1. Introduction

Nonlinear nanophotonics has attracted much interest as a route to control light with light at subwavelength scales [1,2]. As a research focus of this developing field, the efficient frequency up-conversion of coherent light at the nanoscale exhibits promising applications to quantum information processing as well as the design of nonlinear metasurfaces and photonic circuits [3–5]. In recent years, multi-dimensional plasmonic nanodevices, such as zero-dimensional (0D) single isolated nanoparticles [6–9], one-dimensional (1D) nanowires or nanorods [10–13], and two-dimensional (2D) patterned nanoarrays [14–17], have been frequently employed to serve as highly efficient generators of nonlinear lights induced by various optical processes, e.g., second-harmonic generation (SHG), third-harmonic generation, and optical parametric amplification. Within these structures, due to inherently low nonlinear coefficients of traditional plasmonic materials (gold, silver, etc.) as well as relaxing phase-matching conditions in nanoscale devices [2], efficient nonlinear optical processes appear intimately relevant to the excitation of locally enhanced electromagnetic fields (forming so-called hotspots) that match with the frequency of the fundamental excitation, harmonic emission, or both. However, low spatial dimensions inevitably limit the number and/or the size of hotspots that can be generated, and thus impede the coherent interplay between hotspot-induced enhancements and nonlinear dielectrics.

To avoid such limitations, researchers have extensively explored three-dimensional (3D) plasmonic nanodevices to achieve stronger and more stable nonlinear light amplifications with respect to 0D, 1D, and 2D nanostructures [18–26]. Among these nanodevices, plasmonic nanocavities, particularly based on nanopatterned metal-dielectric-metal (MDM) tri-layers, support various primary optical modes, e.g., gap cavity resonances, propagating and localized surface plasmon modes, as well as intriguing hybridized modes stemmed from the coupling between these primary modes [19,25–30]. These characteristic modes offer promising ways to require higher hotspot density, spatially-tunable modal volume, and reduced plasmon damping. Consequently, such 3D MDM plasmonic nanocavities can be qualified as a potential versatile platform suitable for the application in plasmon-enhanced nonlinear spectroscopy. Nevertheless, the relative complexity in geometries and fabrications, e.g., the manipulation of constituent parts with nanometer precisions (particularly in particle-on-film-type nanocavities) and the use of high-cost micromachining processes (such as electron beam lithography or focused ion beam), to some degree, degrade desirable performances of these structures in relevant applications.

Here, we experimentally report the scalable fabrication of 3D plasmonic nanocavities based on MDM designs, namely, 3D MDM plasmonic nanocavities, by integrating relatively low optical-loss materials (i.e., aluminum) with practical methods including nanosphere self-assembly processes and depositing film technologies. We discover that SHG signals emitted from proposed nanodevices greatly outperforms those emitted from dielectric-metal counterparts. Through analyzing polarization-resolved performances, we demonstrate in-plane isotropic characteristics of amplified SHG signals. By means of tuning various geometrical parameters, we are capable of quantifying respective contributions of constituent parts in MDM designs to signal amplifications. Furthermore, we theoretically identify the underlying mechanism governing these phenomena as plasmon hybridization effects between dipolar plasmon resonances and gap cavity resonances.

2. Results and discussion

Figure 1(a) displays structured systems that will be studied by utilizing nanosphere self-assembly processes combined with high vacuum electron-beam deposition technologies (see Appendix A for detailed fabrication schemes). Within these systems, monolayered arrays of polystyrene spheres (PSSs) with 500 nm (D1) diameter are assembled on the as-prepared aluminum-silicon substrate (Step I). Then, the diameter of PSSs can be tuned by regulating different durations ($\Delta $t) in reactive ion etching processes, such that the separation of neighboring PSSs can be readily modulated (Step II). Subsequently, the component of aluminum materials is prepared by high vacuum electron-beam deposition processing, and aluminum shells with different thicknesses (h) can be deposited onto the surface of monolayered PSS arrays (Step III). Notably, because of the presence of homogeneous aluminum shells that cover the convex surface of PSSs, the size of fabricated units should be remodified (labeled as D2). As a result, the 3D MDM plasmonic nanocavity system that lies on the x-y plane consists of two functional layers: the top layer with aluminum shells placed on top of monolayered PSS arrays and the bottom layer made up of a 100-nm-thickness aluminum film deposited on a silicon wafer, which acts as mirrors for preventing the light from leaking out [26]. Monolayered PSS arrays are used as the spacer between these two functional layers to create nanocavities in three dimensions [Fig. 1(a), inset]. Top-view scanning electron microscopy (SEM) images reveal that, for the self-assembly technique, monolayered PSS arrays with D1 = 500 nm exhibits a perfectly honeycomb-like distribution over a large area (up to a micron level), achieving uniform and reproducible responses [Fig. 1(b)]. Additionally, we perform energy-dispersive spectroscopy analyses to display the weight ratio of elements aluminum (Al), oxygen (O), carbon (C), and silicon (Si) for the sampled region (highlighted in the red-marked box) [Figs. 1(b) and 1(c), inset]. Because of the presence of aluminum shells (h = 50 nm), the relative weight ratio of elements Al and O in analyses significantly increases, suggesting that proposed 3D MDM plasmonic nanocavities can be readily attained. The geometric configuration of constituent parts in 3D MDM designs can be further inspected by the side-view SEM image [Fig. 1(c), inset]. Moreover, by means of tuning $\Delta $t, i.e., $\Delta $t = 40 s, prior to the deposition of aluminum materials, the D2 can be uniformly reduced, such that neighboring cell units can be separated by controllable gaps [Fig. 1(d)].

