Nonlinear optics serves as a foundational pillar in modern photonics, establishing a wide area of applications in laser technology, optical microscopy [1,2], and quantum optics [3,4]. Because of the extremely small nonlinear coefficient in optical materials, it is important to develop new photonic structures for enhancing the efficiency of nonlinear optics, which is determined by the strength of the electric field during the light–matter interaction [5–11]. In the past decades, a variety of metallic or dielectric nanostructures have been demonstrated to improve the nonlinear optical processes with high efficiency, including plasmonic metasurfaces [12], Mie resonators [13], photonic crystals [14–16], and waveguides [17,18]. These nanophotonic structures could strongly localize optical field to extend the light–matter interaction time duration or spatial cross-section [19–25]. However, there is a trade-off between the confinement strength of the optical field and tolerance of the coupling angle for the incident light in these nanostructures [26–33].

Recently, a magic angle nanocavity formed by two photonic crystal patterns with a twist angle or a mismatched lattice, i.e., a moiré superlattice nanocavity, has been found to have a highly effective ability to confine optical fields due to ultrahigh Q-factors and extremely small modal volumes Vm [34,35]. Specifically, within the entire moiré Brillouin zone, the moiré superlattice presents flat-bands, characterized by their non-dispersive nature that implies a zero group velocity of light, which suggests that the resonant modes of moiré superlattices remain unaffected by the angle of incidence [36–38]. As a result, light coming from diverse propagation directions, such as when incident light is precisely focused onto nanostructures using an objective lens with high numerical aperture (NA), improves the efficiency of coupling and excitation across various applications. Consequently, these structures epitomize an exceptionally promising new micro-/nano-cavity for investigating nonlinear optical effects. Other optical cavities, such as conventional photonic crystals and (quasi-)BICs also present an extremely high Q-factor and strong capability to confine light fields. However, their frequencies of resonance modes highly depend on the incident directions due to either their lack of flat-bands entirely or the fact that they only exhibit localized flat-bands [39–41].

Here, we experimentally demonstrate significant enhancement of second-harmonic generation (SHG) and third-harmonic generation (THG) from a silicon moiré superlattice nanocavity integrated with a few-layer GaSe crystal. An ultrahigh Q-factor up to 46,000 is realized from the fabricated device. With the on-resonance excitation on the nanocavity, SHG from the GaSe layer is enhanced by a remarkable 10,000-fold. The polarization and spatial characteristics of the SHG and THG confirm that this enhancement is attributable to the flat-band mode of the moiré superlattice nanocavities.

