Gold-polymer hybrid metasurface for polarization-independent enhanced third harmonic generation in the ultraviolet

Abstract

We present a combined experimental and theoretical study of nonlinear light-matter interactions in a three-dimensional gold-polymer hybrid metasurface. In contrast to conventional two-dimensional designs, which by symmetry may support either transverse electric (TE) or transverse magnetic (TM) polarization, our volumetric architecture accepts both TE and TM modes simultaneously, reflecting the dimensionality and versatility required by the photonic devices. The metasurface comprises a periodic lattice of gold nanostructures embedded in a dielectric polymer matrix, creating complex metal–dielectric interfaces that sustain tightly confined plasmonic resonances. When driven by ultrafast near-infrared (NIR) pulses, these resonances concentrate optical energy at the nanoscale, enabling efficient third-harmonic generation and upconversion of visible light into the ultraviolet (UV) and deep-UV regimes with enhanced conversion efficiency. We perform spatial and temporal mapping of the nonlinear response under both TE and TM excitation. Our measurements reveal polarization-agnostic field enhancement and spectral tunability arising from the three-dimensional morphology-capabilities unattainable in planar metasurfaces, where two-dimensional symmetry inherently limits polarization flexibility and functional bandwidth. This quasi-3D platform provides a flexible design toolbox for polarization-independent UV and deep-UV light sources. Potential applications include high-resolution UV spectroscopy, optical multiplexing, data storage, and emerging quantum photonic architectures. By establishing fundamental insights into three-dimensional nonlinear metasurface behavior, our work paves the way for next-generation reconfigurable, multi-polarization nanophotonic devices.

Introduction

Nonlinear frequency conversion in metals has been a cornerstone of nonlinear optics research since its inception, propelled by the large third-order susceptibilities of plasmonic materials despite their inherent absorption in the visible and NIR bands^1–4. Historically, investigations have centered on planar one-dimensional (1D) metasurfaces like 1D periodic gratings, whose symmetry confines device functionality to either TE or TM polarization, or planar two-dimensional (2D) metastructures like 2D periodic pillar arrays. While these platforms have yielded valuable insights, they fall short of representing the volumetric nature of practical photonic components used in practical photonic systems.

Advances in nanofabrication now make possible to produce three-dimensional (3D) metal-dielectric architectures that transcend the planar limit. By embedding metallic nanolayers within dielectric matrices and introducing depth-dependent patterning, these metasurfaces localize electromagnetic (EM) fields in all three spatial dimensions. This field confinement not only supports both TE and TM modes simultaneously but also enables richer light-matter interactions under ultrafast excitation, unlocking higher-order nonlinear processes with unprecedented spatial and temporal control. 3D metastructures offer a versatile design toolbox for next-generation photonic devices. Key advantages include: polarization-independent operation, accepting and enhancing both TE and TM inputs without additional optical components; enhanced spectral tunability through depth-engineered resonances, allowing dynamic wavelength conversion from visible to deep-UV regimes; improved integration with volumetric platforms such as optical fibers, waveguide circuits, and compact sensors, where planar films alone cannot deliver full functionality.

Despite rapid progress in fabricating 3D nanostructures and metamaterials, theoretical models have yet to fully capture their volumetric nonlinear response under high-intensity, ultrashort pulses. Prior studies on second harmonic generation (SHG) and third harmonic generation (THG) from ultra-thin gold layers (20-70 nm) illuminated intrinsic material³ but were intrinsically limited by subwavelength interaction lengths with very low nonlinear conversion efficiencies from simple metallic nanolayers, and planar geometries. In conventional low-dimensional metasurfaces, such as 1D periodic nanowires or gratings possessing mirror symmetry, the distinction between TE- and TM-polarized illumination is fundamental. Only TM excitation generates a longitudinal electric-field component capable of driving surface plasmon modes or exploiting surface-modulated dielectric profiles, while TE illumination remains largely transverse and therefore weakly coupled to plasmonic resonances. In contrast, the present structure is volumetric: the nanohole layer and the embedded gold nanodisks form a vertically stratified, quasi-3D plasmonic crystal. This depth-dependent morphology alongwith the 2D periodicity enables both TE and TM illumination to generate longitudinal field components inside the wells and at the metal–air interfaces. As a result, the resonant field localization–and consequently the nonlinear response–becomes inherently polarization-independent.

