1. Introduction

As an emphasized discipline in nonlinear plasmonics, plasmon-enhanced second-harmonic generation (PESHG) is widely applied to areas ranging from the design of photonic integrated circuits, the development of ultraviolet (UV) nanosources, to the fabrication of metasurfaces with unique functions [1–3]. Due to their abilities of channeling the far-field radiation to subwavelength dimensions, resonant plasmonic nanostructures can serve as an excellent platform for efficient PESHG emissions at nanoscales [3–7]. Within these configurations, extraordinary high nonlinear frequency-conversion efficiencies can be achieved by designing nanodevices with complex geometries that match surface plasmon resonances (SPRs) with the frequency of the fundamental excitation, second-harmonic emission, or both [4–7]. However, for traditional plasmonic materials, e.g., gold and silver, SPRs endure high Ohmic losses in visible and UV regions during interband transitions, leading to the potential damping of nonlinear polarizations or the selective reabsorption of UV radiations [5,7–9]. Therefore, it is highly desirable for researchers to alternatively seek materials with intrinsically low optical losses.

Aluminum, as an abundant and promising plasmonic material, is known to secure a remarkably low absorptivity in the UV range and thus permits broadly tunable plasmonic responses [10–15]. Immediately recently, aluminum nanostructures, e.g., nanoantennas and nanorod arrays, have been proved to be capable of manipulating localized surface plasmon resonances (LSPRs) within wavelengths ranging from infrared to near-UV, and have been designed to acquire higher nonlinear frequency-conversion efficiencies [5,16–21]. Within these nanostructures, the characteristic of the redirection of far-field signal emissions at second-harmonic frequencies may regulate out-coupling processes, which are closely related to radiated SHG powers [21]. However, this regulation generally requires a size-controllable manner with an accuracy of few nanometers. Consequently, these nanopatterns are frequently fabricated by either electron beam lithography or focused ion beams that are involved with limited effective areas, as well as expensive and time-consuming processes.

Here, we experimentally design and fabricate aluminum-shell gratings (ASGs) that combine low optical-loss materials as well as large-area uniform and facile configurations for the efficient generation of near-UV lights induced by nonlinear frequency conversions. The ASGs are characterized by the heterogeneity of component materials relative to fully-aluminum gratings, and contribute to the remarkable enhancement of PESHG performances compared with unpatterned aluminum films. By means of tuning various parameters of the geometry and the polarization dependence, we can reveal phenomena of the occurrence of quasi-Bragg plasmon modes near second-harmonic wavelengths, in which the dominance of grating-coupled SPRs switches from the LSPR-related dependence to the collective interaction of interfacial surface plasmons. This modulation leads to a well-defined coherent interplay between local resonant modes and local-surface nonlinearities, and assists the amplification of near-UV light emissions induced by PESHG processes.

2. Results and discussion

Photoresist-line patterns with 60 nm height are grown on a flat silicon substrate [Fig.  1(a), detailed fabrication procedure described in Appendix A]. Then, during the deposition processing, a conformal aluminum film with 40 nm thickness is deposited. The thin aluminum film covers the entire surface of photoresist-line patterns including the top and the sidewall of ridges as well as the bottom of grooves with different thicknesses [Fig.  1(a), inset]. Coordinates are chosen such that the configuration of ASGs lies on the x-y plane. Figure  1(b) and the inset show top-view scanning electron microscopy images of grating configurations prior to, and after, the deposition of aluminum shells with 180 nm period along the x axis and different widths of y-directional ridges. It is worth noting that, after the deposition process, the width of grating ridges increases from 50 nm to 60 nm, indicating that the thickness of aluminum shells covered on the sidewall of photoresist-line patterns ranges from 0 nm to 5 nm. This deviation can be attributed to the fabrication imperfection such as the inclination of the sidewall of photoresist-line patterns in micro-wave plasma etching processes, as shown in the inset of Fig.  1(c). Moreover, atomic force microscopy images reveal that the arrangement of ASGs exhibits a high degree of homogeneity up to a micron level, contributing to the achievement of uniform and reproducible responses [Fig.  1(c)]. Also, geometric parameters including period, depth, and width of grating units can be intuitively obtained.