Figure 1(a) schematically displays the enhanced nonlinear processes in the GaSe-integrated silicon moiré superlattice nanocavities. The SHG from the GaSe flake is boosted by the local field of the flat-band mode. The strong field localization in moiré superlattice nanocavities originates from Bloch mode coupling induced by the reciprocal lattice of the two sets of twisted photonic crystal, which results in mode locking in momentum space. A flat-band mode arises consequently. In our experiment, to match the resonance wavelength of the flat-band mode around the employed telecom-band pulsed laser, we set the parameters of the silicon moiré superlattice as follows: the period of the photonic crystal is a0=475nm, the radius of nanohole is r0=105nm, and the twist angle of the two photonic crystal patterns is 2.646°. The designed structure supports a flat-band mode that does not reside in any bandgap at the wavelength of 1532.4 nm, as shown in the inset of Fig. 1(a), with a theoretical Q-factor of 517,600 and a mode volume of Vm≈0.01(λ/n)3, promising strong light–matter interaction. The theoretical simulation of the superlattice model was carried out using COMSOL Multiphysics commercial finite element software. Basically, the perfectly matched layer is used as the top and bottom boundary for absorption light. Three pairs of periodic boundary conditions are used as lateral boundary conditions to satisfy the periodic repetition of the moiré superlattice in space. Correspondingly, their Bloch wave vectors kx, ky, and kz should be set separately. By solving the eigenvalue equation, we obtain a series of information such as the band structure, Q value, and electric field strength of the moiré superlattice. The above configurations pertain to the basic setup for simulating linear optical responses. To calculate nonlinear processes such as SHG or THG, a two-step simulation approach is employed. In the first step, the fundamental wave is excited using a periodic port. In the second step, the nonlinear polarization, derived from the electric field obtained in the first step, is used as the source for the generated harmonic signal. The expression for the nonlinear polarization should follow the appropriate nonlinear susceptibility tensor (χ(2) or χ(3)) specific to the material. The power of the generated SHG/THG signal can be obtained by the integration of Poynting flow at the top and bottom boundary. The group velocity vg=dω/dk and group refractive index ng=c0/vg of the flat mode were calculated near Γ point, which presents zero group velocity and infinite group refractive index. As shown in Fig. 1(b), the sufficiently small vg≤150m/s across the entire moiré Brillouin zone extends the duration of light–matter interactions, enabling the potential for enhancing the SHG of the GaSe flake. Figure 1(c) shows the in-plane and cross-section electric field enhancement |Eloc|/|Ein| of the calculated resonance mode in the moiré superlattice nanocavity. It shows a dipole mode strongly localized in the center of the nanocavity in all three dimensions. Figure 1(d) displays the reflected spectrum of the moiré superlattice nanocavity, which presents a Fano lineshape with a narrow linewidth. The inset shows the calculated emission patterns in momentum spaces of the flat-band mode. There is no leakage inside the light cone, which means that the flat-band mode of the moiré superlattice nanocavity has an ultrahigh Q-factor. It can be foreseen that the nonlinear enhancement will be significantly improved, as the nonlinear efficiency dependent on local field enhancement is proportional to Q2/V2, which is more than one order of magnitude higher than that of the one-layer photonic crystal cavity to our knowledge [34]. The synergistic interplay between the high Q-factor and zero group velocity manifests through spatiotemporal dual-localization of optical energy. Specifically, the high Q-factor facilitates prolonged photon confinement within the structure, thereby substantially extending the light–matter interaction duration with nonlinear media. Concurrently, the zero group velocity condition enables extreme spatial energy concentration, leading to dramatic enhancement of localized electric field intensity. This complementary space-time confinement mechanism synergistically amplifies the nonlinear polarization response, establishing optimal conditions for achieving high-efficiency nonlinear optical processes [34].

To estimate the enhancement of SHG in the GaSe flake by the flat-band mode of the silicon moiré superlattice nanocavity, we scanned the incident angle of the quasi-plane fundamental wave from −45° to 45° at a step of 1° in the x−z plane and monitored the reflected power of SHG in the far field domain within [−45°, 45°]. The SHG enhancement is obtained by dividing the SHG efficiency of a free-standing GaSe thin film. As shown in Fig. 1(e), the enhancement factor up to 5×104 is independent on the incident angle and the wavelength of the excitation light. It is noticed that the enhancement of SHG always maintains a high value throughout the range of scanning angles, which benefits from the flat-band mode of the moiré superlattice nanocavity. Compared with the other cavity or structure, the moiré superlattice nanocavity has a considerable excitation efficiency in experiment.

To examine the influence of the GaSe flake on the flat-band mode of the moiré superlattice nanocavity, the home-built cross-polarization microscope was employed with the orthogonal polarizations of the excitation laser and collection signal [52]. As shown in Fig. 2(d), the resonance mode of the silicon moiré superlattice nanocavity was measured clearly before and after the integration of the GaSe flake. A red shift (∼26nm) of the resonance mode was observed after the integration of the GaSe flake due to the change of the surrounding effective refractive index. The Q-factors of the resonance mode were estimated as 46,000 and 30,150, respectively, before and after the GaSe integration, which could be attributed to the perturbation on the symmetric dielectric functions in the vertical direction of the silicon slab by the GaSe layer.