Nevertheless, corrugated nanostructures featuring surface reliefs on the order of 10 to 100 nm are known to modify the spatial distribution of an incident optical EM field. Such structures can be engineered to enhance light–matter interactions on purpose-built metasurfaces by exploiting plasmonic resonances. Surface plasmons (SP) are collective oscillations of free charges on conductive surfaces that couple strongly with an incident EM wave when excited at their resonant wavelength^5–7. Under resonant conditions, plasmonic structures can tightly confine the EM field near the surface of the metal, with the confinement determined by geometrical factors (such as shape, size, and sharpness) as well as physical properties (dielectric functions at a given wavelength) of both the metal and its surrounding dielectric materials. This strong plasmonic coupling significantly boosts light–matter interactions and generates large surface nonlinearities^7–15, enabling higher harmonic generation (HHG) under relatively low input laser intensities and paving the way for manipulating optical fields with unprecedented spatial and temporal resolution.

Based on the highly precise techniques now achievable in nano-fabrication, plasmonic structures can be built entirely from metal or as metal–dielectric composites. Much of the literature has focused on metallic nanostructures that simultaneously offer an intrinsic nonlinear optical (NLO) response and amplify the incident EM field. Examples include arrays for SHG using bow-tie configurations¹⁶, V-shaped nanoantennas coupled with nanorod systems¹⁷, L-shaped nanoparticles¹⁸, split-ring resonators¹⁹, rectangular hole arrays²⁰, and pyramidal recesses²¹, among others. However, metal-dielectric composite structures allow us to take advantage of the complementary linear and nonlinear optical properties of each material, combining the sharply localized SP resonances of metal nanolayers with the inherent strong NLO response of certain dielectrics. Consequently, a growing effort is dedicated to hybrid structures that combine a nonlinear material (serving as the harmonic source) with a plasmonic nanostructure (acting as the harmonic amplifier). Traditionally, hybrid nanostructures have been predominantly applied to boost SHG, since purely metallic plasmonic nanoantennas lack measurable second-order nonlinearity. In contrast, plasmonic structures are notably more efficient in facilitating processes. By analyzing the electric field distribution around these nanostructures, one gains insight into the nature of the excited plasmons and the spectral selectivity of the field enhancement. Moreover, high-harmonic generation from hybrid structures can broaden the range of applications, from compact nanoscale extreme UV sources for microscopy, lithography, and spectroscopy to even attosecond physics, thereby opening up a myriad of new opportunities^9–15. For instance, Chen et al.¹⁰ introduced a periodic two-dimensional array of gold discs embedded in an organic conjugated polymer, demonstrating a spectrally selective THG with up to three times enhancement with respect to that of a flat polymer on gold. Similarly, Ren et al.¹¹ examined a 100 nm thick gold nano-patch array coated with a polycarbonate polymer film doped with a polymethine dye, reporting a maximum THG enhancement factor of about 20 relative to that of a polymer film over a flat gold film. In another study, Albrecht et al.¹² showcased a simpler plasmonic system wherein arrays of non-interacting, rod-shaped gold nanoparticles on a polymethyl methacrylate (PMMA) film exhibited conversion efficiency enhancements that tracked the spectral profile of the plasmonic resonance. Also, in an Au nano-rod/CuO core/shell hybrid nanostructure, Bar-Elli et al. showed a THG enhancement of one order of magnitude, over bare Au nano-rod cores¹³.

In this work, we investigate a gold-polymer hybrid metasurface featuring periodic patterning in the lateral plane and depth-dependent morphology along the vertical axis. The structure combines a nanohole array atop a gold nanodisk lattice within a polymer host, creating a quasi-3D crystal that supports efficient THG into the UV under both TE and TM excitation. By mapping the spatial and temporal nonlinear response with ultrafast NIR pulses, we demonstrate polarization-independent frequency upconversion far exceeding the performance of flat gold films.