 

Fig. 1. (a) Schematic illustration of ASGs. The inset represents the cross-section of ASG units, where H1 denotes the 60 nm height of photoresist-line patterns, H2 the 40 nm thickness of aluminum shells covered on the top region of both photoresist-line patterns and silicon substrates, H3 the thickness of aluminum shells covered on the sidewall of photoresist-line patterns. (b) Top-view scanning electron microscopy image of ASGs, where P_x and W denote 180 nm period along the x axis and 60 nm width of y-directional ridges, respectively. The inset represents the top-view scanning electron microscopy image of photoresist-line patterns prior to the deposition of aluminum shells, where W’ denotes 50 nm width of y-directional ridges. Scale bar: 300 nm. (c) Atomic force microscopy images at a 45° tilted view. The inset and the white line denote the result of surface analyses and the sampled region, respectively.

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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), 130 fs laser pulses tunable from 710 nm to 900 nm (Mira 900, Coherent Inc.) are focused on samples under the normal incidence through a 50x objective lens (Olympus, N. A. = 0.65) and a linear polarizer. The laser power can be modulated by a neutral density filter, and a long-pass filter positioned behind the neutral density filter can further be used to filter out the possible spurious photoluminescence in the laser line. Then, generated SHG signals radiated in the backward direction are collected by the same objective lens, filtered by a short-pass filter, analyzed by a polarizer, and measured using an electron multiplying charge coupled device (EMCCD) camera (Newton 970) attached to a spectrometer (Andor SR550). To study the polarization dependence of SHG responses, we respectively equip the half-wave plate and the polarization analyzer in incident and collected optical paths with rotational stages. Suppose that a plane wave (k) propagates along the z axis and impinges on samples at an incident angle θ with respect to the surface normal. The incident plane (polarization direction) is characteristic of an azimuthal angle α with y-directional ridges. Then, we define the polarization direction of incident beams parallel to y-directional ridges (perpendicular to the grating vector) as α = 0° (180°), and the one perpendicular to y-directional ridges (parallel to the grating vector) as α = 90° (270°). Accordingly, polarization states labeled as P and S mentioned below correspond to the case of α = 90° (270°) and 0° (180°), respectively.

 

Fig. 2. (a) Experimental setups for SHG spectroscopy, where NPBS denotes the non-polarizing beam splitter, HWP the half-wave plate, ND the neutral density filter, LF the long-pass filter, SF the short-pass filter. The inset represents the schematic illustration of polarization-resolved SHG measurements, where blue arrows indicate the polarization direction of detected SHG signals. (b) Exemplary measured laser spectrum (red) and its corresponding measured SHG spectrum (blue) of ASGs. The data have been normalized to the maximal intensity of the measured pump-laser peak. The inset represents the SHG intensity distribution of ASGs and aluminum films (multiplied 100 ×), where error bars represent the deviation of measured SHG intensities over multiple acquisitions from different sample areas. (c) Power-dependent SHG measurements. The inset represents measured SHG intensities versus the square of pump-laser powers (P²). Polar plots of induced SHG intensities as a function of the polarization angle of incident beams for (d) E_S(2ω) and (e) E_P(2ω). Blue dots represent experimental data acquired with the polarization angle of incident beams varying from 0° to 360° with a step of 10°. The red line denotes the peak-valued fitting curve for clarity. The data have been normalized to the maximal intensity.