The polarization dependences of SHG and THG signals from the GaSe-integrated moiré superlattice nanocavity are further investigated by rotating the half-wave plate (HWP) in the measurement setup [53], as indicated in Fig. 4(a). The power coupled into the nanocavity is proportional to sin2(2φ), where φ is the angle between the HWP’s fast axis and x axis of the moiré superlattice nanocavity. The collected reflection pump laser has a function of sin2(2φ−5°), as plotted in Fig. 4(b). Considering the cross-polarization of the experiment setup, the collected SHG has a function of sin6(2φ−5°), as plotted in Fig. 4(c). By tuning the on-resonance pulse laser into the off-resonance, there is another profile of polarization dependence of the SHG signal from the GaSe flake, as shown in Fig. 4(d). It could be fitted with a function of sin26(φ−21°), which is governed by the crystalline symmetry of GaSe. These results are consistent with the axes of the moiré superlattice nanocavity and GaSe’s crystal structure, respectively, implying the enhanced SHG from the resonance mode of the nanocavity [53].

To verify the cavity enhancement of SHG and THG, the spatial mapping on-resonance pump is implied, as shown in Figs. 5(a)–5(c). The device was mounted on a two-dimensional piezo-actuated stage with a moving step of 100 nm, and the generated SHG signal was measured using a photomultiplier tube (PMT); as the cavity-enhanced SHG and THG were pumped by the evanescent field of the cavity resonance mode, efficient SHG and THG can only be observed when the pump laser couples into the cavity. Therefore, the spatial position of the detected SHG and THG was determined by the cavity’s coupling-in region. For this moiré superlattice nanocavity with a flat-band, light could vertically couple into the cavity effectively around the central region, which has a dimension of about 4μm×2.5μm larger than the photonic crystal nanocavity with air-hole defects [53]. In the SHG and THG mapping, a shrunk area with a strong signal was observed. Outside the cavity mode-coupling region, the GaSe layer was only pumped by the vertically illuminated laser, which was too weak to yield observed SHG.

To elucidate the experiment results, the near field distribution of electric field (|E|), second-order nonlinear polarization |P(2)|, and third-order nonlinear polarization |P(3)| for the resonance mode and the SHG and THG of the GaSe-integrated moiré superlattice nanocavity are simulated, respectively, as shown in Figs. 5(d)–5(f). The normal incidence light focuses on the moiré superlattice nanocavity. It is noticed that the near field of |P(2)| only exists in the GaSe thin film, which is determined by the second-order nonlinear polarizations induced in the GaSe flake. And the near field of |P(3)| was only obtained in the silicon moiré superlattice, which is determined by the third-order nonlinear polarizations induced in silicon. The afore-obtained near field distribution reveals that only when the focusing spot of the incident laser overlaps with the mode location of the moiré superlattice nanocavity, the resonance mode could be excited successfully. Obviously, the effective reflected spectra are only observed at the center, which is in good agreement with the experiment results.

It is worth noting that the spatial distribution results described above closely resemble the modulation of exciton mobility and diffusion length induced by the periodic molar potential in the molecular lattice of 2D materials [53]. Similarly, in moiré superlattice photonic crystals, the periodic variation of the dielectric constant folds the original photonic band structure, giving rise to new flat-band modes that alter the group velocity and lifetime of photons. In both cases, spatial periodic modulation—whether through atomic arrangement or dielectric constant—constructs an artificial platform for controlling quantum particles (excitons or photons). This reveals a universal physical framework for band structure engineering and the development of novel device architectures.

In conclusion, we have experimentally demonstrated significant enhancement of SHG and THG from a silicon moiré superlattice nanocavity integrated with a few-layer GaSe crystal. Enhancement factors of 10,000 and 8500 were obtained for SHG and THG, respectively, which is attributed to the flat-band mode of moiré superlattice nanocavities with a high Q-factor and angle-free incidence. The results open a new possibility for efficient nonlinear optical processes based on the silicon photonic chip with low laser power requirements and a large tolerance of the laser incident angle.

Acknowledgment. We thank the Analytical & Testing Center of Northwestern Polytechnical University for providing facilities in EBL, ICP, AFM, and SEM.