High-index dielectric nanoparticles supporting distinct Mie resonances have aroused widespread research interest due to their excellent light manipulation performance at the subwavelength scale [1]. In 2010, resonance-enhanced light scattering from silicon (Si) nanowires was first observed in the visible and near-infrared spectral range [2,3]. Since then, the research on strong electric and magnetic responses and their interactions in high-index nanoparticles has revealed rich resonance-induced phenomena including structural color [4–6], directional scattering [7–10], scattering suppression by an anapole mode [11], significant enhancement of nonlinear optical response [12,13], and so on. Compared with metallic nanoparticles, dielectric nanoparticles support magnetic resonances and possess much lower optical loss. These advantages lead to the strongly localized electric field inside dielectric nanoparticles at optical resonances, greatly improving light-matter interaction.

Increasing quality factors (Q factors) of resonant modes is vital for generating remarkable near-field enhancement [14–16] and achieving strong light-matter interaction [17]. In 2012, it was found that a dielectric nanoparticle placed on a gold (Au) substrate can interact strongly with its mirror image [18]. A further study revealed that the cooperation of the electric dipole (ED) excited in the nanoparticle and its virtual counterpart can be interpreted as a mirror-image-induced magnetic dipole (MMD), leading to enhanced scattering [19]. In addition, the Q factor of the magnetic dipole (MD) resonance supported by the Si/Au nanocavity can be effectively improved by optimizing the polarization and angle of the incident light [20]. For a nanocavity composed of a Si nanoparticle, a silica (SiO2) spacer, and a silver (Ag) substrate, the resonant strength and linewidth of the ED and MD modes can be manipulated by varying the thickness of the spacer layer. It was demonstrated that the thin SiO2 spacer greatly enhanced the MD resonance in the Si nanoparticle and induced phonon-assisted hot luminescence [21]. Besides, when metals are introduced into a system, it is important to reduce Ohmic loss [22]. The SiO2 spacer separates the Si nanoparticle from the Ag substrate, which effectively suppresses the effect of Ohmic loss on the optical modes in the Si nanoparticle. Therefore, a nanocavity composed of a high-index nanoparticle and a dielectric-metal heterostructure acts as a good platform for realizing the enhancement of light-matter interaction at the subwavelength scale.

As the core material for optoelectric devices, Si has excellent characteristics of high refractive index and low material loss in the visible and near-infrared bands. Light emitters based on Si nanostructures have always attracted particular interest as they provide unique opportunities for highly integrated light sources for photonic circuits [23]. An on-chip Si light source could potentially achieve a higher integration density with a compact size and display better performance in terms of energy efficiency [24]. However, the quantum efficiency of bulk Si is limited by indirect bandgap structure [25]. Hence, resonance-enhanced light-matter interaction is essential to improve the luminescence performance of Si nanoparticles or nanostructures. In 2018, white light emission from Si nanoparticles placed on a SiO2 substrate was demonstrated by resonantly exciting their MD resonances with femtosecond laser pulses [26]. The luminescence is caused by the interband transition of hot carriers enhanced by the Auger effect and Purcell effect, which is different from that caused by the intraband transition of hot carriers in GaAs [27]. The efficiency of the white light emission was further enhanced by improving the Q factor of the resonant mode at the excitation wavelength, for example, adopting the MMD resonance of a Si nanoparticle placed on a metal substrate [28] or quasi-bound states in the continuum of a Si nano cuboid [29] and a Si metasurface [30]. These strategies can substantially reduce the threshold for the luminescence burst. In addition, it was reported that the MD resonance of a Si nanoparticle can be effectively enhanced by adding a SiO2 spacer in between the nanoparticle and an Ag substrate [21]. Although it has been known that the optical modes supported by a Si nanoparticle can be modified by a dielectric-metal heterostructure, a systematic study on the linear and nonlinear optical properties of a hybrid nanocavity composed of a Si nanoparticle and a dielectric-metal heterostructure is still lacking.