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To measure the nonlinear response of ASGs, we use the pump laser centered at 800 nm. As expected, the spectral position of the emission peak appears half that of the pump-laser peak, and the bandwidth of the SHG peak reaches approximately half that of the pump-laser peak [Fig.  2(b)]. Also, measured SHG intensities increase quadratically with the increasing excitation power ranging from 5 mW to 25 mW [Fig.  2(c)]. Experimental results mentioned above agree satisfactorily with essential characteristics of SHG [22,23]. More experimental results (data not shown) indicate that, for sufficiently low excitation powers, the SHG response can be described by the square-power-law dependence. Subsequently, for higher excitation powers (at approximately 20 mW), SHG data endure signal fluctuations and gradually deviate from the square-power-law dependence. Then, at ∼ 55 mW, the SHG output, which features a strong and broad two-photon-excited luminescence background [24], experiences a rapid increasing trend and then significantly decreases. Finally, by increasing the excitation power up to 90 mW, namely, the maximum power value detected in our experimental conditions, SHG data saturate. This power-dependent SHG behavior can be attributed to the physical origin of SHG signals that are generated at the surface of plasmonic materials. Hence, any structural deformations may exert a profound impact on SHG signal yields [25]. Inspection of samples by scanning electron microscopy indeed indicates a light-induced structural damage at the excitation power of approximately 55 mW. With these analyses, we can thus give a damage threshold of 55 mW for our proposed ASG structures. Furthermore, the property of PESHG emissions can be found in polarization-resolved SHG measurements [21,26,27]. Figures  2(d) and 2(e) show polar plots of the induced SHG intensity as a function of the polarization angle of incident beams with the polarization analyzer in the collected optical path oriented either along α = 0° (180°) [labeled as E_S(2ω)] or α = 90° (270°) [labeled as E_P(2ω)]. Then, similar two-lobe patterns can be observed, regardless of the polarization direction of detected SHG signals. In both cases, the SHG intensity is conspicuously enhanced when the pump laser is polarized perpendicularly to y-directional ridges (parallel to the grating vector), and is decreased by up to two orders of magnitude when the incident polarization is aligned along y-directional ridges. Note that the orientation of polar plots is slightly tilted from 90° by ∼ 10°. In considering the evolution of pump-laser powers (after the focus of incident beams) as a function of the rotation angle of the half-wave plate, we attribute this deviation to the imperfection of polarization analyzers equipped in optical paths. Additionally, the mirror symmetry breaking of the sidewall in ASG units may further result in the deformation of polar plots of induced SHG intensities [27]. To further quantitatively evaluate the nonlinear conversion efficiency, we define the 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 at a given polarization state [7,28–30]. This FOM thus does not depend on the pump-laser power used for SHG measurements. In our experiments, the value of $P_{\textrm{FF}}^a$ can be obtained in front of samples (after the focus of incident beams) 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, in considering polarization-resolved SHG behaviors, FOMs of nominally 1.4×10⁻⁷ (W^-1) and 2.9×10⁻¹¹ (W^-1) are obtained for ASGs and unpatterned aluminum films, respectively. We can thus reasonably deduce that the nonlinear conversion efficiency of ASGs at near-UV frequencies reaches up to three-order magnitude more highly than that of unpatterned systems [Fig.  2(b), inset].

For the purpose of clarifying the relationship between plasmon-driven enhancements and observed polarization-resolved SHG behaviors, we incorporate the phenomenological field enhancement factor $L(\Omega )$ in considering nonlinear polarizations. The $L(\Omega )$ accounts for the local-field enhancement via $L(\Omega ) = {E_{\textrm{loc}}}(\Omega )/{E_0}(\Omega )$, $\Omega = \omega \textrm{ or 2}\omega$, where ${E_{\textrm{loc}}}(\Omega )$ and ${E_0}(\Omega )$ denote local-field amplitudes and electric far-field amplitudes at both fundamental and second-harmonic frequency, respectively [5,21,27]. Accordingly, effective second-order nonlinear polarizations along P- and S-polarization directions can be taken as [5,27]:

