In photonics, micro- and nano- cavities are critically important for light confinement and the realization of subwavelength lasers1-4. For example, the band-edge mode in photonic crystal (PC) was used to realize electrically pumped surface emitting lasers5-9. With the maturation of nanofabrication, the laser based on a single microcavity is arriving at its performance limitation. The meta-device with a single resonant cavity as the basic unit were proposed to improve the performance of the micro- and nano- lasers10-15. From the interfering resonances described by Feshbach’s theory16, the concept of bound state in the continuum (BIC) has been widely explored in different systems, including photonic17-20, and acoustic20,21 devices. Mathematically infinite (for BIC mode) and physically large (for the so-called quasi-BIC mode) values of the quality factor (Q factor) of the BIC device were also employed to enhance the nonlinear optical effects22, sensing sensitivity23, and features of reasonably low threshold19. In photonic crystal (PC) slabs, BIC corresponds to ‘embedded eigenvalue’ above the light cone of the dispersion diagram. It comes from two main mechanisms: symmetry incompatibility, and destructive interference between the leaky channels18,24. Destructive interference can be described by the Friedrich-Wintgen theory16, spawning a supercavity mode of a subwavelength high-index dielectric resonator25, off-Γ BICs of plasmonic-photonic hybrid systems26, and a special type of nanolaser driven by merging symmetry-protected and accidental BICs27.
The BIC state existing at the Γ-point has been employed earlier for the realization of BIC lasers which are composed of an array of cylindrical nanoresonators suspended in air19. With the active dielectric nanoantenna arrays, directional lasing was realized through a dielectric nanoantenna resonance and BIC confinement15. However, all BIC lasers demonstrated so far are optically pumped, and for long time the realization of electrically pumped BIC lasers was considered as a challenge. In this paper, we report on the first experimental realization of an electrically pumped BIC laser, which has the characteristics of a power of 3.03 mW and a threshold of 373.15 mA.
As shown schematically in Fig. 1a, the BIC laser in this work is a metacavity device which support both the symmetry-protected and accidental BIC modes. The PC is directly etched into the Fabry-Perot (FP) cavity ridge to construct a metacavity. The edge emission is blocked by the high-reflection coatings on the front and back cavity facets. Due to the field penetration to the p-cladding layer, the lasing mode in such a metacavity can be modulated by the PC (Supplementary Fig. S1). The two BIC modes are illustrated in Fig. 1b, which shows a schematic dispersion relation of metacavity extracted from transmissivity larger than half maximum when the light is incident along the Г-X direction. The modes occur where the linewidth of bands almost disappear.
In the simplified 3-layer laser model, the uppermost layer is p-cladding layer with a refractive index of ~ 3.15 and the thickness of 1.8 μm. The middle active layer consists of p- and n-type waveguide layers and multiple quantum wells with a refractive index of ~ 3.28 and the thickness of 0.3 μm. The bottom layer is n-type cladding layer with a refractive index of ~ 3.17 and the thickness of 0.8 μm.
The transmission bands of the compound structure can be calculated in the case of shallow taper PC etching, which is shown in Fig. 2a. The Fano resonance evolution in Fig. 2b extracted from Fig. 2a shows that the line shape is transformed from Fano-like to Lorenz-type at the incident angle of 8.8° when the incident angle increases from 8.5° to 9.1° along the Г-X direction. At 8.8°, the Fano parameter q2, which reflects the symmetry of the Fano-like line shape, equals 0. This trend is consistent with the confirmation range of the quasi-BIC mode28. The localized electric fields of the TE-like accidental BIC mode at 1577.3 nm in the unit cell of a cavity is displayed in Fig. 2c, with obvious characteristics of multi-channel distribution.
The shallow-etched PC of the metacavity is shown in Fig. 3a, with a square lattice and a taper shape along the vertical direction. The lengths and widths of the FP ridge and the PC region are (500 μm, 90 μm) and (50 μm, 50 μm), respectively. The etched depth of taper PC is ~1.23 μm. The non-uniformity of the hole pattern is due to the rough side walls during the inductively coupled plasma etching process. The metacavity laser is pumped by the continuous wave (CW) current at room temperature. The measured P-I-V curves in Fig. 3b exhibit a threshold current of ~ 373.15 mA. The threshold current density is ~ 829 A/cm2, which is much smaller than the previously reported value of ~2000 A/cm2 7.