Mie resonances with high Q factors can not only enhance the interaction between the optical mode and the cavity itself but also enhance the interaction between light and two-dimensional (2D) materials. A dielectric-metal heterostructure can support transverse-electric-polarized (TE-polarized) surface-bound waves [31] under the physical mechanism of optical magnetism [32]. The TE wave, which is dominated by the in-plane electric field, can fully interact with 2D material embedded into the heterostructure. For example, a narrow linewidth TE wave supported by a silicon nitride/silver (Si3N4/Ag) heterostructure can interact with a tungsten disulfide (WS2) monolayer to achieve strong exciton-photon coupling [33]. However, being a surface-bound wave, the confinement of the electromagnetic field in the propagation direction of the TE wave is still lacking. Therefore, it is necessary to introduce a high-index dielectric nanoparticle on the surface of the Si3N4/Ag heterostructure to improve local field enhancement for further enhancing light-matter interaction.

In this paper, we investigate systematically the enhanced light-matter interaction based on Si/Si3N4/Ag hybrid nanocavities. Both low-threshold luminescence burst and strong exciton-photon coupling are demonstrated. First, the enhanced MD resonance in the Si/Si3N4/Ag hybrid nanocavity substantially improves the nonlinear-optical-absorption-induced interband transition of hot electrons. With the help of the Auger effect [34] and Purcell effect, luminescence burst from the Si/Si3N4/Ag nanocavity is stimulated by femtosecond laser pulses with low energy of ∼20.5pJ. Compared with the case of a Si nanoparticle placed on a SiO2 substrate, not only the threshold pulse energy is reduced by 30.8 pJ, but also the luminescence intensity is increased by one order of magnitude. Second, a WS2 monolayer is placed in between the Si nanoparticle and Si3N4/Ag heterostructure to achieve strong exciton-photon coupling with the excitation of s-polarized light. By changing the incident angle of s-polarized light, the resonant wavelength of the optical mode can be adjusted covering the two exciton resonances of the WS2 monolayer. Large Rabi splitting energies of ∼146.4meV and ∼110meV are obtained at the A- and B-exciton (XA and XB) resonances, respectively.

We first examine the effect of a Si3N4/Ag heterostructure on the Mie resonances of a Si nanoparticle based on numerical simulation. As schematically shown in Fig. 1(a), a Si nanoparticle with a diameter of d is placed on a Si3N4/Ag/SiO2 substrate. The thicknesses of the Ag film and Si3N4 spacer are noted as h1 and h2, respectively. The Si nanoparticle is illuminated by a broadband light source propagating along the −z direction and the backward scattering is collected by an objective. We performed the simulation with the commercial software Ansys Lumerical based on the finite-difference time-domain (FDTD) method. In Fig. 1(b), we show the evolution of the scattering spectrum of a Si/Si3N4/Ag nanocavity (d=195nm) when the thickness of the Ag film is fixed (h1=50nm) and that of the Si3N4 spacer layer is increased. It is noticed that the intensity of the optical resonance located at ∼765nm is enhanced significantly when h2 is in the range from 70 to 95 nm. In addition, it is found that the intensity of the optical resonance located around 600 nm begins to increase when h2 rises beyond 95 nm. These behaviors imply that the optical resonances supported by the Si/Si3N4/Ag nanocavity can be effectively manipulated by simply varying the thickness of the Si3N4 spacer layer. Based on multipolar decomposition (see Appendix A), we reveal that the optical resonances appearing around 600 nm and 765 nm are dominated by ED and MD, respectively. The scattering spectra of the nanocavity with different h1 are discussed in Appendix B, which indicates that a 50 nm Ag layer is sufficient to be a good reflector. We examined the effects of a Si3N4/Ag heterostructure (h1=50nm, h2=95nm) on the scattering properties of a Si nanoparticle. As shown in Figs. 1(c)–1(e), we compared the scattering spectra of Si nanoparticles with different diameters on a SiO2 substrate with and without the Si3N4/Ag heterostructure. The results reveal that increasing the diameter of the Si nanoparticle primarily increases the resonant wavelengths of both ED and MD resonances. In addition, it is noticed that the Q factors of the ED and MD resonances are improved by using the Si3N4/Ag heterostructure. The Q factors of the ED and MD resonant modes can be calculated by the formula Q=λ/Δλ, where λ is the peak wavelength in the scattering spectrum of each mode and Δλ is the full width at half maximum (FWHM) of the scattering spectrum. Gaussian fitting functions were used to extract Δλ of each resonant mode from the scattering spectrum. Without loss of generality, taking the result in Fig. 1(d) as an example, the Q factors of ED and MD increase from 7.2 and 8.2 to 18.6 and 11.4, respectively, after the introduction of the Si3N4/Ag heterostructure. The improvement of Q factor results from the destructive interference of the in-plane ED or MD with its mirror mode reflected from the Ag film. Here the Si3N4/Ag heterostructure acts as a Fabry–Perot cavity. The degree of interference cancellation of the out-of-plane radiation can be tuned by varying the thickness of the spacer [16,35].