 

Fig. 1. (a) Schematic diagrams of 3D MDM plasmonic nanocavity systems. Top-view SEM images of (b) monolayered PSS arrays and 3D MDM plasmonic nanocavities with different $\Delta $t, i.e., $\Delta $t = (c) 0 s and (d) 40 s, respectively. Inserted red-marked boxes and pie charts in (b) and (c) show the sampled region of energy-dispersive spectroscopy analyses and the corresponding weight ratio of elements Al, O, C, and Si. The element C stems from PSSs. Insets in (b) and (d) represent corresponding side-view schematic illustrations of fabricated constructs. The inset in (c) exhibits the corresponding enlarged side-view SEM image of designed configurations. Scale bar, 200 nm.

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As the first step of our experimental procedure, we introduce the SHG spectroscopy for estimating the nonlinearity of samples. As shown in Fig. 2(a), 400 fs laser pulses centered at 1028 nm (Origami-10 XP) are focused on samples under the normal incidence through a 50x objective lens (Olympus, N. A. = 0.80). The pumping-laser power can be modulated by a neutral density filter, and a long-pass filter positioned behind the neutral density filter can be used to filter the possible spurious photoluminescence in the laser line. Then, generated SHG signals traveling backward are collected by the same objective lens, filtered by a short-pass filter, and measured using an electron multiplying charge coupled device (EMCCD) camera (iXon Ultra 888) attached to a spectrometer (Andor SR500) with different integral time. To study the polarization dependence of SHG responses, we equip the half-wave plate in incident optical paths with rotational stages. Suppose that the incident beam propagates along the z-axis and impinges on samples under the condition of normal incidences. The incident plane (polarization orientation) is defined by the polarization angle (φ) ranging from 0° to 360°. As expected, the spectral position of the emission peak appears half that of the pumping-laser peak [Fig. 2(b)]. Also, measured SHG intensities increase quadratically as the pumping-laser power increases from 0.1 mW to 0.7 mW with 3 s integral time. Within this range, SHG outputs remain stable, suggesting that no significant damage to our samples is caused by the incident laser radiation. Experimental results mentioned above agree satisfactorily with essential characteristics of SHG [31]. Measurements are also taken on 3D MDM plasmonic nanocavities with different $\Delta $t, i.e., $\Delta $t = 0 s, 10 s, 20 s, and 40 s, under 1 mW pumping-laser power and 1 s integral time. The result demonstrates that the intensity of collected SHG signals significantly increases in cases of $\Delta $t = 40 s with respect to cases of $\Delta $t = 0 s, 10 s, and 20 s [Fig. 2(c)]. To quantitatively evaluate this signal amplification, we define a figure of merit (FOM), namely, $\xi = P_{\textrm{SHG}}^a/{(P_{\textrm{FF}}^a)^2}$, where $P_{\textrm{SHG}}^a$ and $P_{\textrm{FF}}^a$ denote average powers of SHG and fundamental frequency (FF) beams [21,22,32]. Therefore, this FOM does not depend on the excitation power used for SHG measurements. In proposed experiments, the value of $P_{\textrm{FF}}^a$ can be obtained in front of samples (behind the neutral density filter) via using a power meter. The value of $P_{\textrm{SHG}}^a$ can be estimated by considering the collection efficiency of objective lens, transmission/reflection/polarization coefficients of optical components, and the quantum efficiency of the EMCCD camera, respectively. As a result, FOMs of nominally 7.6×10⁻¹¹ (W⁻¹) and 3.5×10⁻¹⁰ (W⁻¹) are obtained for 3D MDM plasmonic nanocavities with $\Delta $t = 0 s and 40 s, respectively. These obtained FOMs imply that the nonlinear conversion efficiency of 3D MDM plasmonic nanocavities with $\Delta $t = 40 s reaches up to one-order magnitude more highly than that of 3D MDM plasmonic nanocavities with $\Delta $t = 0 s. Additionally, we characterize the polarization dependence of SHG responses in 3D MDM plasmonic nanocavities with $\Delta $t = 40 s. As shown in Fig. 2(d), with the normally incident light polarization angle (φ) rotates ranging from 0° to 360° in steps of 10°, collected signals remain almost constant from the rotation of incident beams. While referring to previous studies [33], we can theorize that it is the in-plane isotropy caused by the geometrical configuration, i.e., the hexagonal arrangement and the convex surface of nanocavity units, that leads to the polarization-independent property of amplified nonlinear responses. This property may also be physically related to the far-field radiation pattern of distinctive resonant modes in plasmonic nanocavities [33]. This interesting phenomenon will be discussed in the following section. Accordingly, proposed 3D MDM plasmonic nanocavities can be regarded as efficient nanosystems that are capable of overcoming the limitation of polarization-selective excitations related to traditional bulky nonlinear devices [19].

