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.

Electrically pumped topological laser with valley edge modes

Abstract

Quantum cascade lasers are compact, electrically pumped light sources in the technologically important mid-infrared and terahertz region of the electromagnetic spectrum1,2. Recently, the concept of topology3 has been expanded from condensed matter physics into photonics4, giving rise to a new type of lasing5,6,7,8 using topologically protected photonic modes that can efficiently bypass corners and defects4. Previous demonstrations of topological lasers have required an external laser source for optical pumping and have operated in the conventional optical frequency regime5,6,7,8. Here we demonstrate an electrically pumped terahertz quantum cascade laser based on topologically protected valley edge states9,10,11. Unlike topological lasers that rely on large-scale features to impart topological protection, our compact design makes use of the valley degree of freedom in photonic crystals10,11, analogous to two-dimensional gapped valleytronic materials12. Lasing with regularly spaced emission peaks occurs in a sharp-cornered triangular cavity, even if perturbations are introduced into the underlying structure, owing to the existence of topologically protected valley edge states that circulate around the cavity without experiencing localization. We probe the properties of the topological lasing modes by adding different outcouplers to the topological cavity. The laser based on valley edge states may open routes to the practical use of topological protection in electrically driven laser sources.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Design of a terahertz quantum cascade laser with topologically protected valley edge modes.
Fig. 2: Fabrication and characterization of the topological THz QCL.
Fig. 3: Topological laser with an array of evanescent outcouplers.
Fig. 4: Topological laser in a directional outcoupling configuration.

Data availability

The data sets generated during and/or analysed during the current study are available in the DR-NTU(Data) repository https://doi.org/10.21979/N9/PECAGQ.

References

  1. 1.

    Faist, J. et al. Quantum cascade laser. Science 264, 553–556 (1994).

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Köhler, R. et al. Terahertz semiconductor-heterostructure laser. Nature 417, 156–159 (2002).

    ADS  Article  Google Scholar 

  3. 3.

    Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  5. 5.

    Wittek, S. et al. Towards the experimental realization of the topological insulator laser. In CLEO: QELS_Fundamental Science FTh1D-3 (Optical Society of America, 2017).

  6. 6.

    Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).

    Article  Google Scholar 

  7. 7.

    Harari, G. et al. Topological insulator laser: theory. Science 359, eaar4003 (2018).

    Article  Google Scholar 

  8. 8.

    Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Ma, T. & Shvets, G. All-Si valley-Hall photonic topological insulator. New J. Phys. 18, 025012 (2016).

    ADS  Article  Google Scholar 

  11. 11.

    Gao, F. et al. Topologically protected refraction of robust kink states in valley photonic crystals. Nat. Phys. 14, 140–144 (2018).

    CAS  Article  Google Scholar 

  12. 12.

    Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Vitiello, M. S., Scalari, G., Williams, B. & De Natale, P. Quantum cascade lasers: 20 years of challenges. Opt. Express 23, 5167–5182 (2015).

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Dhillon, S. S. et al. Terahertz transfer onto a telecom optical carrier. Nat. Photonics 1, 411–415 (2007).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Gao, J. R. et al. Terahertz heterodyne receiver based on a quantum cascade laser and a superconducting bolometer. Appl. Phys. Lett. 86, 244104 (2005).

    ADS  Article  Google Scholar 

  16. 16.

    Dean, P. et al. Terahertz imaging using quantum cascade lasers—a review of systems and applications. J. Phys. D 47, 374008 (2014).

    Article  Google Scholar 

  17. 17.

    Sirtori, C., Barbieri, S. & Colombelli, R. Wave engineering with THz quantum cascade lasers. Nat. Photonics 7, 691–701 (2013).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Zeng, Y., Qiang, B. & Wang, Q. J. Photonic engineering technology for the development of terahertz quantum cascade lasers. Adv. Opt. Mater. https://doi.org/10.1002/adom.201900573 (2019).

    Article  Google Scholar 

  19. 19.