The energy band structure of Si and the carrier dynamics in a Si nanoparticle excited by femtosecond laser pulses are depicted schematically in Fig. 2(a). Since the energy gap between the conduction and valence bands at the Γ point is 3.4 eV, the interband transition of electrons is initiated by two- or three-photon-induced absorption (2PA or 3PA) of femtosecond laser pulses. The enhancement factors of 2PA and 3PA (I2 and I3) are proportional to the fourth and sixth power of the electric field inside the Si nanoparticle, respectively, i.e., I2=(1/V)∫Si(|E|/|E0|)4dV, I3=(1/V)∫Si(|E|/|E0|)6dV, where E0=1 is the amplitude of the incident electric field and V is the volume of the Si nanoparticle. Therefore, it is expected that the 2PA and 3PA of a Si nanoparticle will be effectively enhanced at the ED and MD resonances, generating high-density carriers in the Si nanoparticle. Owing to the Auger effect, the non-radiative recombination lifetime (τnr) of hot electrons can be significantly increased (from 0.1–1.0 ps to 10–100 ps). Theoretically, the fluorescence quantum efficiency (η) of a Si nanoparticle can be described by the formula η=1/(1+τr/τnr), where τr represents the radiative recombination lifetime of hot electrons at the emission wavelength. Relying on the Purcell effect, the radiative recombination lifetime can be reduced by exploiting the high-order Mie resonances of the Si nanoparticle, such as the electric quadrupole (EQ) and magnetic quadrupole (MQ) resonances. Therefore, the combination of the Auger effect and the Purcell effect can dramatically enhance the nonlinear photoluminescence (PL) of a Si nanoparticle.

Figure 2(b) illustrates the scattering and 2PA/3PA spectra calculated for the Si/Si3N4/Ag hybrid nanocavity (d=195nm, h1=50nm, h2=95nm). One can see that the enhancement factors of 2PA and 3PA reach peak values at the ED (∼592nm) and MD (∼765nm) resonances of the Si/Si3N4/Ag nanocavity. The electric field distributions at the ED and MD resonances are shown in Figs. 2(c) and 2(d), respectively. Remarkably, the electric field is strongly localized in the Si nanoparticle at the MD resonance, leading to larger enhancement factors of 2PA and 3PA than those at the ED resonance. Compared with the Si nanoparticle placed on a SiO2 substrate (see Appendix C), the enhancement factors of 2PA and 3PA are improved by ∼21 and ∼95 times, respectively.