 

Fig. 2. (a) Experimental setups for SHG spectroscopy, where ND denotes the neutral density filter, LF the long-pass filter, HWP the half-wave plate, DBS the dichroic beam splitter, SF the short-pass filter. (b) Power-dependent SHG measurements. Inset: measured SHG intensities versus the square of pumping-laser powers, P². (c) The SHG spectra of 3D MDM plasmonic nanocavities with different $\Delta $t, i.e., $\Delta $t = 0 s, 10 s, 20 s, and 40 s, respectively. Insets denote corresponding side-view schematic illustrations of 3D MDM plasmonic nanocavities with $\Delta $t = 0 s and 40 s, respectively. (d) Normalized SHG signals for normally incident polarization angles (φ) ranging from 0° to 360° at an incident wavelength λ_inc = 1028 nm. Plasmonic nanocavity units’ honeycomb-like distribution is shown in inset.

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To quantitatively identify respective contributions of constituent parts in proposed 3D MDM designs to this signal amplification, we experimentally conduct a comparative study among samples with different geometric parameters. First, we conduct this study between monolayered PSS arrays and 3D MDM plasmonic nanocavities with $\Delta $t = 0 s. As expected, the SHG signal emitted from the latter one appears much stronger than that emitted from the former one [Fig. 3(a)]. Notably, due to the inherent weak nonlinear response of monolayered PSS arrays, the excitation condition corresponding to these two samples should be respectively reset as 1 mW pumping-laser power and 2 s integral time for 3D MDM plasmonic nanocavity systems and 10 mW pumping-laser power and 2 s integral time for monolayered PSS arrays. For a fair comparison, we obtain FOMs of nominally 8.5×10⁻¹¹ (W⁻¹) and 1.1×10⁻¹³ (W⁻¹) (with 1 s integral time) for these two samples, respectively. Considering the SHG intensity distribution of 3D MDM plasmonic nanocavities with different $\Delta $t, we can thus deduce that the existence of the top layer, particularly the aluminum shell, helps boost the generation of second-harmonic lights in 3D MDM plasmonic nanocavity systems by up to three orders of magnitude (e.g., in cases of $\Delta $t = 40 s) when compared to that in dielectric-metal counterparts. Second, we introduce 3D MDM plasmonic nanocavities with different values of $\Delta $t and h to identify characteristics of this signal amplification. As shown in Fig. 3(b), as $\Delta $t increases from 0 s to 30 s in steps of 5 s, the size (D2) distribution among samples of various h, i.e., h = 10 nm, 50 nm, and 100 nm, exhibits a similar decreasing trend, highlighted by the red line [Fig. 3(b), left panel]. By comparison, corresponding $\Delta $t-dependent SHG intensity distributions deviate from this monotonic trend [Fig. 3(b), right panel]. To further identify such deviation, the dependency of amplified SHG signals with the evolution of fabricated units’ sizes can be attained (see Table 1). The result demonstrates that the D2 among samples with different h endures a similar 60% decrease with the increase of $\Delta $t, while the maximal signal amplification (approaching one-order-magnitude enhancement) appears to be located at three different D2 ($\Delta $t), i.e., D2 ($\Delta $t) = 346.6 (± 6.9) nm (20 s) for h = 10 nm, 322.3 (± 15.3) nm (25 s) for h = 100 nm, and 204.5 (± 9.6) nm (30 s) for h = 50 nm. Third, we utilize atomic layer deposition processing to introduce an isolated layer, i.e., a 10-nm-thickness Al₂O₃ film, for separating two functional layers (See Appendix A for detailed fabrication procedures). The top-view SEM image [Fig. 3(c), inset] suggests that no significant geometrical deformations as well as modifications of component materials can be observed, albeit the introduction of isolated layers. The side-view SEM image indicates that the ordered array of cell units is grown on the flat Al₂O₃ film-aluminum-silicon substrate. By tuning different $\Delta $t, i.e., $\Delta $t = 0 s, 10 s, 20 s, and 40 s, we conduct the SHG intensity distribution with 1 mW pumping-laser power and 1 s integral time [Fig. 3(c)]. The result demonstrates that, through introducing the isolated layer, the $\Delta $t-dependent signal power can be conspicuously suppressed by approximately a 10-fold reduction with respect to 3D MDM plasmonic nanocavity counterparts. However, the maximum emission power continues to appear in cases of $\Delta $t = 40 s. We can thus assert that the bottom layer, particularly the aluminum film underneath, also serves as an essential component for constructing 3D MDM plasmonic nanocavities.