Although the crystal is not uniform along the z direction, it does not exhibit complete periodicity either, rendering it a ”quasi-3D” system. Previous studies on similar quasi-3D plasmonic structures have highlighted their sensitivity, efficiency, and biocompatibility (attributed to gold) as refractometric sensors^22–25, and the standard nanofabrication technique used to fabricate the hybrid metasurface (details in section3) is quite well established. In our work, we exploit the narrow spectral linewidth resonance of the crystal to achieve a significant enhancement in the nonlinear surface properties of gold at the nanoscale. This enhanced nonlinearity is experimentally quantified in terms of the THG from the patterned crystal, compared to that of an unpatterned gold nanolayer, demonstrating that the structure functions as an efficient light source in the deep UV range. The experimental observations are further corroborated and elucidated by theoretical calculations and simulations.

Gold–polymer hybrid structure design

The metasurface is composed of large-area, periodic arrays of cylindrical wells imprinted into an SU8 photoresist layer of a thickness of nm, deposited on top of a silicon substrate. Each well has a diameter of nm and a depth of nm, with a center-to-center spacing between the holes of nm, and the pattern is periodic along the x and y directions, arranged in a hexagonal lattice. A uniform gold layer (with thickness nm) covers the entire nanostructure - both the top surface and the recessed regions - resulting in a quasi-3D plasmonic crystal. As shown in Fig. 1a and b, the top layer consists of a 2D array of nano-holes in the gold film, while a second, distinct level of isolated gold disks is formed at the bottom of the embossed wells. Figure 1b presents a side view, and Fig. 1c displays a top view of the hexagonal lattice, where the dashed rectangle shows one unit cell of the hexagonal lattice. The presence of two distinct plasmonic layers separated by a dielectric volume leads to vertical mode hybridization. The nanohole layer and the nanodisk layer each support localized resonances, and their near field coupling produces vertically split modes with spatially separated hotspots. This behavior is evident in the field maps of Fig. 3 and cannot be reproduced by a planar effective surface model.

Fig. 1.

Sample schematic representation (a) 3D view of the quasi-3D hybrid structure, with the following dimensions nm, and nm (b) zoom in side view displaying the two layers of periodicity i.e. the upper layer of thin gold film with a nanohole array and the underlying gold nanodisk array, (c) top view scheme of the hexagonal lattice, with the dashed rectangle showing one unit cell of the hexagonal lattice, as modeled in the computation.

Fig. 3.

(a)–(b) Vertical map of E field localization (c)–(d) Horizontal map of E field localization, in the wavelength of resonance. The left column (Figs. (a) and (c)) corresponds to the dielectric PhC at nm and The right column (Figs. (b) and (d)) corresponds to the Quasi-3D structure at nm.

Full 3D finite-difference time-domain (FDTD) simulations employing appropriate periodic boundary conditions^26–28 were performed to precisely model the reflection and transmission spectra, as well as the EM field distributions in and around the metal nanostructure. The simulations were conducted for both TM and TE polarization, however, due to the symmetry of the structure its resonant properties are independent of the incident light polarization (supporting simulations are provided in the Supporting Information). To investigate the optical response of the complex structure and properly understand the origin of its characteristic resonances, we decompose our structure into three distinct structures and simulated them individually as follows: a resist-only configuration (Fig. 2a), a periodic gold double layer configuration suspended in air (Fig. 2b), and the complete hybrid system (Fig. 2c). For each case, both the reflectivity and transmittance were modeled, and the corresponding electric field distributions at the critical wavelengths were determined. The PhC is formed by a hexagonal lattice of holes patterned in SU8 polymer, where a single unit cell of the lattice (Fig. 1c) is a rectangle of length p and in the x, and y direction respectively, giving rise to two different resonant wavelengths (as shown in Fig. 2e), independent of the incident light polarization. We then simulate a periodic double layer configuration in gold, where the top layer is a 2D array of nano-holes in the gold film, and a 2D array of isolated gold disks in the bottom, fully suspended in air. This second system is characterized by a pure plasmonic resonance (Fig. 2f).

