Boosting light-matter interactions in nanoscale by using photonic nanostructures lies at the heart of photonics-based science and technology, because related studies can not only enrich our basic understandings by discovering novel phenomena (such as room-temperature strong coupling at quantum limit, spaser, and giant nonlinear response) [1–3] but also have brought about advanced applications [4,5]. To enhance light-matter interactions, a large variety of photonic platforms, such as photonic crystals, dielectric microcavities, and plasmonic resonators, have been developed throughout the last decades [6,7], creating great value for various fields ranging from physics, chemistry, biology, and medicine to geology and art, cultivating fruitful applications like surface-enhanced Raman spectroscopy, photocatalysis, biosensors, and photothermal therapy [8–16].

Generally, the resonant modes of photonic structures can greatly enhance the electric field (EF) in hot spots (i.e., the regions with strong EF enhancements), and therefore they are extensively applied to enhance light-matter interactions [17]. Despite the remarkable advances made by the resonant modes, small hot spots and highly inhomogeneous EF distribution of the resonant modes greatly limit their capacity in enhancing light-matter interactions in a large scale. It is also difficult to simultaneously generate multiple resonant modes with strong EF enhancements in a broadband spectral range. This makes it very hard to realize strong optical enhancements simultaneously at the wavelengths of both pumping and radiation, and therefore limits the enhancement effects in various optical processes such as nonlinear conversion and photoluminescence [18–20]. To date, a photonic platform that can simultaneously address these problems is lacking.

To overcome the abovementioned challenges, we propose the arrayed hyperbolic metamaterials (AHMMs) consisting of two-dimensional periodic hyperbolic pillars. Hyperbolic metamaterials (HMMs) are famous for supporting the infinite photonic density of states (PDOS), large EF enhancements, and broadband electromagnetic manipulation [21,22], which enable the possibility of multiresonant modes in a broadband spectral range. Furthermore, due to the bulk material response [23], the hot spots of their resonant modes can be homogeneously distributed in the interstitial space of adjacent pillars. This also leads to a vast spatial overlapping inside the structure gaps, giving rise to the simultaneous functioning of these modes and benefiting multiwavelength applications. To demonstrate the promising potential of the AHMM, we applied the AHMM to enhance a high-order nonlinear response of rare-earth upconversion nanoparticles (UCNPs). The N-photon upconversion emissions of rare-earth UCNPs, especially the high-order processes (i.e., N>2), offer a wide variety of applications including deep-tissue biophotonics, multioptical coding, and so on [24,25]. However, these high-order nonlinear processes are greatly suffering from their low intensities [26]. Herein, by using the AHMMs, we obtained giant enhancements of high-order nonlinear processes simultaneously (i.e., 1800 and 3350 times luminescence enhancements for three- and four-photon processes, respectively). These results validate the excellent performance of the AHMM in serving as a photonic platform for enhancing light-matter interactions, indicating promising potential in various applications, such as multiple frequency conversion, nanoscale lasers, and quantum information processing [27–30].

A clean silicon wafer was prepared as the primal substrate. Four pairs of Au and Al2O3 layers were alternatively deposited by using electron beam evaporation (Ohmiker-50B), with the thickness of Au and Al2O3 layers being ∼10nm and ∼20nm, respectively. The deposition rates of both materials were set to be 1.0 A/s, and the base pressure of the evaporation chamber was 6×10−8Torr (1 Torr = 133.322 Pa). After that, nanopatterns were engraved into the uniform HMM by a focused ion beam system (AURIGA, ZEISS) to form the final structures. The dose of an ion beam was 0.5nC/μm2, and the beam current was 50 pA under 30 kV.

The designed UCNPs were synthesized following previously reported protocols with some modifications [31–33]. In this synthesis process, a 5mLLn(CH3CO2)3 (Ln = Y/Yb/Tm) stock solution (0.2 M, 1 M = 1 mol/L) was added into a 100 mL round bottom flask, followed by the addition of 7.5 mL oleic acid (OA) and 17.5 mL 1-octadecene (ODE). The mixture was heated to 150°C under stirring for 40 min to form the lanthanide-oleate precursor solution and then cooled down to room temperature. Then 10 mL of NH4F-methanol solution (0.4 M) and 2.5 mL of NaOH-methanol solution (1.0 M) were pipetted into a 15 mL centrifuge tube, and then the mixture solution was quickly injected into the flask. Subsequently, the mixture was heated to 50°C and kept at that temperature for at least 0.5 h. Then it was heated to 110°C under vacuum to remove methanol. After the methanol was evaporated, the mixture was heated to 300°C and incubated at that temperature for 1.5 h under an argon atmosphere, and then cooled down to room temperature. The UCNPs were precipitated by the addition of ethanol, followed by centrifugation at 7500 r/min for 5 min. The obtained UCNPs were washed several times using ethanol and cyclohexane and were finally redispersed into cyclohexane for subsequent use.