 

Fig. 3. (a) A comparative study of SHG performances between monolayered PSS arrays (multiplied 10 ×) and 3D MDM plasmonic nanocavities with $\Delta $t = 0 s. (b) Size (left) and SHG intensity (right) distributions for 3D MDM plasmonic nanocavities with different $\Delta $t and h. (c) The $\Delta $t-dependent SHG intensity distribution for 3D MDM plasmonic nanocavities without (w/o) and with (w/t) (multiplied 2 ×) isolated layers. Insets exhibit corresponding SEM images and energy-dispersive spectroscopy analyses for 3D MDM plasmonic nanocavities with isolated layers ($\Delta $t = 0 s). Error bars shown in (b) and (c) represent the deviation of measured SHG intensities or units’ sizes over multiple acquisitions from different sample areas.

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Table 1. The ${\Delta}$t-dependent D2 (nm) and D2-dependent Signal Amplification Among Samples with Given h.

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To further characterize the underlying mechanism, we experimentally measure corresponding reflectance spectra of 3D MDM plasmonic nanocavities with specific $\Delta $t and h, i.e., $\Delta $t = 20 s, 25 s, 30 s and h = 10 nm, 50 nm, 100 nm, using a white light source. Figure 4(a) demonstrates that these samples exhibit reflectance dips near the emission wavelength (514 nm), e.g., dips A, B, and C for cases of $\Delta $t = 20 s, 25 s, and 30 s, respectively. For clarification, we further label these dips as A(B, C)-10, A(B, C)-50, and A(B, C)-100 for cases of h = 10 nm, 50 nm, 100 nm, respectively. Then, as $\Delta $t increases from 20 s to 30 s in steps of 5 s, these reflectance dips shift to higher energies (shorter wavelengths). Particularly, the smaller dielectric cavity volume (the increased $\Delta $t) corresponds to the reduced linewidth for dips A(B, C)-50. By contrast, dips A(B, C)-10 and A(B, C)-100 continue to exhibit the similar linewidth as the increase of $\Delta $t. Additionally, dips A-10 and B-100 spectrally overlap with the emission wavelength, suggesting that observed maximum emission powers located at two different $\Delta $t in cases of h = 10 nm and 100 nm [highlighted by blue triangular cones in Figs. 3(b) and 4(a)] may be governed by plasmon-driven second-harmonic enhancements ($I_{}^{(2)}(2\omega ) \propto {|{L(2\omega )} |^2}$). Regarding our previous work [34], proposed nanosystems featuring this enhancement mechanism can avoid the potential sample damage caused by significant fundamental absorption processes ($I_{}^{(2)}(2\omega ) \propto {|{L_{}^2(\omega )} |^2}$). Note that, due to the causality far off resonance, the field enhancement induced by plasmonic modes at the fundamental frequency should vanish in proposed nanosystems (data not shown). By comparison, the maximum emission power in cases of h = 50 nm continues to increase as $\Delta $t shifts from 10 s to 30 s [Fig. 3(b)], even if plasmonic fields are excited near the emission wavelength (e.g., dips A-50 and B-50). To provide more physical insights, we carry out simulations with the aid of finite element method commercial software (COMSOL Multiphysics) to demonstrate corresponding far-field reflectance spectra. Optical constants of aluminum are taken from Ref. [35], and the refractive index (n) of PSSs can be set as 1.6 (See Appendix B for detailed simulation procedures). As shown in Fig. 4(b), both modeled systems display similar spectral shapes, as indicated by experimental results [Fig. 4(a)]. Also, as the dielectric cavity volume decreases ($\Delta $t increases), these dips experience a similar blue-shift fashion (indicated by cyan arrows), which resembles that shown in experiments. These spectral characteristics imply that the dimension of modeled systems is chosen to match previously-designed structures. Notably, the difference in the spectral position between experimental and simulation results can be attributed to the emergence of cauliflower-like morphologies on the face-up surface of experimentally-fabricated units [inspected by the SEM image in Fig. 1(d)]. Such a certain degree of surface roughness facilitates the occurrence of LSPR-dominated hotspots, leading to the redshift of experimentally-observed dips in comparison with the spectral position of simulation counterparts. Besides that, these LSPR-dominated hotspots may also lead to the inevitable broadening of the linewidth, particularly in cases of $h$ = 10 nm and 100 nm, as indicated in Fig. 4(a). The large plasmon resonance linewidth of LSPR structures can be associated with the large intrinsic absorption loss and the strong radiative damping of metals at optical wavelengths [36,37].