To identify the mechanism that governs these field enhancement factors, we measure incident angle (θ)-dependent reflectance spectra by using a white light source and a linear polarizer. As shown in Fig.  3(a), when using P-polarized light sources, we observe that ASGs exhibit a well-modulated resonant dip D1 near the second-harmonic wavelength (400 nm), whereas no significant resonant behaviors can be observed near the fundamental wavelength (800 nm). Moreover, as θ increases from 0° to 60°, the dip D1 experiences a redshift with a gradual degradation of resonant intensities. By comparison, for the S-incident polarization, the resonant dip D2 at a central wavelength of about 300 nm can be attained, whereas there also exist no resonant dips at the fundamental frequency [Fig.  3(b)]. Then, with the increase of θ, the dip D2 blue-shifts toward the deep UV region. Additionally, small interband-absorption effects originating from aluminum materials can be observed around 800 nm both in P- and S-polarized reflectance spectra, leading to the inevitable damping of plasmon-driven resonances [11,25,31–33]. We can reasonably deduce that, due to the causality far off resonance and the occurrence of interband transitions, the field enhancement caused by plasmonic modes at the fundamental frequency should vanish, and both polarization-dependent SHG signals are thus moderately influenced by $L(\omega )$. Accordingly, by dividing P- and S-polarized SHG intensities, we can eliminate the absorbance process at the fundamental frequency, and define the polarization-resolved enhancement factor as

This simple model demonstrates that the value of $\gamma$ can be used to quantitatively evaluate the relative contribution of $L(2\omega )$ along P- and S-polarization directions to the nonlinear signal amplification. It is worth noting that this simple model gives rise to the limitation of a two-lobe pattern along given polarization orientations in polar plots of induced SHG intensities [27], indicating the consistency with our experimental results [Figs.  2(d) and 2(e)]. Under this circumstance, we obtain $\gamma$ of nominally 7.9, revealing that SHG signals originating from P-polarized nonlinear polarizations are strongly amplified by one order of magnitude in out-coupling processes when compared to that originating from S-polarized nonlinear polarizations. It should be pointed out that, differing from the previously-obtained three-order-magnitude SHG enhancement in pure metal and dielectric gratings [34,35], the enhancement of SHG emissions in our proposed ASG configurations can be attributed to the plasmon-induced enhancement at second-harmonic frequencies ($I_{}^{(2)}(2\omega ) \propto {|{L(2\omega )} |^2}$). This fundamental mechanism can not only efficiently scatter local second-harmonic lights to the far-field, but also avoid the potential sample damage caused by significant fundamental absorption processes ($I_{}^{(2)}(2\omega ) \propto {|{L_{}^2(\omega )} |^2}$). Moreover, in considering polarization-resolved SHG behaviors, we conduct excitation wavelength (λ_ex)-dependent SHG performances as well as corresponding comparative studies to reveal the relative contribution of component-material dependences and frequency dependences in PESHG processes. The detailed experimental result and the relevant discussion are described in Fig.  5 and Appendix B. Accordingly, we conclude that photoresist-line patterns in ASG structures collectively contribute to the generation of SHG responses, whereas the amplification of signal powers predominantly depends on the plasmon-induced enhancement at emission frequencies. Additionally, when taking into account the bandwidth of resonant dips located at emission frequencies (especially the dip D1), we can reasonably deduce that the range of operating frequencies of ASG structures spans over an approximately 400-nm spectral range.

 

Fig. 3. Measured incident angle (θ)-dependent reflectance spectra with (a) P- and (b) S-polarized white light sources, respectively. The black dotted rectangle in (a) represents individual reflectance spectra of ASGs with different incident angles, that is, θ = 0°, 10°, 20°, 30°, and 40°. Vertical dashed lines indicate fundamental (800 nm) and second-harmonic (400 nm) wavelengths. The inset in (b) indicates a comparative study of the angular dispersion of resonance wavelengths correspond to first-order Bragg plasmon modes, e.g., m = 1 (black circle), m = -1 (red circle), and D2 (blue circle) for the S-incident polarization. (c) Simulated reflectance spectra as a function of the value of H3. White and red dotted lines in (a)-(c) indicate the change of spectral positions of resonant dips. Individual reflectance spectra in (a) and (c) are vertically offset from one another by 100 for clarity.