Fig. 2.

(a)–(d) Quasi-3D structure and its breakdown into components, as modelled in FDTD simulations (e)–(h) Transmittivity and reflectivity of the corresponding systems.

When the two isolated structures are compiled together, we get the response of the characteristic hybrid-plasmonic system, displaying two resonances at 790 nm and 1060 nm (Fig. 2g). The samples are fabricated on a silicon substrate and have non-pattern SU8 layer at the bottom of the holes. When the whole structure (Fig. 2d) is simulated, the two resonances remain in place and the one at 1060 nm is slightly attenuated (Fig. 2h). The resonance at 790 nm is attributed to a surface lattice resonance (SLR), which results from the coupling between the Rayleigh anomaly (RA) and the localized surface plasmon resonance (LSPR) and it will be the resonance of interest for our nonlinear studies. SLRs are inherently nonlocal collective modes arising from the coherent coupling between LSPR and in-plane diffractive orders of periodic nanoparticle arrays. Unlike purely localized plasmonic modes, SLRs exhibit spatially extended EM field distributions that redistribute optical energy away from the lossy metal–dielectric interface and into the surrounding low-loss dielectric environment. This nonlocal mode character significantly suppresses ohmic dissipation in the metal, which constitutes the dominant contribution to linewidth narrowing in SLRs. While collective lattice interactions can also reduce radiation loss through interference effects, recent studies have shown that dissipation suppression plays a primary role in achieving ultranarrow spectral features. Consequently, the high quality factors associated with SLRs originate from the combined mitigation of dissipation and radiation losses, with dissipation control being the dominant mechanism. This suppression leads to significantly stronger electric field enhancement and localization compared to those of LSPR^29–35. The pronounced dips in the transmission spectrum are caused by light confinement within the holes at specific wavelengths, with the resonance positions being highly sensitive to the geometrical parameters of the structure, namely, the period (p), diameter (d), gold layer thickness (), and hole depth () (the tunability of the structure is further explored in the Supporting Information).

This hybrid metal-dielectric plasmonic resonance not only intensifies the localization of the electric field but also confines it spatially at the metal-air interface. This is evident in the maps of the E field distribution in the vertical and horizontal cross-sections of the structure shown in Fig. 3 where we plot the local electric field distribution inside one single period of the structure, at the wavelength of resonance 790 nm. The value is normalized to the amplitude of the incident E field i.e. E/E0, and the color bar indicates the maximum of the local E field. Figure 3a and b were recorded with a discrete Fourier transform (DFT) power/profile meter placed vertically across the sample, to retrieve the vertical cross section of the E field distribution. Fig. 3c and d were recorded similary, with a DFT monitor placed horizontally across the sample. In case of the resist-only PhC configuration, the E field is largely localized in the hole, both in vertical (Fig. 3a) and horizontal (Fig. 3c) cross-sectional view. The comparison between the dielectric only PhC (Fig. 3a,c) and the hybrid metal–polymer structure (Fig. 3b,d) shows that the introduction of the gold layers completely reshapes the field distribution inside the volume. This strong spatial localization at the plasmonic interface promotes stronger light–matter interactions at the metal-air interface, thereby enhancing the nonlinear dynamics at the nanoscale. A comparison of Fig. 2g and h further shows that adding the SU8 layer and the silicon substrate reduces the overall transmission but leaves the reflective spectral features–including the plasmonic resonance–essentially unchanged. This indicates that the polymer and substrate act primarily as passive dielectric supports, while the resonant field localization and the resulting THG enhancement are governed almost entirely by the metal geometry and the metal–air interfaces.

Sample fabrication

We present a simple yet robust fabrication method based on soft-imprinting (see Fig. 4)³⁶. Silicon chips were first cleaned in ultrasonic baths of acetone and isopropyl alcohol for 5 min each. Subsequently, the SU8 photoresist (MicroChem 2000.5) was spin coated at 2000 rpm for 30 s and soft baked at 60C, resulting in a uniform layer approximately 600 nm thick.

Fig. 4.