At 400 mA, the accidental BIC induced single mode lasing power reaches 3.03 mW. The lasing peak is observed at 1578.0 nm with the side mode suppression ratio (SMSR) of 25 dB and the full width at half maximum (FWHM) of ~0.04 nm (limited by the spectrometer resolution of 0.02 nm), which is shown in Fig. 3c. The total Q factor of ~39450, which is higher than that of band-edge mode laser6,7, is achieved, verifying the high Q characteristics of the BIC theory. The lasing peak has only a red shift of 0.7 nm and a little spread of 0.06 nm when the current is continuously increased to 600 mA, showing an excellent thermal stability and topological protection behavior of the accidental BIC mode (Supplementary Fig. S2). The far-field pattern of lasing in Fig. 3d shows two intensity maxima at 8.7° and -15.45°. When the injected current increases from 0.3 A (below threshold) to 0.4 A (above threshold), the metacavity laser evolves from spontaneous radiation to the accidental BIC induced single mode lasing process. The electrical injection lasing patterns in the PC area are captured by a charge-coupled device (CCD) camera (Supplementary Fig. S3). As shown in Fig. 3e, the slightly out of focus images can be utilized to identify the dipole-like intensity pattern. This is the far-field characteristics of the accidental BIC lasing.
If the PC is etched deeply, a stronger modulation on modes in the active layer will be anticipated due to a fraction of field confined better in the PC layer. We are able to see the evolution of different BIC more clearly. As shown in Fig. 4a, the PC with a square lattice is deeply etched with the depth of 1.72 μm and has a tape shape along the vertical direction. The lengths and widths of the FP ridge and the PC region are (500 μm, 20 μm) and (20 μm, 12 μm), respectively. Compared with Fig. 3a, the hole pattern looks different, this is because the residue of the SiO2 mask is not removed after the etching process. The corresponding transmission bands of the compound structure are calculated and shown in Fig. 4b. For the PC with C4 symmetry, the symmetry-protected BIC keeps present persistently and is difficult to be influenced by the imperfection of the compound structure. In Fig. 4c, the TE-like accidental BIC mode is clearly found at the wavelength of 1555.6 nm. At the incident angle of 7.751°, the Fano parameter q2=0. Figure 4d and e show the electric field localizations in the 3-layer compound structure of the symmetry-protected and accidental BIC modes, respectively. The electric field of the symmetry-protected BIC mode is mainly distributed in the PC layer. In this situattion, the scattering loss from the PC will inevitably raise the lasing threshold. In comparison, the electric field distribution of the accidental BIC has a large overlap between the active layer and n-
cladding layer. Therefore, the mode confinement factor is increased, resulting in the increase of mode gain. Consequently, the accidental BIC mode is easier to lase.
The lasing characteristics of the BIC laser with deeply etched taper PC are also demonstrated. In the single-mode accidental BIC lasing experiment, the P-I-V results reveal the maximal output power at 240 mA is 1.98 mW, which is shown in Fig. 4f. The lasing spectra in Fig. 4g display that when the injected current is increased to 200 mA, the accidental BIC lasing is observed at the wavelength of 1558.3 nm with a SMSR of 29 dB. The SMSR reaches 31 dB at 240 mA, and the FWHM is ~0.1 nm. When the current keeps increasing to 400 mA, the symmetry-protected BIC lasing occurs at the wavelength of 1566.8 nm with the FWHM of ~0.1 nm. As shown in Fig. 4f, the output power in the situation of multimode lasing at 480 mA reaches 4.54 mW. For the first time, the accidental BIC and symmetry-protected BIC lasings are obtained simultaneously under a CW electrical injection at the room temperature. The threshold current is only 140 mA, which is much lower than those of band-edge mode PCSELs, and also lower than that of the shallowly etched PC metacavity laser due to laser material/geometry-dependent characteristics of threshold29. The obtained far-field angle is 17.7° due to the off-Γ accidental BIC.
As it is known, all the reported BIC lasers are based on BIC mode at Г (symmetry-protected or resonance-trapped)15,19 or symmetry-protected BIC mode lasing taking precedence of off-Г accidental BIC mode lasing27. But to the metacavity laser here, the accidental BIC has the prior lasing at low injected current due to FP mode resonance hybridized with that of PC in the compound structure. Since PC is etched in the cladding layer, it modulates the modes in the active layer weakly by confining a fraction of field in the PC layer, not like other BIC lasers that directly define PC in the active layer to strongly modulate the modes15,19,27,30-32. This endows accident BIC lasers with advantages in inverse design to meet application-specific demands, e.g., beam scanning of Lidar under low power consumption. In addition, to the metacavity structure, it will be not only easy to form BIC surface emitting by breaking symmetry (e.g., accidental BIC), but also convenient to facilitate BIC edge emitting by maintain symmetry to suppress surface leakage. Therefore, the flexible metacavity provides a versatile platform for multi-dimensional utility.
In conclusion, we demonstrate the first electrically driven BIC laser at optical communication band with high powers and low lasing thresholds. The lasing action from the BIC mode originates from the interfering resonances under continuous electrical injection at room temperature. Our electrically driven BIC laser operates at the threshold current density below 830 A/cm2 and has an output power above 3 mW. Substantially reduced threshold currents, increased powers, and cost-effective fabrication move the BIC lasers closer to their practical applications in mode multiplexing, sensing, and quantum information processing.