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.
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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.
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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.
The authors declare no competing interests.
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Extended data figures and tables
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.
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′.
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.
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. d–f, 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.
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.
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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
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