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In principle, for a diffraction grating, the excitation of surface plasmons via Bragg scattering leads to [36]

To verify the influence of the structural heterogeneity on grating-coupled SPRs, we carry out 3D-FDTD simulations to demonstrate far-field reflectance spectra of ASGs with various geometrical parameters and polarization states of the light. The dimension of the modeled system is chosen to match the previously designed structure. Optical constants of aluminum are taken from Ref. [31], and the refractive index of photoresist can be set as 1.67. The detailed simulation procedure is described in Appendix C. As shown in Fig.  3(c), regarding the S polarization state, we simulate far-field reflectance spectra of ASGs with different values of H3 ranging from 1 nm to 30 nm. In this simulation, the modeled system is constructed with the same period, height, and width, but different H3. Then, the decrease of H3 stands for the evolution of the structural heterogeneity that switches from fully-aluminum gratings to ASGs. Notably, as H3 decreases from 30 nm to 10 nm, one distinct resonant dip centered at about 200 nm can be attained. As H3 decreases from 5 nm to 1 nm, the resonant dip experiences a redshift trend, and is finally located at a central wavelength of approximately 300 nm. More simulation results exhibit that, for ASGs (with H3 = 1 nm), the resonant dip blue-shifts toward the deep UV region with the increase of θ from 0° to 45°, and a 4-fold reduction in the maximum intensity for θ = 45° can be attained (see Fig.  6 in Appendix D). Very satisfactory agreement between simulation and experimental results is observed. Such an agreement suggests that the occurrence of the dip D2 can be regarded as if it originates from the heterogeneity of component materials in ASGs.

Similarly, we also conduct a comparative study between fully-aluminum gratings and ASGs for the P polarization state. As shown in Fig.  4(a), for fully-aluminum gratings, only one distinct resonant dip D3 centered at about 200 nm can be observed. According to our theoretical calculations [Fig.  3(b), inset], this resonant dip can be attributed to Bragg plasmon modes. By comparison, both modeled ASGs (with H3 = 2 nm) and fabricated structures display several resonant dips including a conspicuous absorption (D1) near the second-harmonic wavelength (400 nm) [Figs.  4(b) and 4(c)]. To provide more physical insights, we perform 3D-FDTD simulations to demonstrate local-field distributions at these dips for the P polarization state [Fig.  4(d)]. The local-field distribution at D3 is modulated by the lightning rod effect both at the upper and bottom corner of grating ridges, which resembles that at D3’. This result reveals that both dips D3 and D3’ stem from Bragg plasmon modes similarly. Additionally, electromagnetic fields at dips D4, D5, and D1 are primarily concentrated on the sidewall of ASG units, resulting in the emergence of interfacial surface plasmons on both air-aluminum and photoresist-aluminum interfaces [40,41]. Especially for the dip D1, the occurrence of interfacial surface plasmons on air-aluminum interfaces proceeds to modify the dominance of grating-coupled surface plasmon resonances switches from the LSPR-related dependence to the collective interaction of interfacial surface plasmons. This modulation leads to the long-range collective interaction of propagating surface modes [42], and increases the mode volume by reshaping the coupled local-field energy distribution that extensively spills out from the corner of grating units. Consequently, the occurrence of energy-loss channels allows local SHG energies to resonantly out-couple with the far-field, and results in the inevitable broadening of the bandwidth, as shown in both experimental and simulation results. These plasmonic resonances can be regarded as a modification of Bragg plasmon modes, and therefore can be tentatively labeled as quasi-Bragg plasmon modes. More importantly, the electric moment of these modes is aligned with the orientation of the normal component of surface susceptibilities $\stackrel{\leftrightarrow}{\chi}_{\mathrm{nnn}}$ (labeled as local-surface nonlinearities) [16] for aluminum materials on the sidewall. Within the hot spot region, a well-defined symmetry (orientation) matching between local resonant modes and local-surface nonlinearities leads to the generation of strong nonlinear currents [7,28], and contributes to the efficient out-coupling of local SHG lights to the far-field. More geometry-dependent simulations have also been conducted to confirm (a) the transition of the dominance of grating-coupled surface plasmon resonances between the LSPR-related dependence to the long-range collective interaction, (b) its influence on the well-defined symmetry (orientation) matching and the emergence of quasi-Bragg plasmon modes (see Figs.  7 and 8 in Appendix E).