    Schröder, H. W., Stein, L., Frölich, D., Fugger, B. & Welling, H. A high-power single-mode CW dye ring laser. Appl. Phys. (Berl.) 14, 377–380 (1977).

    ADS  Article  Google Scholar 

  20. 20.

    Pérez-Serrano, A., Javaloyes, J. & Balle, S. Longitudinal mode multistability in ring and Fabry–Pérot lasers: the effect of spatial hole burning. Opt. Express 19, 3284 (2011).

    ADS  Article  Google Scholar 

  21. 21.

    Gordon, A. et al. Multimode regimes in quantum cascade lasers: from coherent instabilities to spatial hole burning. Phys. Rev. A 77, 053804 (2008).

    ADS  Article  Google Scholar 

  22. 22.

    Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).

    CAS  Article  Google Scholar 

  23. 23.

    Peano, V., Houde, M., Marquardt, F. & Clerk, A. A. Topological quantum fluctuations and traveling wave amplifiers. Phys. Rev. X 6, 041026 (2016).

    Google Scholar 

  24. 24.

    Zhou, X., Wang, Y., Leykam, D. & Chong, Y. D. Optical isolation with nonlinear topological photonics. New J. Phys. 19, 095002 (2017).

    ADS  Article  Google Scholar 

  25. 25.

    Barik, S. et al. A topological quantum optics interface. Science 359, 666–668 (2018).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  26. 26.

    St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photonics 11, 651–656 (2017).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Zhao, H. et al. Topological hybrid silicon microlasers. Nat. Commun. 9, 981 (2018).

    ADS  Article  Google Scholar 

  28. 28.

    Dong, J. W., Chen, X. D., Zhu, H., Wang, Y. & Zhang, X. Valley photonic crystals for control of spin and topology. Nat. Mater. 16, 298–302 (2017).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Kang, Y., Ni, X., Cheng, X., Khanikaev, A. B. & Genack, A. Z. Pseudo-spin–valley coupled edge states in a photonic topological insulator. Nat. Commun. 9, 3029 (2018).

    ADS  Article  Google Scholar 

  30. 30.

    Shalaev, M. I., Walasik, W., Tsukernik, A., Xu, Y. & Litchinitser, N. M. Robust topologically protected transport in photonic crystals at telecommunication wavelengths. Nat. Nanotechnol. 14, 31–34 (2019).

    ADS  CAS  Article  Google Scholar 

  31. 31.

    Lu, J. et al. Observation of topological valley transport of sound in sonic crystals. Nat. Phys. 13, 369–374 (2017).

    CAS  Article  Google Scholar 

  32. 32.

    Sandoghdar, V. et al. Very low threshold whispering-gallery-mode microsphere laser. Phys. Rev. A 54, R1777–R1780 (1996).

    ADS  CAS  Article  Google Scholar 

  33. 33.

    Seclì, M., Capone, M. & Carusotto, I. Theory of chiral edge state lasing in a two-dimensional topological system. Phys. Rev. Res. 1, 033148 (2019).

    Google Scholar 

  34. 34.

    Belkin, M. et al. High-temperature operation of terahertz quantum cascade laser sources. IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    Williams, B. S., Kumar, S., Callebaut, H., Hu, Q. & Reno, J. L. Terahertz quantum-cascade laser at λ ≈ 100 μm using metal waveguide for mode confinement. Appl. Phys. Lett. 83, 2124–2126 (2003).

    ADS  CAS  Article  Google Scholar 

  36. 36.

    Gao, Z. et al. Valley surface-wave photonic crystal and its bulk/edge transport. Phys. Rev. B 96, 201402 (2017).

    ADS  Article  Google Scholar 

  37. 37.

    Wu, X. et al. Direct observation of valley-polarized topological edge states in designer surface plasmon crystals. Nat. Commun. 8, 1304 (2017).

    ADS  Article  Google Scholar 

  38. 38.