Photoluminescence (PL) spectra of the UCNPs were measured by a confocal microspectroscopic system. The pump laser, a continuous wavelength laser at 980 nm, was focused on the sample by a 100× focusing lens (N.A. = 0.9) with a spot size of 3.8 μm in diameter. Then, the photoluminescence from samples was collected through the same focusing lens with a collecting angle of ∼65° and a shortpass filter (900 nm) blocking the laser signal. Finally, a spectrometer (Princeton Instruments Acton SP2750) was applied to obtain the PL spectra.

The simulation was performed using a commercial software, Lumerical FDTD Solutions. The refractive indexes of Au and Al2O3 were from the experimental data of CRC and Palik. The finest mesh size was set to be 0.5 nm inside and near the structure. A dipole source ranging from visible light to near infrared was used to get the Purcell factor (P) and external quantum efficiency (η). The Purcell factor result is equivalent to dividing the power emitted by a dipole source in the environment by the power emitted by the dipole in a homogeneous environment (bulk material), since the emission rate is proportional to the local density of optical states (LDOS), and the LDOS is proportional to the power emitted by the source. The external quantum efficiency of a dipole source was defined as the division of radiative flux to the total photon flux. In FDTD Solutions, we could get the radiative flux by a large enough power monitor set in the far-field (more than a wavelength) and use the transmission box surrounding the dipole at the very near field scale (2 nm) to obtain the total photon flux. Then the value of η was calculated by dividing them. The simulation time was set to 1000 fs to ensure the convergence of the results.

When a dipole emitter is placed at a distance of h above the planar multilayer with the polarization perpendicular (⊥) or parallel (‖) to the multilayer interface, the normalized dissipated power (Pd) of this dipole can be written as [34,35]dP⊥ddu=32k0kz(uε1)3(1+rpe2ikzh),(1)dP||ddu=34k0kzuε1[1+rse2ikzh+kz2ε1k02(1−rpe2ikzh)],(2)where k0 is the magnitude of the wavevector in a vacuum, u=kx/k0 is the wavevector component parallel to the multilayer surface normalized by the vacuum wavevector, kz=k0ε1−u2 is the component of the wavevector perpendicular to the multilayer interface, ε1 is the relative permittivity for the host material, and rp, rs are the reflection coefficient at the interfaces for a p- or s-polarized wave, respectively.

With the consideration of our mature fabrication techniques, we set the thicknesses of Au and Al2O3 layers as 10 nm and 20 nm, respectively. Therefore, one can calculate that the hyperbolic region begins from 540 nm, where the AHMM shows much better performance in boosting light-matter interactions over uniform HMM. Similar to previous studies [36,37], the enhancement of the light-matter interaction discussed in this paper is also described by calculating the Purcell factor of a quantum emitter (QE, which is a dipole source) placed near our studied metamaterials [Fig. 1(c)]. In contrast with the results obtained by placing the QE near uniform HMM, the QE located in the gap of AHMM exhibits higher Purcell factors, and the value of the Purcell factors reaches multiple peaks under varied QE wavelengths. These peaks actually correspond to the resonant modes of HMM, which represent propagating modes within the HMM that result from hybridization of the individual surface plasmon polariton (SPP) modes associated with each metal-dielectric interface [38]. To further understand the broadband Purcell response, the normalized dissipated power spectra are calculated. Figure 1(d) shows the normalized dissipated power spectra for a perpendicular dipole placed 10 nm above the hyperbolic Au−Al2O3 multilayer surface. The emission wavelength of this dipole varies from 450 nm to 1000 nm, and the calculation methods for the dissipated power with the varied wavelength are given in Section 2.E. The Purcell factor of a dipole can be calculated by integrating its dissipated power from 0 to ∞ wavevector [34,35]. For example, the Purcell factor of a dipole with an emission wavelength at 900 nm can be obtained by integrating the data marked by the white line in Fig. 1(d). As shown by Fig. 1(d), one can find that except for the spectral range around the instinct plasmon mode of Au at about 530 nm, the large dissipated power can also be found over a broadband spectral region in the high wavevector region (i.e., the top-right corner marked by a white-dashed line), which is a unique character for hyperbolic nanostructures [34]. Owing to the existence of this large dissipated power in the top-right corner, the hyperbolic multilayer can support large Purcell factors in a broadband spectral range. In short, the optical behavior of our AHMM can be attributed to the Bloch-like gap plasmon polaritons with high modal confinement inside the multilayer [37–39].

