

  3. Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Scott Dhuey & Adam Schwartzberg

Authors
  1. Rushin Contractor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wanwoo Noh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Walid Redjem
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wayesh Qarony
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Emma Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Scott Dhuey
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Adam Schwartzberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Boubacar Kanté
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

B.K. conceived the project, proposed the idea, and guided the theoretical and experimental investigations. R.C. performed the theoretical calculations. W.N. fabricated the devices. W.R. performed the measurements. W.Q., E.M., S.D. and A.S. contributed to the fabrication of the larger-size devices requested by the reviewers. All authors contributed to discussions and R.C, W.R. and B.K. wrote the manuscript.

Corresponding author

Correspondence to Boubacar Kanté.

Ethics declarations

Competing interests

The Regents of the University of California have filed a patent application (US provisional application 63/304,581) on technology related to the processes described in this article.

Peer review

Peer review information

Nature thanks Alejandro Martinez and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Supplementary information

Supplementary Information

This file contains Supplementary Sections A–J, including Supplementary Table 1, Figs. 1–18 and References.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Contractor, R., Noh, W., Redjem, W. et al. Scalable single-mode surface-emitting laser via open-Dirac singularities. Nature 608, 692–698 (2022). https://doi.org/10.1038/s41586-022-05021-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-022-05021-4

This article is cited by

Comments

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.

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