 

Fig. 4. (a) Measured and (b) simulated far-field reflectance spectra of 3D MDM plasmonic nanocavities with different $\Delta $t and h, i.e., $\Delta $t = 20 s, 25 s, 30 s and h = 10 nm, 50 nm, 100 nm. Cyan color bars in (a) and (b) denotes the emission wavelength of collected signals in SHG experiments. Simulated local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips A, B, and C at different resonant wavelengths, i.e., (c) dip A at 505 nm, dip C at 430 nm for h = 50 nm (black dotted box) and (d) dip B at 480 nm, dip C at 445 nm for h = 100 nm (red dotted box). Black lines respectively describe the geometrical configuration of thin aluminum shell, dielectric cavity, and aluminum film as well as the critical plane of thin aluminum shells along the z direction.

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To understand characteristics of these resonant dips, we conduct simulations to exhibit corresponding local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips A, B, and C at different resonant wavelengths [Figs. 4(c) and 4(d)]. The optical mode excited at a resonant wavelength of approximately 505 nm can be attributed to the plasmon hybridization of both dipolar plasmon resonances and gap cavity resonances [Fig. 4(c), left panel]. Under this circumstance, localized electromagnetic fields excited by dipolar plasmon resonances are primarily concentrated at the opposite side of aluminum shells, while local-field enhancements originated from gap cavity resonances exhibit the near-field energy localization in the core of dielectric cavity regions. Such plasmon hybridization exhibits both characteristics of these two contributions and offers a potential energy exchange channel, in which, near-field energies trapped at air-metal interfaces can be transferred into intracavity regions. As discussed before, since the main source for large optical losses in proposed nanosystems can be ascribed to plasmonic components, the concentrated light at the air-metal interface may face higher optical losses when compared to that inside the dielectric cavity. Therefore, the occurrence of energy exchange channels contributes to the lower rate of energy losses and leads to a higher quality factor as well as the narrowing of resonance linewidths, indicating the consistency with experimental results [Fig. 4(a)]. Besides that, the continued decrease of dielectric cavity volumes further modifies the energy exchange channel, resulting in a greater degree of incident electromagnetic energy trapping in the whole volume of dielectric cavities [Fig. 4(c), right panel]. As a result, an increase of local-field energy densities across the air-aluminum interface (below the critical plane of thin aluminum shells) occurs, and helps expand the modal volume of gap cavity resonances (hereinafter referred to as “spatially-extended gap cavity resonances”). Besides that, in centrosymmetric plasmonic metals, dominating SHG originates at the metal interface driven by electromagnetic fields normal to the interface [2,8]. This phenomenon can be described by the nonlinear polarization $P_ \bot ^S(2\omega ) = \chi _{ \bot \bot \bot }^{(2),S}E_ \bot ^2(\omega )$, where $P_ \bot ^S(2\omega )$, $\chi _{ \bot \bot \bot }^{(2),S}$, and ${E_ \bot }(\omega )$ respectively denote nonlinear polarizations, dominant surface nonlinear susceptibility components, and normal components of local fundamental fields at the metal interface. Therefore, SHG emissions in proposed 3D MDM designs originate from $P_ \bot ^S(2\omega )$ induced at the interface of the metal both at gap junctions and on face-up surfaces of aluminum shells. In cases of $\Delta $t = 30 s and h = 50 nm, these spatially-extended gap cavity resonances facilitate a well-defined symmetry (orientation) matching between local modes and $P_ \bot ^S(2\omega )$ at gap junctions, resulting in the generation of strong nonlinear currents [21,34]. Such a vertically-aligned polarization moment also has a rotational symmetry around the normal direction, in line with the isotropic polarization dependence of SHG radiations [Fig. 2(d)]. Furthermore, the signal suppression shown in Fig. 3(c) can thus be explained by the inevitable interference of the incident energy coupling with nonlinear dielectrics due to the introduction of isolated layers into two functional layers. It is also worth noting that, due to the causality far off resonance, the local-field enhancement induced by plasmon hybridization processes near emission frequencies may inevitably decrease in cases of $\Delta $t = 30 s and h = 50 nm. However, as shown in Figs. 3(b) and 3(c), measured $\Delta $t-dependent signal amplifications display a monotonously-increasing trend, suggesting that the geometry-dependent modification of local-field energy densities in 3D MDM plasmonic nanocavities continues to amplify retrieved harmonic signals, even in the absence of plasmon-driven second-harmonic enhancements. We can thus reasonably deduce that proposed nanosystems governed by this geometry-dependent enhancement mechanism can be featured with the frequency-related insensitiveness. Additionally, while referring to the definition of the Q-factor ($\lambda /\Delta \lambda$) [38], we calculate the Q-factor of nominally 22 for the dip C-50. Considering the value of Q-factors (from a few hundred to around ten thousand) of all-dielectric metasurfaces under normal excitation conditions reported so far [14], the relatively-low Q-factor can be attributed to the modal loss in plasmonic nanocavities. This phenomenon is mainly contributed by the intrinsic ohmic damping as well as extrinsic radiation and scattering losses [39]. The intrinsic ohmic damping is primarily determined by constituent metal itself, while the extrinsic loss can be attributed to the edge scattering and the surface roughness. More n-dependent simulations have been conducted to identify the influence of n-dependent modulations in dielectric spacers on the Q-factor (see Appendix C and Fig. 5 for detailed simulation results and relevant discussions). In light of plasmon-driven SHG mechanisms, collective interactions of both huge near-field amplifications (e.g., the requirement of high-Q resonances) and well-defined light-matter interactions (e.g., a high degree of the spatial overlap between resonant modes and nonlinear susceptibilities of materials) appear mandatory for the signal amplification [2]. Accordingly, our proposed nanodevices provide a platform suitable for simultaneously modulating resonant modal volumes and near-field localizations over wider spectral ranges, such that a well-defined light-matter interaction can be attained within the hot spot region at multi-frequency.