In order to strictly study the emission enhancing effect, we measured UCNPs with nearly the same particle number on the AHMM and Si substrate. Typical emission spectra of UCNPs on AHMM are presented in Fig. 6(c), where three emission peaks with λemi=800nm, 650 nm, and 745 nm can be clearly observed. Through extracting the peak value with the corresponding power separately and taking them in logarithm, one can see that the slopes (υ=∂logI/∂logPexc, where I and Pexc are the intensity of unconversion emission and excitation power, respectively) of the fitted curves are about 2, 3, and 4 when Pexc is below 0.15 mW (defined as region 1), presenting strong evidence for the two-, three-, and four-photon luminescence [Fig. 6(d)] [44]. Also, it is well-known that the upconversion luminescence of rare-earth UCNPs exhibits the phenomenon of saturated absorption, which has also been observed from Fig. 6(d). Since the number of ions in UCNPs that can be excited from the ground state is finite, when the Pexc exceeds a threshold, it is reasonable to find that almost all the ions have been pumped to the excited state. In such a case, the number of photons absorbed by UCNPs will be reduced. Thereby, the υ value will gradually decrease with the increasing of Pexc. In Fig. 6(d), except for region 1 when the UCNPs are unsaturated with excitation light, another two regions can be observed. For one region, the υ values are basically reduced to half of the original ones (Pexc varying from 0.15 mW to 6 mW), suggesting that the UCNPs enter a saturated state (defined as region 2). For another, as the Pexc continues to increase (region 3, beyond 6 mW), the υ values of all the three curves further reduce until they are close to 0, indicating that the UCNPs have reached a supersaturated state, and the UCNPs no longer absorb more photons no matter how much the Pexc increases.

For the UCNPs on the Si substrate, the phenomenon of saturated absorption can also be noticed. When the excitation is lower than 1.4 mW, one can find the υ of two-photon upconversion (i.e., λemi=800nm) is 1.97. In this Pexc range, the intensity of three- and four-photon emissions is too weak to read, so their results are blank. With the increasing of Pexc, υ of two-photon upconversion decreases to 1.03, and we can observe the three- and four-photon emissions with measured υ of 1.46 and 1.9, respectively. Based on these results, one can conclude that the saturation threshold of UCNPs on the Si substrate is 1.4 mW, which is nearly 1 order of magnitude larger than that of UCNPs on AHMM. The huge decreasing of the saturation threshold caused by AHMM results because the AHMM can increase excitation efficiency by creating higher pumping photon flux to excite Yb3+ to the excite state [41]. Note that after our samples have experienced the PL measurements with Pexc increasing from low to high, its spectral intensity is reproducible under the same Pexc. This fact indicates that the applied excitation light has not damaged our samples.

Following the discussion of the saturation threshold changing caused by AHMM, we go further to investigate the emission intensity enhancements of UCNPs enabled by AHMM. The enhancement factor is defined as the ratio of emission peak value of UCNPs on AHMM to that of UCNPs on the Si substrate [Fig. 6(e)]. One can find that all the three multiphoton upconversion emissions have been enhanced by the AHMM. However, since the three- and four-photon processes (i.e., λemi=650nm and 745 nm) have optical enhancement at both excitation and emission wavelengths, their enhancement factors are obviously larger than that of the two-photon process (i.e., λemi=800nm). The three-photon and four-photon processes achieved the highest enhancements of 1800 and 3350 times, respectively. Compared to previous studies, our enhancement result of the three-photon process in rare-earth UCNPs systems is 1 order of magnitude larger [48–51]. Furthermore, we obtained a record for the enhancement of the four-photon process (the related reports of four-photon process enhancement in rare-earth UCNPs systems are rare), providing an effective and inspired way for the future study of this field. In addition, one can see that the emission enhancement factors have a large decline when the Pexc is over 6.0 mW. The reason is that UCNPs on AHMM enter the supersaturation state under such high Pexc, and the υ values of their multiphoton processes become smaller than that of UCNPs on the Si substrate [see Fig. 6(d)]. Since the enhancement factors of three- and four-photon emissions are larger than that of two-photon upconversion, the luminous intensities of three- and four-photon emissions gradually increase to a level comparable to the two-photon process for the UCNPs on our AHMM. More digitally, we use the two ratios of I650/I800 and I745/I800 to describe this tendency. The different colors (red and blue) and symbols (circle and triangle) represent the ratios of three- and four-photon processes in the silicon substrate and AHMM in Fig. 6(f). It is intuitional that the blue line is always maintained at about 12%, while the red line increases from 14% to 50% as the power increases, indicating that our AHMM structure does help improve the efficiency of the high-order nonlinear process.