 

Fig. 4. Simulated reflectance spectra of (a) aluminum gratings and (b) ASGs for the P polarization state, respectively. (c) The measured reflectance spectrum of ASGs for the P polarization state. Insets in (a) to (c) represent corresponding schematic illustrations of aluminum grating and ASG units, respectively. (d) FDTD Simulations for local-field distributions mapped on the x-z plane for dips D3, D3’, D4, D5, and D1, respectively. The enlarged field plot indicates that electromagnetic-field vectors at the dip D1 exhibit a strong normal component on the sidewall.

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3. Conclusion

In conclusion, we have experimentally designed a highly-efficient PESHG platform by constructing a heterogeneous model of ASGs that consist of thin aluminum shells integrated with periodic dielectric line patterns. A comparative study reveals that, in considering polarization-resolved SHG behaviors, the generation of near-UV lights from proposed platforms can be increased by up to three orders of magnitude when compared to the generation from unpatterned systems. This enhancement can be attributed to the occurrence of quasi-Bragg plasmon modes near second-harmonic wavelengths. Subsequently, these modes can be regarded as if they arise from the structural heterogeneity and are characterized by long-range collective interactions of propagating surface modes. Pumping on these modes results in the well-defined coherent interplay between local resonant modes and local-surface nonlinearities within the hot spot region, and facilitates the efficient out-coupling of local SHG lights to the far-field. An understanding of quasi-Bragg plasmon modes crucially reveals the mechanism governing grating-coupled SPRs at near-UV frequencies. It further avoids interference that may degrade these modes’ intended performance in relevant applications, such as the optimized component in photonic integrated circuits as well as the design of efficient UV nanosources and nonlinear metasurfaces, e.g., polarization-modulated nonlinear optical encoding media.

Appendix A

Fabrication schemes

The configuration of ASGs was fabricated by nanoimprint lithography combining with depositing film technology. The nanoimprint lithography has great advantage of fabricating high-quality long-range order nanostructures even though depending on the mask. The nanopattern was fabricated on the silicon substrate. The photoresist layer of TU7-60 (Obducat Technologies A B, Sweden) with approximately 60 nm thicknesses was span onto the silicon wafer. The Eitre-6 NIL system (Obducat Technologies A B, Sweden) was used to replicate nanopatterns from the nickel mold with 180 nm period and 60 nm width to the photoresist. Thermal-nanoimprint on the nickel mold was then taken with the intermediate polymer sheet (IPS, Obducat Technologies A B, Sweden) at 150 ℃ with 40 bar pressure for 3 min. Upon the removal from the hard mold, a nanopattern could be formed on the IPS surface, and acted as the soft mold during the UV-nanoimprint process. The replica IPS soft mold was placed on the TU7-60-coated silicon surface, and was imprinted at 65 ℃ under 30 bar pressure for 5 min as well as UV-exposed for 1 min. To isolate the photoresist-line nanopattern after the separation of IPS form the resist, we precisely removed the residual layer on the bottom via Q150 micro-wave plasma etching system (Alpha, Germany) with a gas mixture of O₂ (30 sccm) and Ar (50 sccm) plasma at a chamber pressure of 50 Pa and a power density of 50 W for 60 s, resulting in the decrease of the width of grating ridges. Finally, the aluminum film with 40 nm thickness was deposited onto the photoresist nanopattern via utilizing the high vacuum electron beam depositing system (Temd-500, China).

