Spin-Momentum-Locked Edge Mode for Topological Vortex Lasing

Spin-momentum locking is a direct consequence of bulk topological order and provides a basic concept to control a carrier’s spin and charge flow for new exotic phenomena in condensed matter physics. However, up to date the research on spin-momentum locking solely focuses on its in-plane transport properties. Here, we report an emerging out-of-plane radiation feature of spin-momentum locking in a non-Hermitian topological photonic system and demonstrate a high performance topological vortex laser based on it. We find that the gain saturation effect lifts the degeneracy of the paired counterpropagating spin-momentum-locked edge modes enabling lasing from a single topological edge mode. The near-field spin and orbital angular momentum of the topological edge mode lasing has a one-to-one far-field radiation correspondence. The methodology of probing the near-field topology feature by far-field lasing emission can be used to study other exotic phenomena. The device can lead to applications in superresolution imaging, optical tweezers, free-space optical sensing, and communication.

Figure 1

Operation principle of the topological vortex laser. (a) SEM image of a topological vortex laser with a -shaped cavity indicated by the red line and arrows. The corresponding spin direction of the cavity mode is indicated by the out-of-plane arrows. (b) Zoomed-in SEM image of the topological interface. The red line represents the topological interface, the blue hexagon indicates a unit cell in the topological photonic crystal, and the orange hexagon indicates a unit cell in the trivial photonic crystal. (c) Calculated discrete cavity modes of the topological vortex laser (red and green dots). Gray curves are the calculated bulk bands of the topological photonic crystal. Black lines indicate the Dirac cone of an infinite long topological interface. (d) Schematic of the dispersion curves of the topological edge modes and conventional whispering gallery modes. Topological edge state lasing requires no in-plane momentum in principle, which decouples the radiation direction from the resonant plane. In contrast, the dominant radiation field of the conventional whispering gallery modes is in plane and omnidirectional due to momentum conservation. (e) Schematic of the topological vortex laser with circularly polarized vortex beam far-field radiation. The near-field spin and orbital angular momentum have a one-to-one far-field radiation correspondence.

Figure 2

Lasing evidences of the topological vortex laser. (a) Upper: Spontaneous emission spectrum obtained from a bulk photonic crystal region. The spectrum shows a clear suppressed intensity gap induced by a photonic band gap indicated by the orange region. Middle: Spontaneous emission spectrum of the topological interface, showing pronounced resonant peaks within the band gap. Bottom: lasing spectrum of the vortex laser under a pump power of $545\mathrm{kW}{\mathrm{cm}}^{-2}$. (b) Spontaneous emission pattern. (c) Lasing emission pattern. In (b) and (c), dashed green line indicates the -shaped topological interface. (d) Integrated output power as a function of pump intensity in log scale. The slope in the spontaneous emission state and lasing state is 1.13 and 1.18, respectively. Dots, data; curve, fitting.

Figure 3

Out-of-plane radiation feature of the lasing spin-momentum-locked edge mode. (a)–(b) Momentum space patterns of the lasing beam obtained from experiment (a) and full wave simulation (b). The white dashed circles in (a) and (b) indicate the numerical aperture of the collection objective. (c) Schematic of the laser emission from a spin-momentum-locked topological edge mode. The near-field spin and orbital angular momentum has a one-to-one far-field radiation correspondence. (d) Lasing emission intensity after a linear polarizer with varied polarization angles. Adding a quarter-wave plate before the linear polarizer, the emission beam will become linearly polarized. (e) Off-center self-interference of the lasing beam, showing two fork-shaped patterns located near two phase singularities (marked with red stars), which indicates that the laser emission is a vortex beam with a topological charge of $-2$, corresponding to the azimuthal order of the cavity mode.

Figure 4

Direct evidence of backscattering free and high side-mode suppression ratio. (a) Lasing spectra of the two edge states of opposite momenta with opposite spins. The identical emission wavelength indicates that there is no coupling between the two modes despite the strongly irregular cavity shape. (b) Self-interference pattern of the $|2,-⟩$ mode [bottom panel in (a)] measured by the shearing interferometer in the momentum space. The pattern is similar to the one of $|-2,+⟩$ shown in Fig. 3 but with flipped fork-shaped patterns which indicate that the signs of orbital angular momenta of the two modes are opposite. (c) Side-mode suppression ratio (SMSR) versus the pump intensity, where we can see that the side-mode suppression ratio increases dramatically with the onset of lasing.