We studied the nonlinear optical emission of a Si/Si3N4/Ag hybrid nanocavity (d∼190nm, h1∼50nm, h2∼95nm) under the excitation of femtosecond laser pulses. The detailed experimental setup is described in Appendix D. In Fig. 3(a), we show the evolution of the PL spectrum of the Si/Si3N4/Ag nanocavity with increasing pumping energy. The excitation wavelength was set at the MD resonance of the nanocavity (∼750nm) based on the scattering spectrum shown in Fig. 3(b). In each case, the emission from the nanocavity was recorded by using a charge-coupled device (CCD), as shown in the insets of Fig. 3(a). When the pulse energy was increased from 3.9 to 15.8 pJ, the hot electron luminescence from the nanocavity increased only slightly. Notably, a burst of white light emission from the nanocavity was observed when the pulse energy exceeded 20.5 pJ. The cooperation of the intrinsic excitation and the Auger effect leads to a large number of hot electrons in the high-energy states (around the Γ point), which significantly enhances the nonlinear optical emission. In Fig. 3(b), we compared the scattering spectra of the nanocavity before and after the luminescence burst. It is noticed that the scattering intensities of the nanocavity at the MD and ED resonances are greatly enhanced after the luminescence burst. This phenomenon can be ascribed to the annealing of the Si nanoparticle by the high temperature induced by the laser pulses, improving the quality of the crystalline structure. In addition, the scattering peaks of MD and ED are blue-shifted and red-shifted, respectively. It is caused by the giant optical force applied by femtosecond laser pulses on the Si nanoparticle. Under the optical force, the nanoparticle is squeezed in the out-of-plane direction and stretched in the plane along the polarization direction of the incident light [36]. In addition, the MQ resonance at ∼560nm is excited by the large-angle components of the broadband incident light focused by using an objective with a numerical aperture (NA) of 0.8 (see Appendix A). In Fig. 3(c), we present the dependence of the integrated PL intensity on the excitation pulse energy observed for the nanocavity. It can be seen that the PL intensity increases exponentially when the excitation pulse energy exceeds 20.5 pJ. For comparison, we also examined the nonlinear optical emission of a Si nanoparticle placed on a SiO2 substrate. Based on the scattering spectra shown in Fig. 3(e), the excitation wavelength was chosen at 745 nm so that the MD resonance was resonantly excited. As shown in Fig. 3(d), the luminescence burst could be observed only when the excitation pulse energy was raised to 51.3 pJ. This behavior is also shown in Fig. 3(f) where the dependence of the integrated PL intensity on the pumping pulse energy is presented. By comparing the results shown in Figs. 3(c) and 3(f), it can be seen that the threshold for the luminescence burst is greatly reduced in the Si/Si3N4/Ag nanocavity when the Si3N4/Ag heterostructure is used as the substrate. More importantly, it is found that the PL intensity of the Si/Si3N4/Ag nanocavity is one order of magnitude larger than that of the Si nanoparticle on the SiO2 substrate.

The above results indicate clearly that the interaction between the Si nanoparticle and the femtosecond laser pulses can be effectively enhanced by the modified MD resonance supported by the Si/Si3N4/Ag nanocavity, which possessed a larger Q factor. As a result, a low pulse energy threshold (∼20.5pJ) for the luminescence burst is achieved under the excitation of 750 nm femtosecond laser pulses. It should be emphasized that the generation of hot electrons in the conduction band is dominated by the 3PA process when the excitation wavelength is chosen at 750 nm. In this case, the threshold for the luminescence burst is larger than that reported in the previous study where the use of 720 nm femtosecond laser pulses implies that the 2PA and 3PA processes contribute simultaneously to the generation of hot electrons [28].

Recently, it was found that a Si3N4/Ag heterostructure can support TE waves with significantly reduced damping rates as compared with conventional surface plasmon polaritons (TM wave). More interestingly, the electric field of a TE wave is localized on the surface of the Si3N4 layer [31], which is beneficial for the interaction with a 2D material attached to the Si3N4/Ag heterostructure [33]. A further enhancement between the TE wave and the 2D material is expected if a Si nanoparticle is placed on the Si3N4/Ag heterostructure, forming a Si/Si3N4/Ag nanocavity. In this case, the lateral confinement of the electric field in the Si/Si3N4/Ag nanocavity leads to the electric field enhancement at the MD, ED, and MQ resonances supported by the nanocavity.