Appendix B

Study on the relative contribution of frequency dependences and component-material dependences in PESHG processes

In considering polarization-resolved SHG behaviors, we conduct λ_ex-dependent SHG performances of ASG with W = 70 nm, indicating that, at approximately 840 nm, λ_ex-dependent peak values reach a maximum [Fig.  5(a)]. It should be pointed out that, when λ_ex sweeps into the region from 840 nm to 900 nm, the inevitable increase of signal background noises (highlighted in the red dotted box) that have originated from optical elements (especially the NPBS) in optical paths finally results in the loss of λ_ex-dependent SHG signals. Consequently, in our measurements the tuning range of λ_ex ranges from 740 nm to 840 nm. By sweeping λ_ex in this spectral region, signal intensities monotonically decrease as the emission frequency shifts from 420 nm to 370 nm. Noting that each measured SHG response has been maximized by optimizing the optical path for keeping the excitation power as a constant. To identify the underlying mechanism, we experimentally perform a comparative study to reveal the relative contribution of frequency dependences in PESHG processes [Fig.  5(b)]. Compared with results shown in Fig.  3(a), the measured reflectance spectrum of ASG with W = 70 nm displays the redshift of the dip D1 near emission wavelengths (highlighted by purple dashed lines). Near fundamantal wavelengths, however, the contribution of plasmonic fields can be neglected, owing to the existence of off-resonance states and interband transitions in measured spectral windows (data not shown). Therefore, we can attribute the measured SHG intensity distribution to the occurrence of the resonant dip D1 at emission frequencies. Additionally, when taking into account the bandwidth of resonant dips (∼ 370 nm to 600 nm), we can reasonably deduce that the range of operating frequencies of ASG structures spans over an approximately 400-nm spectral range. For clarifying the relative contribution of component-material dependences in PESHG processes, we newly fabricate reference samples consisting of photoresist-line patterns and silicon substrates prior to the deposition of aluminum shells [Fig.  5(c), inset], and conduct a comparative study of measured SHG spectra between corresponding ASG and reference samples [Fig.  5(c)]. The result demonstrates that the SHG signal of ASG appears much stronger than that of reference samples, implying the significant role of deposited aluminum shells played in the amplification of nonlinear scattering signals. As shown in Fig.  5(d), we measure the reflectance spectrum of reference samples, revealing that photoresist-line patterns display obvious optical absorption effects ranging from near-ultraviolet to visible spectral regions. Additionally, λ_ex-dependent SHG performances of reference samples [Fig.  5(d), inset] exhibit that λ_ex-dependent signal intensities gradually decrease as the emission frequency shifts from 420 nm to 385 nm, signifying that the λ_ex-dependent SHG intensity distribution is moderately influenced by the optical absorption effect. Accordingly, we conclude that photoresist-line patterns in ASG collectively contribute to the generation of SHG responses, whereas the amplification of signal powers predominantly depends on the excitation of quasi-Bragg plasmon modes at emission frequencies.

 

Fig. 5. (a) λ_ex-dependent SHG responses of ASG with W = 70 nm. All peak values are normalized by data at 420 nm. The inset shows the measured SHG spectrum excited at 840 nm. (b) The measured reflectance spectrum with P-polarized white light sources for ASG with W = 70 nm. The inset shows the corresponding top-view scanning electron microscopy image and the schematic of ASG. (c) Measured SHG spectra excited at 800 nm for ASG with W = 70 nm and the photoresist-line pattern with W’ = 60 nm. These data have been normalized to the maximal intensity of the measured SHG spectrum for ASG. The inset shows the corresponding top-view scanning electron microscopy image and the schematic of the photoresist-line pattern. (d) The measured reflectance spectrum with P-polarized white light sources for the corresponding photoresist-line pattern. The inset displays corresponding λ_ex-dependent SHG responses. All peak values are normalized by the data of ASG at 420 nm.

