Nature - USA (2020-02-13)

Nature | Vol 578 | 13 February 2020 | 249

outcoupling rates. Coupled-mode theory predicts that each topologi-
cal lasing mode is composed of an equal-weight superposition of a CW
and CCW pair (see Methods). The coexistence of CW and CCW modes

also explains why the defect along the cavity in Fig.  2 does not spoil the

running-wave character, even in the presence of backscattering induced

by the defect. To test this, we fabricated a sample with an additional

b

Intensity (a.u.)

Intensity (a.u.)

d e

Intensity (a.u.)

c

Intensity (a.u.)

2.05A

2.31A

2.08A

1.84A

Case 1

Case 2

Case 3

1.82A Case 1 1.95A

Case 2

Case 3

Case 1

Case 2

Case 3

2.10A

0

2

4

0

2

4

0

2

4

3.03.1 3.23.3 3.43.0 3.1 3.23.3 3.43.0 3.13.2 3.33.4

0

2

0

2

0

2

0

2

0

2

0

2

Frequency (THz)

Frequency (THz) Frequency (THz) Frequency (THz)

3.03.1 3.23.3 3.4

1.93A

a

Case 1

Case 2

Case 3

Fig. 3 | Topological laser with an array of evanescent outcouplers.
a, Schematic of the structure. A triangular loop cavity (green triangle) hosting
topological edge states is surrounded by an array of outcoupling defects (blue
rectangles) distributed around the perimeter of a larger triangle. The defects
are eight lattice periods away from the topological interface, allowing for

evanescent outcoupling. The inset shows different defect-covering

configurations for the spectral measurements. b, Emission spectra at different

pump currents (vertically shifted for clarity), with all defects uncovered.

c–e, Emission spectra at various pump currents for the three different defect-

covering configurations shown in the inset of a.

Output facets

a

3.33.4 3.5

1

0

Non-topological modes (2.96 A)

3

2

1

0

Left covered

Right covered

Frequency(THz)

Intensity (a.u.)

3

2

3. 6

d

200 μm

Max

Min

b

Intensity (a.u.)

3 2 1 0 3 2 1

Left covered

Right covered

Topological modes (2.55 A)

Frequency (THz)

3.0

0

3.1 3.2 3.3

c

Fig. 4 | Topological laser in a directional outcoupling configuration.
a, Schematic of the structure. A straight valley edge-state waveguide is
introduced below the bottom arm of the triangular loop cavity (topological
interfaces are indicated by green lines), with outcoupling gratings on the left
and right ends. The output facets are selectively covered to observe the
directionality of the lasing modes. b, Intensity distribution for a typical

topological eigenmode obtained via a 3D numerical calculation. c, d, Emission

spectra for the topological lasing modes (c) and non-topological lasing

modes (d) with left and right output facets covered. For the topological lasing

modes, the spectra have similar peak intensities, whereas for the non-

topological lasing modes the spectra are completely different. The two sets of

lasing peaks are measured under different pump currents.