Introduction

Bloch modes can have distinct topological phases when their global geometric feature in a whole Brillouin zone is considered1,2. In 2008, Haldane and Raghu introduced band topology to the realm of photonics3. Since then, photonic analogues of varied topological phases including quantum Hall effect and quantum spin Hall effect have been intensively studied4,5,6,7,8,9,10,47. Using such a quantum lasing threshold, we obtain the lasing threshold to be about 1.0 kW/cm2 from the curve. The high radiation rate of the radiation channel enables the topological polarization singular laser with high quantum efficiency exceeding 24% (Fig. 4c, Supplementary Section 7). Figure 4b also shows that the reduction of linewidth coincides with the threshold. The corresponding spectra around threshold are shown in Fig. 4d. The narrowest linewidth reaches to ~0.14 nm, corresponding to a lasing quality factor of 11,000.

Fig. 4: Threshold behavior in light-light and linewidth evolution curves.
figure 4

a Experimental emission patterns in real space. b Light-light curve of the device in log-log scale together with the linewidth evolution curve under varied pump power. c External quantum efficiency of the device under varied pump power. d Spectra around threshold. Circles: data; lines: fitting. e Interference patterns by superposing two split lasing emission beams at two different differential path lengths. Top: differential path length equals to 0. Bottom: differential path length equals to ~7.5 mm. f Visibility at varied differential path lengths, which is in Lorentz lineshape with a full-width at half maximum (FWHM) of 9.5 mm. Such a FWHM corresponds to a coherence time of 0.023 ns, and a spectral FWHM of ~0.11 nm, which matches with the one measured by spectrometer. Circles: data, line: fitting.

Full size image

To complement the linewidth analysis from measured lasing spectra, we also conduct the first-order coherence measurement shown in Fig. 4e, f. Figure 4e shows the interference patterns by superposing two splitted lasing emission beams at two different differential path lengths (Supplementary Section 8). When the differential path length equals to 0, we see clear interference fringes with a visibility of ~0.68. When the differential path length increases to 7.5 mm, the visibility decreases to ~0.21. Figure 4f shows the visibility at varied differential path lengths, which is in Lorentz lineshape with a full-width at half maximum (FWHM) of 9.5 mm. Such a FWHM corresponds to a coherence time of 0.023 ns, and a spectral FWHM of ~0.11 nm, which matches with the one measured by spectrometer.

The emission wavelength of the topological polarization singular laser can be tuned by varying the lattice constant and the diameter of the nanoholes. By adjusting these two parameters, we have demonstrated topological polarization singular lasers with lasing emission wavelength from 1313 nm to 1569 nm (Supplementary Section 9). The position of the polarization topological singularity in the momentum space can be robustly tuned by varying the ratio of the nanoholes diameter over lattice constant, which can be utilized to finely control the radiation property of a resonant mode (Supplementary Section 10). The lasing size of our device is scalable. We have demonstrated lasing at other three different sizes of 5.8 μm × 7.9 μm, 7.9 μm × 13.2 μm, 12.1 μm × 18.1 μm (Supplementary Section 11). The robust and high tunability of the topological polarization singular laser offers unique opportunities for realizing high performance lasers at various wavelengths and scales for practical applications.

Discussion

A normal laser has one single desired lasing radiation channel where its quality factor is tuned as a whole. To achieve mode selection in single-channel laser, conventional paradigm focuses on increasing the contrast of quality factors of different modes to differentiate them in gain competition. However, with other parasitic loss channels, the quality factor of the lasing radiation channel is not the higher the better. Conventional paradigm on mode selection lacks the ability to finely tune the quality factor of the lasing radiation channel in a control manner.