(a) Schematic representation of the fabrication process. (b) Real image of the sample showing the periodically patterned and the unpatterned part (c) Scanning electron microscope (SEM) image of the sample.

The SU8 layer was then patterned using a hybrid soft PDMS–hard PDMS stamp featuring pillars arranged in a hexagonal lattice. Imprinting was performed at 90C under a pressure of 2 bar for 30 s, followed by demolding at 50C. This imprinting process created holes in the resist with a diameter of approximately 367 nm, a depth of around 390 nm, and a center to center distance of 800 nm.

After patterning, the nanostructured resist films were exposed to UV light for 10 min to induce crosslinking, and then post-baked at 150C for 30 min. Finally, a 50 nm gold layer was deposited using a thermal evaporator (MBraun). This directional deposition coated both the top surface and the recessed regions with gold, while leaving the nanohole sidewalls uncoated, thereby completing the fabrication of the plasmonic nanostructures. Figure4b shows a picture of the sample studied and Fig. 4c shows the scanning electron microscope image of the sample (top view).

Experimental setup for the measurement of THG

To efficiently detect the THG from the nanostructures, we constructed the setup shown in Fig. 5a. The setup allows us to measure the efficiency of power conversion from the incident pump to the generated TH frequency, defined as , ranging from down to . The light source is a tunable Ti:Sapphire femtosecond laser operating around 800 nm with a pulse duration of approximately 170 fs (at full-width half maxima), a repetition rate of 76 MHz, and an average power of 1 W. The Ti:Sapphire laser could be tuned only within a narrow range of approximately nm around 800 nm. This tunability allowed us to scan across the resonance near 790-800 nm but did not permit access to the second resonance located near 1060 nm. Moreover, as shown in Fig. 2h, the 1060 nm mode is attenuated once the polymer layer and silicon substrate are included, leading to possibly reduced field enhancement. For these reasons, the nonlinear measurements were performed around 800 nm, where both the experimental source and the resonant response of the structure are optimal. A half-wave plate at the laser output controls the polarization (TE or TM) of the pump beam, while a long-pass filter eliminates any spurious nonlinear signals generated by other optical components along the setup. The pump beam is focused on the sample using a plano-convex lens with a focal length of 10 cm to achieve intensities between 1 and 4 GW/cm. The gold samples are mounted on an x–y–z translation stage, which is fixed to a motorized rotary support that adjusts the angle of incidence with a precision of .

Fig. 5.

(a) Schematics of the experimental set-up used to measure reflected third harmonic signals generated by the gold grating as a function of angle of incidence, polarization, and incident wavelength. (b) Schematic representation of to E field localization and THG at normal incidence (c) setup modification to detect the THG at normal or near normal incidence.

Figure 5a also illustrates the TH detection arm, which consists of an anti-reflection coated (UV-enhanced) collimating lens, two mirrors acting as ”ultrafast harmonic separators” (reflecting the THG wavelength while allowing the pump wavelength to pass), and a narrow bandpass filter that transmits primarily around the TH frequency while nearly completely attenuating the pump radiation. A Wollaston polarizer then separates the TM and TE polarization components of the TH signal for simultaneous detection, and a photomultiplier tube (PMT) is used to detect the harmonic signals. Additionally, a chopper placed immediately after the input laser modulates the beam with a square-wave profile to facilitate signal detection.

A comprehensive calibration procedure accounting for the transmission characteristics of each optical component as well as the wavelength-dependent responsivity of the PMT allows us to accurately estimate the conversion efficiencies as the ratio of the TH energy to the energy of the incident pump beam. The entire detection system, which is the most critical part of the setup, is mounted on a rotary platform that enables a precise setting of the detection angle for reflection measurements. A detailed alignment and calibration process was also carried out for this detection setup. To calculate the conversion efficiencies, the transmittance of the filters, lenses, and mirrors, as well as the responsivity of the detectors placed after the sample, were carefully accounted for. We also verified that the high average excitation levels did not induce cumulative thermal effects or long-term degradation. During extended measurements (several hours), we monitored the resonance position, linewidth, and THG output power and observed no measurable spectral drift, broadening, or reduction in signal. Optical inspection of the sample after the experiments revealed no visible damage. These observations confirm that the metasurface operates stably under the excitation conditions used in this work. Gold, Su8 or Si, neither of these materials oxidize or deteriorate over time, if stored in a cool and dry place, so the structure is robust and the linear and nonlinear properties will remain unperturbed over time.