As shown schematically in Fig. 4(a), a Si/Si3N4/Ag nanocavity is created by placing a Si nanoparticle on a Si3N4/Ag heterostructure. The nanocavity can be excited by the TE wave propagating on the surface of the Si3N4/Ag heterostructure stimulated by s-polarized incident light in the Kretschmann-Raether configuration [37]. In the experiment, we chose a Si nanoparticle with a diameter of d∼190nm. The SEM image of the Si nanoparticle is shown in the inset of Fig. 4(b). We first examined the scattering spectrum of the Si/Si3N4/Ag nanocavity under normal illumination, as shown in Fig. 4(b). We could identify the MQ, ED, and MD resonances supported by the Si/Si3N4/Ag nanocavity, which appear at the wavelengths of ∼530nm, ∼600nm, and ∼725nm, respectively. Then, we examined the scattering of the Si/Si3N4/Ag nanocavity excited by s-polarized light with different incident angles, which can generate TE waves on the surface of the Si3N4/Ag heterostructure. The scattering spectra of the Si/Si3N4/Ag nanocavity measured at different incident angles are shown in Fig. 4(c). The actual incident angle θ at the SiO2/Ag interface is calculated considering the refraction caused by the prism (np∼1.5) and the SiO2 (ns∼1.46) substrate. In each case, one can identify two scattering peaks in the scattering spectrum. One is fixed at ∼725nm while the other one has a blue shift with the increase of incident angle. It has been known that the wavelength of the TE wave decreases when the incident angle is increased. On the other hand, the Si nanoparticle supports three optical resonances located at ∼530nm. ∼600nm, and ∼725nm, corresponding to the MQ, ED, and MD resonances [denoted by shadows in Fig. 4(c)]. These two features are reflected in the scattering spectra of the Si/Si3N4/Ag nanocavity. The intensity of the TE wave is enhanced when its wavelength coincides with the optical resonances supported by the Si nanoparticle. The MD resonance can be found in all scattering spectra. However, its intensity is dramatically reduced at large incident angles when the wavelength of the TE wave is shifted to shorter wavelengths. It is expected that the electric field will be enhanced in the Si/Si3N4/Ag nanocavity due to the coupling between the TE wave and the Mie resonances.

In order to gain a deep insight into the scattering properties of the Si/Si3N4/Ag nanocavity, we calculated the scattering spectra of the Si/Si3N4/Ag nanocavity at different incident angles by using the FDTD method, as shown in Fig. 4(d). As the incident angle increases from 44° to 62°, the resonant wavelength of the TE wave has a blue shift from ∼765 to ∼500nm. Remarkably, when the wavelength of TE wave overlaps with the intrinsic wavelength of the Mie resonances of the Si nanoparticle, scattering is enhanced and vice versa. The strongest scattering intensity is observed at ∼600nm, where the wavelength of the TE wave coincides with the ED resonance. It implies that the TE wave can be effectively coupled into the ED resonance. In the previous work, a polystyrene (PS) nanoparticle was used as the probe for the TE wave [33]; however, the intensity of the TE wave is only slightly modified due to the low refractive index of PS (see Appendix E). In contrast, the use of a high-index Si nanoparticle in this work can not only act as a probe but also achieve strong near-field enhancement. Therefore, the interaction between the TE wave and a 2D material will be enhanced in the Si/Si3N4/Ag nanocavity.

To verify the above expectation, we inserted a WS2 monolayer into the Si/Si3N4/Ag nanocavity and examined the exciton-photon interaction, as schematically shown in Fig. 5(a). The SEM and forward scattering images of the Si/Si3N4/Ag nanocavities with an embedded WS2 monolayer are shown in the insets. In the experiment, the region in which the spectrometer collects the scattering spectrum can be limited to ∼1μm2 surrounding the Si nanoparticle, thus eliminating the influence of other scattered signals. We chose a Si nanoparticle with d=190nm and measured the angle-resolved scattering spectra of the Si/Si3N4/Ag nanocavity with an embedded WS2 monolayer, as shown in Figs. 5(b) and 5(c). The CCD images of the scattered light are shown in the insets. By comparing the spectra with the results in Fig. 4(c), it can be found that the refractive index and material loss introduced by the WS2 monolayer make the position of the resonant peak shift towards the longer wavelength at the same excitation angle. When the incident angle increased from 62.9° to 65.8°, a split of the scattering peak is observed, implying the coupling between the TE wave and XB of the WS2 monolayer. With the decreasing incident angle, the wavelength of the TE wave is shifted to longer wavelengths. Similarly, one can see a split of the scattering peak when the TE wave is moved to ∼615nm. It suggests the coupling between the TE wave and the XA of the WS2 monolayer.