Similarly, the local-field enhancement at either 480 nm or 445 nm can also be attributed to the plasmon hybridization of both two contributions [Fig. 4(d)]. However, due to the limited penetration of plasmon-driven fields [40], the energy exchange channel supported by plasmon hybridization effects is prevented such that localized electromagnetic fields at both two resonant wavelengths are primarily concentrated on the face-up surface of 100-nm-thickness aluminum shells. We can thus conclude that the excitation of LSPR-dominated hotspots may dominate the amplification of SHG emissions that originate from $P_ \bot ^S(2\omega )$ induced at the interface of the metal on face-up surfaces of aluminum shells. More elaborately, previous results have demonstrated that strong nonlinear optical effects can be achieved by tuning LSPRs to meet one (or both) of fundamental excitation/second-harmonic emission frequencies [6,8,9,16,17], or vice versa, the enhancement of nonlinear optical processes governed by LSPR-dominated hotspots should critically follow such frequency-selective rule. The consistency of this fundamental mechanism with experimentally-observed results is highlighted by blue triangular cones shown in Figs. 3(b) and 4(a). Moreover, the simulated far-field reflectance spectrum exhibits two additional resonant dips near the dip C-100 [Fig. 4(b), lower panel]. More simulations have been conducted to confirm characteristics of these resonant dips (see Fig. 6 in Appendix D), demonstrating that localized electromagnetic fields at these three different wavelengths are primarily concentrated on the face-up surface of aluminum shells. Considering the hybridization effect of these similar LSPR-dominated hotspots, we can thus ascribe the broad spectral feature shown in experiments [Fig. 4(a)] to a combination of several plasmonic multipoles [41]. Incidentally, the 10 nm thickness of aluminum shells becomes comparable to the skin depth of constituent materials (∼ 15 nm for aluminum at 2.3 eV) [42]. Taking into account the broadening of reflectance dips, we can thus reason that the 10-nm-thickness aluminum shell inefficiently squeezes incident electromagnetic energies into the intracavity region. Therefore, we can understand that observed enhanced SHG emissions in cases of h = 100 nm and 10 nm can both be attributed to the excitation of LSPR-dominated hotspots alone. More geometry-dependent simulations have also been conducted to identify the influence of fabricated units’ periods on amplified SHG responses (see Appendix E and Fig. 7 for detailed simulation results and relevant discussions). With these analyses, we can thus conclude that configurations featured with aluminum shells with an appropriate thickness and fabricated units with a suitable period are required to construct proposed 3D MDM plasmonic nanocavity systems. Finally, we would like to briefly comment about the possibility of using other traditional plasmonic materials (i.e., gold and silver) and its influence in results. Regarding our previous work [21], the up-conversion of near-infrared signals into the visible domain within plasmonic nanostructures may trigger energy-loss channels (e.g., interband transitions of noble metals), leading to the potential damping of nonlinear polarization currents or the selective reabsorption of nonlinear signal emissions. In particular, the interband-transition energy state of gold at approximately 2.58 eV (480 nm wavelength) [43,44] closes to our measured spectral ranges. Therefore, the competitive effect of interband transitions and surface plasmon resonances may notably suppress the SHG emission power within plasmonic nanodevices made of gold. Alternatively, the interband-transition energy state of silver at approximately 3.93 eV (315 nm wavelength) [43,45] lies above measured spectral windows, hence avoiding interband-transition-induced absorption losses to some degree. However, the oxidation of silver nanostructures severely degrades plasmonic responses over time, limiting long-term nonlinear device applications [42]. By comparison, aluminum nanostructures permit broadly tunable plasmonic responses ranging from the near-infrared to the ultraviolet, and the self-terminating oxide layer provides long-term stability. In our experiments, amplified nonlinear responses remain essentially stable even though these aluminum nanodevices have been placed at room temperature under atmospheric conditions after several months.