The gold nanohole structure exhibits its sharpest resonance at normal incidence, while increasing the angle broadens the resonance and reduces its depth (Supplementary Fig. S5). Additionally, in our previous study on SHG and THG from 20 nm and 70 nm gold nanolayers, we observed that the emission from the bare metal displayed an angular dependence, favoring maximum THG at normal incidence³. Consequently, our current work focuses on the experimental detection of the THG emitted from the periodic quasi-3D gold structure, induced by the plasmonic resonant field localization, and compares it to that of a 50 nm thick gold layer, to precisely quantify the THG enhancement.

To capture the TH signal at normal or near-normal incidence (Fig. 5b) while retaining the core components of the setup, we modified our detection system by incorporating a D-shaped UV-enhanced mirror. Experimentally, we pump the structure at a small but nonzero angle () for two practical reasons. First, pumping at exactly would direct the reflected pump beam straight back into the Ti:Sapphire laser cavity, which destabilizes the oscillator or damages internal optics. A slight tilt prevents back reflection while still maintaining near normal incidence and the lowest possible angle we could pump our sample was at . In this configuration, the D mirror was used to redirect the reflected beam into the detection arm. As depicted in Fig. 5c, this mirror is designed to operate at a very small angle, ensuring that the path of incident light remains undisturbed. The D mirror performs best at 45, where it maximizes the reflection of the UV signal and minimizes the reflection of the 800 nm pump. During the calibration process and the precise calculation of TH conversion efficiencies, the reflection characteristics of the D mirror were carefully accounted for. Second, as mentioned above, at small angles because the resonance remains sharp and well defined, hence the nonlinear response is maximized. At larger angles, scattering increases and the resonance broadens rapidly, reducing the field enhancement and therefore the THG efficiency.

Results and discussion

Figure6a displays a narrow plasmonic resonance centered at 790 nm. The theoretical spectral response in reflection was computed using full 3D FDTD simulations^26–28, and the experimental spectrum-recorded at near-normal incidence with TM-polarized light, shown as the red continuous curve, is in excellent agreement with the theoretical prediction (black dashed curve).

Fig. 6.

(a) Plasmonic resonance centered around 790 nm at normal incidence for the fundamental beam; (b) Simulated and experimentally detected spectral profile of the resonant THG enhancement (left y-axis) and THG conversion efficiency (right y-axis) around the wavelength of resonance; (c) Simulated and experimentally detected angular profile of the resonant THG enhancement (left y-axis) and THG conversion efficiency (right y-axis) at several near zero angles of incidence.

The gold coating is thick enough that the transmission through the sample is nearly zero, as confirmed by both simulation and experiment. The depth and position of the resonance depend critically on several geometrical parameters, including the period (p), diameter (d), and the depth of the holes (), as well as the thickness of the deposited gold layer (). Notably, the experimental resonance linewidth is broader than the simulated one, likely because the excitation source deviates slightly from an ideal plane wave as it propagates through free space before reaching the sample, as well as the imperfections in the sample post fabrication.