Based on the angle-resolved scattering spectra measured for the Si/Si3N4/Ag nanocavity with an embedded WS2 monolayer, we could extract the dispersion relation of the lower and upper polaritons formed by the coupling between the TE wave and the two excitons of the WS2 monolayer. The results for the XA and XB are shown in Figs. 5(d) and 5(e), respectively. The criterion for the strong coupling of optical mode and exciton is ER>γTE+γex, where ER is the Rabi splitting energy, and γTE and γex are the linewidths of the TE wave and exciton resonance, respectively [38,39]. Theoretically, the linewidths of A- and B-excitons can be derived from the imaginary part of the relative permittivity of the WS2 monolayer [40]. In the analytical discussion, we use the theoretical linewidths of A- and B-excitons, which are 33 and 81 meV, respectively [33]. The linewidths of the TE wave obtained from Fig. 4(d) are 91 and 65 meV, respectively, at the wavelengths of A- and B-excitons. As shown in Fig. 5(d), the Rabi splitting derived from the lower and upper polariton branches at the XA was estimated to be ∼146.4meV, satisfying the strong coupling criterion. In addition, this value is larger than those observed in Si/Au nanocavities (∼97meV) [41] and PS/Si3N4/Ag nanocavities (∼130.1meV) [33]. As discussed above, the intensity of the TE wave is greatly enhanced at ∼600nm by the ED resonance supported by the Si nanoparticle. Consequently, the in-plane electric field is enhanced due to the strong interaction between the TE wave and the ED resonance, leading to the enhanced exciton-photon coupling observed at the resonant wavelength of the XA. Similarly, shown in Fig. 5(e), the Rabi splitting at the resonant wavelength of the XB was derived to be ∼110meV from the fitting of the lower and upper polariton branches. The strong coupling condition is also fulfilled in this case. The corresponding simulation results are shown in Fig. 12 of Appendix F. The calculated Rabi splitting energy (∼139.2meV) for A-exciton agrees well with the measured value (∼146.4meV). However, the Rabi splitting energy obtained by simulation is ∼227meV, which is twice the measured one (∼110meV). By reviewing the results in Fig. 4(c), we can see that the scattering is very weak near the wavelength of the B-exciton. At the same time, the radiation intensity of the B-exciton is much weaker than that of the A-exciton. These two reasons cause the scattered signal to be easily covered by the noise in the experiment. The signal noise caused by the divergence of the light source and the irregular shape of the Si nanoparticles also lead to the deviation of the experiment compared with the simulation results. In addition, a recent study revealed that the dissipation of coupled subsystems, such as optical modes and exciton, will cause the deviation between measured spectral splitting and theoretical eigenlevel splitting [42]. It enriches the understanding of strong light-matter interactions at room temperature.

In conclusion, based on Si/Si3N4/Ag nanocavities, we investigated numerically and experimentally the enhanced interaction between femtosecond laser pulses and Si nanoparticles and that between a TE wave and a WS2 monolayer. First, it was revealed that a Si/Si3N4/Ag nanocavity can support an MD resonance with a larger Q factor than that supported by a Si nanoparticle placed on a SiO2 substrate. By resonantly exciting the MD resonance of the Si/Si3N4/Ag nanocavity with femtosecond laser pulses, we observed the luminescence burst from the Si nanoparticle with a threshold of ∼20.5pJ. Compared with a Si nanoparticle placed on a SiO2 substrate, the threshold for the luminescence burst achieved in the Si/Si3N4/Ag nanocavity is reduced by more than a half while the PL intensity is increased by one order of magnitude. Second, the coupling between the TE waves generated on the surface of the Si3N4/Ag heterostructure and the Mie resonances supported by the Si nanoparticle can effectively enhance the in-plane electric field, which leads to an enhanced exciton-photon coupling in a Si/Si3N4/Ag nanocavity with an embedded WS2 monolayer. Relying on the electric field enhancement achieved at the ED and MQ resonances of the Si/Si3N4/Ag nanocavity, Rabi splitting energies as large as ∼146.4meV and ∼110meV were observed at the XA and XB of the WS2 monolayer. It indicates an enhanced exciton-photon coupling at the XA as compared with PS/Si3N4/Ag nanocavities. The Si/Si3N4/Ag hybrid nanocavity proposed in this work provides a useful platform for realizing the strong interaction of light with nanoparticles and 2D materials, which is beneficial for achieving nanoscale light sources.