In order to more clearly reveal the emission enhancing origin in our AHMM system, the theoretical enhancement factors for the three- and four-photon emissions are theoretically analyzed. In our system, the emission enhancement (f) can be given by f∝fexc·femi, where the fexc and femi are the enhancement factors at excitation and emission wavelengths, respectively. In the nonlinear upconversion process, the fexc follows the relationship of fexc∝IN∝E2N, where I is the intensity of excitation light, E is the EF enhancement, and N equals the fitting slope of the emission intensity-excitation power dependence curve in a double logarithm (i.e., the parameter υ mentioned in this paper) [52,53]. On the other hand, the Purcell factor is proportional to the imaginary part of Green’s function in a medium [36], and it can be regarded as P(ω)=ImG(r,ω)∝E2. Therefore, the f can be given as f∝PexcN·Pemi, where Pexc and Pemi are the Purcell factors at the excitation and emission wavelengths, respectively. In addition, the absorption of AHMM should be considered. So, adding the external quantum efficiency (η), we considered the theoretical f in our system follows the relationship of f∝PexcN·Pemi·η. The values of η are obtained by FDTD simulations, and detailed calculation methods are given in Section 2.D.

Based on our experimental results, the three- and four-photon processes actually occurred when the UCNPs are in the saturated region. According to their υ values, one can find that N should be 1.5 and 2 for the three- and four-photon processes. Thus, taking the values of Pexc, Pemi, and η at the required wavelengths [η at 650 nm and 745 nm are 4.8% and 1.3%, respectively; the values of P are given in Fig. 6(d)], the f for three- and four-photon emissions [i.e., f(650) and f(745)] can be calculated as 2570 and 4580, respectively. These results are quite near the experimental results. Furthermore, we can compare the ratio of f(745) to f(650) from both the theoretical and the experimental aspects, and find the values are also quite similar (1.78 and 1.86, respectively). The good agreement of the theoretical and experimental results further confirms the correctness of our work. It is noticed that improving emission directivity can also enhance emission intensity. However, in our cases, we calculated the emission directivity of a point source (i.e., a dipole) placed on a Si substrate and the middle of AHMM, and find that over 92% power radiated from this dipole is confined in a radiation angle of 65° and 38°, respectively. Since the collecting angle of our optical measurement system is ∼65°, it can be concluded that the improvement of emission directivity caused by AHMM only has limited contributions to the emission enhancement.

In summary, we demonstrated a novel AHMM structure with large and multiple resonant modes for boosting light-matter interactions. Besides, this AHMM structure not only enables homogeneous hot spots in the gap region but also makes the hot spots overlap well in space for different resonant modes. We applied the AHMM structure to simultaneously enhance the high-order nonlinear emissions of UCNPs. The enhancement of the three-photon process is 1 order of magnitude larger than previous records in the three-photon enhancement of rare-earth UCNPs, and we even achieve a 3350 times enhancement of four-photon emission. The reasons for these unprecedented results can be attributed to two advantages of our AHMM. First, the EF distributions of various hot spots in AHMM are homogeneous in the spatial area, providing an environment of strong EF enhancement covering the whole UCNP inside the AHMM. Second, the hot spots are extremely overlapped in space for resonant modes matching the excitation and emission wavelengths of the nonlinear optical process, ensuring the two resonant modes function simultaneously. Our findings demonstrated a promising platform for the giant enhancement of light-matter interaction, which has potential to construct a high-efficiency nonlinear light source and multiplex photonic devices, providing new thoughts in designing functional photonic nanostructures.

Acknowledgment. X.H.W. and Z.K.Z presented the concept, conceived the research outline, and supervised the project. H.F.X. performed the sample fabrications, characterizations, and optical measurements. Z.M.Z and Q.Q.Z. synthesized the UCNPs. H.F.X made the numerical simulations. H.F.X., Z.M.Z., Z.K.Z., J.C.X., and Q.Q.Z. analyzed the theoretical and experimental results. H.F.X., J.C.X., Z.K.Z., and X.H.W. co-wrote the paper with inputs from all the authors. All the authors discussed the results.