    Vitiello, M. S. & Tredicucci, A. Tunable emission in THz quantum cascade lasers. IEEE Trans. Terahertz Sci. Technol. 1, 76–84 (2011).

    ADS  CAS  Article  Google Scholar 

  39. 39.

    Fathololoumi, S. et al. Terahertz quantum cascade lasers operating up to ~200 K with optimized oscillator strength and improved injection tunneling. Opt. Express 20, 3866–3876 (2012).

    ADS  CAS  Article  Google Scholar 

  40. 40.

    Rockstuhl, C. & Scharf, T. Amorphous Nanophotonics (Springer, 2013).

  41. 41.

    Spreeuw, R. J. C., Neelen, R. C., van Druten, N. J., Eliel, E. R. & Woerdman, J. P. Mode coupling in a He–Ne ring laser with backscattering. Phys. Rev. A 42, 4315–4324 (1990).

    ADS  CAS  Article  Google Scholar 

  42. 42.

    Suh, W., Wang, Z., & Fan, S. Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities. IEEE J. Quantum Electron. 40, 1511–1518 (2004).

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

This work is supported by funding from the Singapore Ministry of Education (MOE), grants MOE2016-T2-1-128 and MOE2016-T2-2-159, and the National Research Foundation Competitive Research Program (NRF-CRP18-2017-02). U.C., Y.C. and B. Zhang acknowledge support from the Singapore MOE Academic Research Fund Tier 2, grants MOE2015-T2-2-008 and MOE2018-T2-1-022 (S), and the Singapore MOE Academic Research Fund Tier 3 grant MOE2016-T3-1-006. L.L., A.G.D. and E.H.L. acknowledge the support of the EPSRC (UK) HyperTerahertz programme (EP/P021859/1), and the Royal Society and the Wolfson Foundation.

Author information

Affiliations

Authors

Contributions

Y.Z. and B.Q. fabricated the laser devices. Y.Z., J.L. and Y.J. performed the device characterization. L.L., A.G.D. and E.H.L. performed QCL wafer growth. Y.Z., U.C. and B. Zhu performed the simulations. Y.Z., U.C., B. Zhu, B. Zhang, Y.C. and Q.J.W. performed the theoretical analysis and contributed to manuscript preparation. B. Zhang, Y.C. and Q.J.W. supervised the project.

Corresponding authors

Correspondence to Baile Zhang, Yidong Chong or Qi Jie Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Extended data figures and tables

Extended Data Fig. 1 Design of the 2D VPC.

a, Photonic band structure for the TM modes of a 2D triangular photonic crystal of hexagonal air holes in dielectric (refractive index 3.6), with unbroken inversion symmetry. The unit cell and Brillouin zone are shown inset. b, Band structure after breaking inversion symmetry by setting d1 ≠ d2. Inset, unit cell, with d1 = 0.58a, d2 = 0.26a. The Dirac points at K and K′ are lifted. c, d, Plots of the absolute value of the out-of-plane electric field |Ez| (colour maps) and Poynting vector (white arrows) within each unit cell at the K and K′ points. For both the lower band (c) and upper band (d), the modes in the two valleys are time-reversed counterparts, as shown by the opposite circulations of electromagnetic power.

Extended Data Fig. 2 Berry curvatures calculated using 2D Bloch wavefunctions for the lowest TM band.

a, Near the K′ valley. b, Near the K valley.

Extended Data Fig. 3 Edge states of the 2D VPC.

a, Supercell comprising two inequivalent VPC domains separated by a domain wall (highlighted by a red box). b, Projected band diagram for the supercell. The red (blue) curve indicates the valley edge mode for the K (K′) valley. c, d, Out-of-plane electric field |Ez| (colour maps) and Poynting vector (white arrows) for the edge modes at K, K′.