3. Conclusion

In conclusion, we experimentally report a nearly three-order-magnitude amplified second-harmonic response emitted from 3D MDM plasmonic nanocavities, in comparison with that emitted from dielectric-metal counterparts. A thorough geometry and polarization study enables us to not only quantify the relative contribution of constituent metal parts in 3D MDM designs to the signal amplification, but also identify that polarization-dependent limitations of amplified signals can be overcome. Validated by simulations, these phenomena can be attributed to the plasmon hybridization of both dipolar plasmon resonances and gap cavity resonances. This plasmon hybridization effect offers efficient energy-coupling channels that facilitate the spatial modulation of coupled near-field energies. As a result, a well-defined coherent interplay between hotspot-induced enhancements and nonlinear polarizations can be readily obtained. Our results may provide a promising means to design a 3D plasmonic system with the potential in cost-efficient and high-performance nonlinear optical devices.

Appendix A

Fabrication schemes

Step I: To remove the surface contamination, silicon wafers were initially cleaned with ultrasonic processing respectively in deionized water, acetone and ethanol for 10 min, prior to being immersed in piranha solution (H₂SO₄ : H₂O₂= 3 : 1 volume ratio) with 240 °C boiling for 30 min and then being washed by deionized water several times. After the cleaning process, a high vacuum electron-beam deposition equipment (aTEMD-500 China) was used to deposit aluminum materials. Afterwards, a 100-nm-thickness aluminum film was deposited onto the cleaned silicon wafers under a high vacuum of 9.9 × 10⁻⁴ Pa and a deposition rate of 5 Å/s. To conduct comparative studies, a 10-nm-thickness Al₂O₃ film, as an isolated layer, could be introduced to the surface of as-prepared aluminum-silicon substrates by atomic layer deposition processing (TFS-200-PEALD Finland). The mixed solution containing 240 µL PSS solution and 250 µL ethanol was prepared and sonicated for 30 s in a micro-centrifuge tube. Subsequently, the diluted PSS solution was removed into a 5 mL injector readily for the further processing. At the initial stage in self-assembly processes, as-prepared substrates were placed at the bottom of the petri dish acting as supporting templates, while a cleaned silicon wafer on the edge with a tilt angle of 45° was acting as an auxiliary role in experiments. Then, deionized water was slowly added into the petri dish till the waterline exactly reached the tilted silicon wafer. The injector with as-prepared PSS solution was then fixed on an injection pump, while the syringe needle of injector was placed adjacently. Afterwards, the injection rate was adjusted and the tilted silicon wafer was used as a supporting platform, such that each drip of the solution was homogeneously dispersed on the water surface. After a monolayer thin film of PSSs that floated on the water surface was observed, the injection pump should be turned off immediately. Thereafter, a peristaltic pump was operated at a speed of 10 mL/min for 4 hours, aiming to purify the monolayered PSS array through exchanging the water under PSSs. This operation was followed by pumping water (7 mL/min) until the monolayer film was totally settled on as-prepared aluminum-silicon or Al₂O₃ film-aluminum-silicon substrates. These samples were stored at the room temperature after they were completely dried prior to the further processing. Step II: These samples were utilized as supporting templates and subsequently experienced the reactive ion etching processing with various $\Delta $t aiming to adjust the diameter of PSSs. Step III: Aluminum shells with different h were deposited onto these completely etched templates by the high vacuum electron-beam deposition process under the same experimental condition as mentioned above. Eventually, the configuration of 3D MDM plasmonic nanocavities with and without isolated layers was obtained.

Appendix B

Simulation procedures

We adopted the finite element method commercial software (COMSOL Multiphysics) to calculate far-field reflectance spectra and local-field distributions of corresponding 3D MDM plasmonic nanocavity systems. Optical constants of aluminum were taken from Ref. [35], and the refractive index of PSSs was 1.6. A port condition was set to excite plane waves (with an incident power of 1 W) propagating in the z direction with an electric-field polarization along either x- or y-axis. Perfectly-matched-layer boundary conditions were used on z-directional surfaces of the simulation domain, and periodic boundary conditions were applied in the x-y plane. The auto non-uniform mesh was chosen in the entire simulation domain for the higher numerical accuracy. Note that, considering 100-nm-thickness aluminum shells nearly approaching one half that of PSSs in cases of $\Delta $t = 30 s, corresponding modeled systems should be re-modified to match the experimentally-fabricated structure. However, this modification would not significantly alter the near-field distribution of hybridized resonant modes.