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Appendix C

Simulation procedure

We adopted the commercial software package (FDTD Solutions 2018a, Lumerical Solutions Inc.) to calculate local-field distributions and electromagnetic-field vectors. The dimension of the modeled system was chosen to match the previously designed structure. Then, optical constants of aluminum were taken from Ref. [31], and the refractive index of photoresist was 1.67. This system was excited by a normally incident, unit magnitude plane wave propagating in the z direction with an electric-field polarization either along the x-axis (P-polarized light) or along the y-axis (S-polarized light). Perfectly matched layer boundary conditions were used on the top and bottom surfaces of the simulation domain, and periodic boundary conditions were applied on the left and right surfaces. The auto non-uniform mesh was chosen in the entire simulation domain for the higher numerical accuracy. The mesh refinement was the conformal variant 6. Monitors of the frequency-domain field profile and the frequency-domain field and power were placed. The magnitude of incident electric fields was taken to be unity (1.0 V/m). Consequently, the enhancement of electromagnetic fields could be further evaluated.

Appendix D

Simulated Incident angle-dependent reflectance spectra for S-polarized light sources

 

Fig. 6. Simulated reflectance spectra as a function of incident angles ranging from 0° to 45° for S-polarized light sources.

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Appendix E

Geometry-dependent simulations

Geometry-dependent simulation results shown in Fig.  7 demonstrate that electromagnetic fields of isolated ASG units aggregate on the sidewall of grating ridges, while the coupled local-field energy primarily spills out from the corner of grating units, resulting in the LSPR-related electromagnetic interaction. By comparison, the distribution of the coupled local-field energy on air-aluminum interfaces can be substantially modified when placed at an array of similar particles. Particularly, due to the transition of the dominance of grating-coupled surface plasmon resonances to the long-range collective interaction, a strong normal component of electromagnetic-field vectors at the dip D1 appears on the sidewall, facilitating the well-defined symmetry (orientation) matching between local resonant modes and local-surface nonlinearities. The influence of long-range collective interactions on quasi-Bragg plasmon modes can be demonstrated in Fig.  8. With the decrease of the grating period along the x axis (P_x) from 180 nm to 100 nm, the resonant dip D1 blue-shifts toward the deep UV region, whereas the dip D4 disappears and the dip D5 remains unchanged [Figs.  8(a) and 8(b)]. A 10% reduction in the bandwidth of the dip D1 can also be observed for ASG with P_x = 100 nm. Figure  8(c) further reveals that the decrease of the grating period provides an innate nanogap between two neighboring grating units to confine the incident optical field through the near-field coupling effect. This effect also introduces significant perturbations of the normal component of electromagnetic-field vectors related to the collective interaction of interfacial surface plasmons in interparticle regions. Consequently, the emergence of quasi-Bragg plasmon modes endues the interference, and may result in the rapid degradation of the well-defined symmetry (orientation) matching between local resonant modes and local-surface nonlinearities. We can thus reasonably deduce that the occurrence of quasi-Bragg plasmon modes is closely related to the long-range collective interaction of propagating surface modes, with the dependence on the lattice spacing.

 

Fig. 7. FDTD Simulations for local-field distributions and electromagnetic-field vectors mapped on the x-z plane for (upper) the isolated ASG unit and (bottom) ASG with P_x = 180 nm at the dip D1, respectively.

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Fig. 8. Simulated reflectance spectra of ASGs with different periods along the x axis (P_x), e.g., P_x = (a) 180 nm and (b) 100 nm, for the P polarization state, respectively. (c) FDTD Simulations for local-field distributions and electromagnetic-field vectors mapped on the x-z plane for dips D1 in ASG with P_x = (upper) 180 nm and (bottom) 100 nm, respectively.

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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); Natural Science Foundation of Jiangxi Province (20192ACB20032); Scientific Research Funds of Huaqiao University (605-50X19028); Open Project Program of Fujian Key Laboratory of Light Propagation and Transformation (KF2019202).

Acknowledgments

We like to thank Professor Junbo Han, Miss Yue Zeng, Dr. Han Gao, and Dr. Weimin Yang for experimental assistance and helpful discussion.

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.

References

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