Extended Data Fig. 4 Comparison between 2D and 3D TM photonic band structures.

a, Bulk band structures of the 2D VPC (black) and 3D VPC (red). The grey regions delimited by black dashes denote the light cone. The 2D VPC is regarded as infinite in the out-of-plane (z) direction. The 3D VPC is modelled after the experiment, that is, metal–semiconductor–metal heterostructure with central dielectric thickness of 10 μm. b, Projected band diagrams for a topological waveguide in 2D (black) and 3D (red). The lattice configuration is the same as in Extended Data Fig. 3a, with 10 quasi-hexagonal holes on each side of the domain wall. The edge states are plotted as thick solid curves for clarity.

Extended Data Fig. 5 Emission characteristics of a conventional ridge laser fabricated on the quantum cascade wafer.

a, Emission spectra at different pump currents. b, Light–current–voltage curves of the ridge laser.

Extended Data Fig. 6 IPR for trivial and topologically non-trivial modes.

a, b, Schematics showing the topologically non-trivial (a) and trivial (b) cavities. The 1D interfaces along which the IPR is calculated are indicated by red and blue lines. For the design of the trivial cavity, see Extended Data Fig. 8a. c, IPR versus frequency for eigenmodes in the band gap for each type of cavity. The topological cavity’s eigenmodes have consistently lower IPR, indicating that they are more uniformly extended along the loop. df, Intensity distributions for three representative eigenmodes of the trivial cavity. For comparison, eigenmodes of the topological cavity are shown in Fig. 2c (top) of the main text.

Extended Data Fig. 7 Light–current–voltage curves of the topological laser with different designs.

a, The topological laser without an outcoupling defect. b, The topological laser with a side defect. c, The topological laser device with a corner defect. The corresponding device emission spectra are shown in Fig. 2d. All intensities in three sub-figures are measured with the same intensity scale. It can be inferred from these curves that the emission power is greatly enhanced by the outcoupling defect.

Extended Data Fig. 8 Topologically trivial laser with triangular loop cavity formed by a conventional photonic crystal waveguide.

a, SEM image of the fabricated structure. Inset, close-up view of the waveguide with single hole orientation, which consists of five rows of size-graded holes (with size scale factors s1 = 0.77, s2 = 0.87, s3 = 1). A defect (39 μm × 33.5 μm) is included to improve outcoupling efficiency. b, Calculated eigenmode Q factors for the structure with a side defect. The shaded area indicates the photonic bandgap of the valley Hall lattice. c, Electric field (|Ez|) plots for typical calculated eigenmodes of the trivial cavity. The white square indicates the position of the side defect. d, Emission spectra of the topologically trivial lasers with a side defect (top panel) and corner defect (bottom panel) at different pump currents. The spectra are vertically offset for clarity. The emission peaks of two lasers are different and do not present a clear and regularly spaced pattern in frequency space.

Extended Data Fig. 9 Quiver plots of Poynting vectors for two degenerate modes in a topologically non-trivial triangular loop cavity.

a, b, Starting from two degenerate eigenmodes returned by the numerical solver, denoted by ψ1 and ψ2, the plotted modes are (a) ψ1 + iψ2 and (b) ψ1 − iψ2. These have CCW and CW characteristics, respectively.

Extended Data Fig. 10 Lasing peak intensity curves for topological and non-topological lasing modes in the same laser device in a directional outcoupling configuration.

The schematic of the device is shown in Fig. 4a of the main text. a, b, Here, peak intensities are plotted versus pump current for the topological modes (a) and non-topological modes (b) of the same sample. P1, P2 and so on represent different emission peaks. Solid (dashed) curves correspond to the measurement with left (right) side of the device covered. Emission spectra at two representative pump currents are shown in Fig. 4c,d of the main text. For the topological lasing modes, the spectra from two output facets have comparable peak intensities, whereas for the non-topological lasing modes the peaks differ in intensity and frequency in the two cases.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zeng, Y., Chattopadhyay, U., Zhu, B. et al. Electrically pumped topological laser with valley edge modes. Nature 578, 246–250 (2020). https://doi.org/10.1038/s41586-020-1981-x

Download citation

Further reading

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

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