Appendix C

Study on the influence of n-dependent modulations in dielectric spacers on the Q-factor

As shown in Fig. 5(a), we carry on n-dependent simulations by tuning n = 2.0 and 3.5 (referenced to the refractive index of silicon materials) to demonstrate corresponding far-field reflectance spectra. Consequently, as n increases, the dip C-50 (at 430 nm) experiences a obvious redshift fashion, while one additional reflectance dip can be observed near the 650 nm wavelength in the case of n = 3.5. For clarification, we label these dips as C′-50 (at 480 nm) for the case of n = 2.0 as well as C^″-50 (at 520 nm) and D-50 (at 650 nm) for the case of n = 3.5, respectively. To understand characteristics of these resonant dips, we conduct simulations to exhibit a comparative study of local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips C-50, C′-50, C^″-50, and D-50 [Fig. 5(b)]. Similarly, the local-field enhancement at dips C-50, C′-50, and C^″-50 can be attributed to the plasmon hybridization of dipolar plasmon resonances and gap cavity resonances. In particular, n-dependent modulations in dielectric spacers are shown to be sufficient to trigger the modification of energy exchange channels, leading to a stronger confinement of electromagnetic wave inside the cavity. This phenomenon helps reduce the edge-scattering loss that occurs primarily at the critical plane of thin aluminum shells along the z direction [39]. This is in contrast with the dip D, which is characterized by typical in-plane (the x-z plane) circulating displacement currents excited inside the cavity. Based on this distinctive resonant feature, we speculate that the dip D corresponds to a plasmon-induced magnetic resonance [30]. Nevertheless, it is noteworthy that, unlike the significant n-dependent spectral shift, the n-dependent modulation in dielectric spacers continues to display the similar spectral shape for dips C′-50 and C^″-50, indicating the insensitiveness of n-dependent linewidth tunability within proposed nanosystems. While referring to the definition of the Q-factor ($\lambda / \Delta \lambda$) [38], we can thus deduce that adopting high refractive index dielectric materials in 3D MDM designs can moderately increase the Q-factor.

 

Fig. 5. (a) Simulated far-field reflectance spectra of 3D MDM plasmonic nanocavities with different n, i.e., n = 2.0 and 3.5. (b) Simulated local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips C, C′, C^″, and D.

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Appendix D

 

Fig. 6. Simulated local-field distributions for reflectance dips C-100 near the emission wavelength at different resonant frequencies. Coordinate axes indicate two different view angles.

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Appendix E

Study on the dependency of amplified SHG signals with fabricated units’ periods

 

Fig. 7. (a) Simulated far-field reflectance spectra of 3D MDM plasmonic nanocavities with different P, i.e., P = 500 nm, 250 nm, and 220 nm. The inset represents the corresponding side-view schematic illustration of fabricated units with a given edge-edge distance (D3). (b) Simulated local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips E and F for the case of P = 250 nm as well as dips G and H for the case of P = 220 nm.

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For a hexagonal close-packed arrangement, the period of monolayered PSS arrays can be labeled as P = D1 = 500 nm. To identify the influence of the period on results, we carry on P-dependent simulations by tuning P = 250 nm and 220 nm to demonstrate corresponding far-field reflectance spectra, while other geometrical parameters are kept constant (e.g., in cases of $\Delta $t = 30 s and h = 50 nm). Accordingly, suppose that the size of individual fabricated units keeps a constant of nominally 200 nm, the distance between neighboring units’ edges [labeled as D3, see inset to Fig. 7(a)] can be reduced by decreasing P from 500 nm to 220 nm, i.e., D3 = 300 nm (P = 500 nm), 50 nm (P = 250 nm), and 20 nm (P = 220 nm). As shown in Fig. 7(a), as P decreases, the dip C experiences a redshift fashion and divides into two branches. For clarification, we label these dips as E (at 430 nm) and F (at 610 nm) for the case of P = 250 nm as well as G (at 460 nm) and H (at 610 nm) for the case of P = 220 nm, respectively. Notably, the smaller D3 corresponds to the broadened linewidth with respect to the case of D3 = 300 nm. To further characterize the underlying mechanism, we carry on simulations to demonstrate corresponding local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips E, F, G, and H, respectively [Fig. 7(b)]. The result implies that localized electromagnetic fields at these resonant wavelengths are primarily concentrated on the face-up surface of aluminum shells, forming a strong dipole-dipole interaction between neighboring units. Accordingly, we can deduce that the excitation of LSPR-dominated hotspots may dominate the amplification of SHG emissions among these cases. Additionally, the dominance of dipolar resonances (bright modes) within these P-modulated structures inevitably results in the increase of extrinsic scattering losses, leading to the concomitant broadening of the bandwidth, as shown in Fig. 7(a).

Funding

National Natural Science Foundation of China (12004121, 21673192, 91850119); Natural Science Foundation of Fujian Province (2020J05057); Ministry of Science and Technology of the People's Republic of China (2016YFA0200601, 2017YFA0204902); Scientific Research Funds of Huaqiao University (605-50X19028).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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