One of the main aims of this study is to quantify the THG enhancement factor as precisely as possible, compared to plain gold. In laboratory environment, we recorded THG generated from the patterned and unpatterned part of the sample simultaneously, under the same laboratory conditions. As indicated in Fig. 4a, the last step of the fabrication was thermal deposition, which deposits an uniform 50 nm layer of gold on the whole dielectric structure, the elevated parts, the subdued parts, as well as some region outside the structured dielectric. The regions are indicated in Fig.4b, where the outer square is a region of sputtered gold flat layer, its thickness is well controlled by the thermal evaporator machine, and in case of our samples is 50 nm. As indicated in Fig. 5a, the sample is mounted on an x-y-z translation stage, so that the we can focus the beam inside or outside the structured material, as necessary. To corroborate, we carried out two separate sets of simulations, for spectral characteristics of THG from flat layer of 50 nm gold and THG from the structured gold, thus comparing them and obtaining the spectral curve of the enhancement. The theoretical prediction, also calculated via FDTD^37–39 and represented by the black dotted curve, shows a maximum enhancement factor of 108 (Fig. 6b), with respect to the THG from a plain layer of gold of nm. The conversion efficiency is highly sensitive to the peak power, pulse width, and shape of the pump pulse. In our nonlinear simulations, the source amplitude was defined to match the average pump laser intensity recorded experimentally: Amplitude = V/m with the source pulse duration set to fs. The conversion efficiency () is defined as the ratio of the total reflected TH pulse energy to the total incident pump pulse energy. Because the excitation source delivers ultrashort pulses that may undergo spatio temporal dispersion and pulse broadening, the peak intensity at the sample is not uniquely defined. Intensity based efficiency metrics are therefore appropriate mainly for CW illumination, whereas energy based definitions remain robust for ultrafast pulses and provide a consistent measure of the nonlinear conversion. depends on the average excitation intensity and the third-order nonlinear susceptibility () of gold. To account for this, a wavelength-dependent database for bulk gold was incorporated into the FDTD database. Fig. 6b also illustrates the spectral response of the resonant THG emission, which is corroborated by our experimental measurements taken at near-normal incidence by tuning the Ti:Sapphire laser pump around the resonance wavelength. The experimentally retrieved resonant THG from the quasi-3D structure, represented by red dots, indicates a maximum enhancement factor of 98, with respect to the experimentally detected THG from the unpatterned layer of gold (Fig. 6b purple curve) under the same laboratory conditions. To further substantiate the polarization-independent behavior, we performed additional simulations under TE-polarized excitation across the same spectral range used for TM illumination. In Fig. 6b we plot the resulting TE-polarized THG efficiencies as the green dotted curve with square markers, to show excellent agreement with the TM-polarized response near the plasmonic resonance. The close overlap between the two datasets confirms that the quasi-3D architecture supports polarization-agnostic field enhancement, consistent with the presence of longitudinal field components for both polarizations inside the vertically structured plasmonic crystal. We also note that the classical concept of skin depth applies only to semi infinite metals. In ultra-thin or nanostructured metallic layers, interference and boundary conditions dominate the field distribution, rendering the skin depth picture inadequate. Previous theoretical and experimental studies^40,41 have shown that the effective third order nonlinearity of gold is strongly surface dominated and reaches its maximum for thicknesses around 5 nm - well below the nominal 20-30 nm skin depth at 800 nm. The nonlinear polarization is confined to a few nanometers at the metal surface, arising primarily from bound electron contributions. Consequently, even in a 50 nm film, THG originates almost entirely from the surface region. The comparison to a 50 nm flat gold film is therefore appropriate, as both structures share the same surface dominated mechanism, while the quasi-3D metasurface benefits from resonant field localization that enhances the nonlinear overlap.

Additional measurements were conducted to assess the resonant behavior of the THG as the angle of incidence approaches normal incidence. Fig. 6c presents three sets of experimental data: THG efficiency from a plain 50 nm gold layer (violet curve), THG efficiency from the quasi-3D structure when illuminated by the pump at 800 nm (blue curve), and THG efficiency from the quasi-3D structure when illuminated by the pump at 791 nm (red curve). As observed, we tend to approach the resonant THG peak as we approach normal incidence. Experimentally we are able to precisely retrieve the resonant THG peak at 2 angle of incidence, which shows a maxima at 791 nm, slightly red shifted from the 790 nm resonance at strictly normal incidence. The simulated curve of the resonant THG peak (black dotted curve with round markers) is slightly wider and shows a smoother transition into and out of the resonance, while the red curve shows a narrower, more abrupt peak. This is due to the diffraction and losses in the real sample, and as soon as we move out of the resonance, we abruptly lose the quality of the resonance. Experimentally, we also retrieve the resonant THG curve for a further red-shifted pump wavelength of 800 nm, which shows a maxima at 4 angle of incidence (blue curve) and its corresponding simulated curve represented by black dotted curve with square markers. In all four curves, as the angle of incidence increases and we move out of the resonance, the THG efficiency decreases significantly, while the THG from plain layer of gold shows no such significant transition. The angular dependence of the THG efficiency in Fig. 6c arises from the same mechanism that governs angle dependent shifts in a Fabry–Pérot cavity: as the incident angle increases, the in plane wavevector changes and the SLR resonance detunes from the pump wavelength. For experimental reasons mentioned in section4, the pump beam is incident at a small angle () and this slight tilt also coincides with the maximum nonlinear response, since the resonance remains sharp near normal incidence. As the angle increases further, the quality of the resonance reduces rapidly, leading to a reduction in field enhancement and THG efficiency.