In this work, we find that a Bloch band can have radiation field carrying topological charges from its second Brillouin zone but not the first one. The finding not only expands band topology to a partial component of one single Bloch mode but also provides an unconventional mode selection mechanism. The new mode selection mechanism bases on a laser with two radiation channels which are topological polarization singular channel and its paired linearly polarized radiation channel. Because topological polarization singularity does not carry energy to far field, the presence of the singular channel enables the lasing mode with a higher quality factor than other modes for single-mode lasing. The robust and movable features of topological polarization singularity in momentum space provide a controllable way to finely tune the quality factor. In the meanwhile, the presence of the radiation channel secures the lasing mode with high radiation efficiency. Future work can be conducted on synergistically optimizing cavity size, the order of the cavity mode, resonant wavelength and the position of the polarization singularity for high-performance lasing at various wavelengths and scales for practical applications.

Methods

Device fabrication

To fabricate topological polarization singular lasers, we use a nanostructured membrane of InGaAsP multiple quantum wells to serve as gain and photonic crystals simultaneously. The membrane consists of 6 well layers sandwiched in barrier layers and is capped by 10 nm InP. The well layers are Inx=0.56Ga1−xAsy=0.938P1−y in 10 nm thickness. The barrier layers are Inx=0.734Ga1−xAsy=0.57P1−y. A 70 nm layer of SiO2 is deposited via plasma enhanced chemical vaper deposition to serve as a dry etch hard mask. We use electron beam lithography to define nanoholes in square-lattice with high resolution on the resist. Subsequently, the SiO2 hard mask is defined by inductively coupled plasma (ICP) etching. Another ICP dry etching process is used to etch through the 200 nm multi-quantum wells layer after removing the resist. Next, the SiO2 mask is removed by HF solution. Finally, to form a suspended membrane, we use HCl:H2O (3:1) to etch away the InP substrate (Supplementary Section 12).

Full wave simulation

Cavity modes are simulated by finite-element method. We use the periodic structure to obtain the band structure, quality factor, and polarization pattern, and we use the structure with finite size to calculate field distributions and polarization of the lasing mode. The permittivity of the membrane is set to be 11.9. A perfect matched layer is added in the simulation to serve as boundary condition. To simulate rectangle pump laser spot, we add an imaginary relative permittivity of \(-0.03\) and 0.26 inside and outside the pump area. The experimental observed modes are identified by comparing their field distributions in real and momentum spaces and polarization in momentum space.

Optical characterization

The topological polarization singular lasers are pumped at room temperature by a pulsed laser at 1064 nm, where its pulse width and repetition rate are 5 ns and 12 kHz, respectively (Supplementary Section 13). To simplify the optical setup, an objective (100×, 0.82 numerical aperture) is used for the focus of excitation beam and collection of emission beam simultaneously. The collection parts need the high NA. The excitation part does not require the high NA, as the excitation beam is much larger than the free space wavelength in any direction. The signals are then guided to a near-infrared camera and a spectrometer for imaging and spectral analyzing. In order to obtain two polarization singularities along kx direction, a rectangle mask is used in the pum** system to obtain a rectangle pum** spot (Supplementary Section 5). The absorptance of the semiconductor membrane with photonic crystal structure in the topological polarization singular laser is about 47% calculated from the simulation of the designed structure considering the material loss. The material loss is derived by measuring the transmittance and reflectance of the semiconductor membrane transferred on a transparent SiO2 substrate with a pump beam at 1064 nm. The external quantum efficiency is calculated by \(\frac{{P}_{{{{{{\rm{OUT}}}}}}}/{hv}}{{P}_{{{{{{\rm{IN}}}}}}}/{{hv}}_{{{{{{\rm{IN}}}}}}}}\), where \({P}_{{{{{{\rm{IN}}}}}}}\) and \({{hv}}_{{{{{{\rm{IN}}}}}}}\) are pump power and pump photon energy respectively, and \({P}_{{{{{{\rm{OUT}}}}}}}\) and \({hv}\) are output power and emitted photon energy respectively. The resolution of our spectrometer is ~0.1 nm.

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.