The exceptional sensitivity of the nanohole structure, which also makes it an excellent sensing platform^22–25, seems to limit its THG efficiency, compared to the simple full metal structure (example a periodic gold grating that we studied⁸). In configurations designed to harness the third-order nonlinearities of gold, a gold grating typically offers robust electric field confinement at the trench corners⁸, substantially enhancing light-matter interactions. This is primarily because THG relies on the field penetration depth to exploit the bulk third-order nonlinearity () of the metal. Although plasmonic resonances intensify the electric field at the surfaces and corners of the holes or disks, most of the field still extends into the interior of the holes (Fig. 3d). Consequently, the maximum field intensity does not effectively overlap with the gold, resulting in significantly lower THG signals. Although SU8 and silicon possess nonzero third-order susceptibilities, their contribution to the measured THG is negligible for two reasons. First, the simulated field distributions show that the resonant electric-field maxima occur at the gold–air interface, where the plasmonic mode is tightly confined. SU8 experiences significantly weaker field enhancement, and the silicon substrate is largely screened by the polymer layer. Second, the magnitude of for gold under ultrafast excitation is substantially larger than that of SU8 or silicon when weighted by the local field intensity. Using representative literature values and the simulated field-overlap integrals, we estimate that more than 90% of the nonlinear polarization originates from the gold layer. This discussion contributes to our understanding of these complex hybrid structures under resonant illumination conditions, and opens the possibility to further improve the sample configuration for larger nonlinear generation.

This conclusion is consistent with our earlier theoretical and experimental studies on thin metallic layers. In particular, refs.⁴⁰ and⁴¹ demonstrated that the effective third-order nonlinearity of gold is strongly surface-dominated and reaches its maximum for ultra-thin layers on the order of 5 nm-much thinner than the nominal skin depth. These works show that the nonlinear polarization is concentrated within a few nanometers of the metal surface, arising primarily from bound-electron (Lorentz) contributions rather than bulk Drude terms. The strong field localization at the metal–air interface in our quasi-3D structure therefore naturally leads to a gold-dominated THG response. A simple order-of-magnitude estimate further supports this interpretation. Using for gold under femtosecond excitation and for SU8 and silicon in the NIR, and weighting these values by the simulated field-overlap integrals, we find that the gold contribution exceeds that of SU8 by more than two orders of magnitude and that of silicon by more than three. Thus, the nonlinear response is overwhelmingly governed by the plasmonically enhanced fields at the gold interfaces. Nevertheless, varying the geometric parameters such as using square or round holes, adopting square or hexagonal lattice periodicities, and modifying the hole depth and diameter-can lead to different outcomes. This sensitivity and tunability of the plasmonic resonance open up broad possibilities for the design, characterization, and fabrication of these structures, especially in sensing applications (for example, detecting a biomolecule in a solvent).

Figure 6 shows the measured enhancement of the THG signal emitted at the angle of reflection. However, the periodicity of the structures can lead to constructive interference of the generated TH in specific directions, producing diffraction orders and making it challenging to capture the total emitted signal. In our structure, the pump wavelength is effectively absorbed, but the generated third harmonic at 263 nm, which is smaller than the periodicity of the structure, is consequently diffracted. Figure 7a presents a SEM image of the sample and Fig. 7b presents the corresponding hexagonal diffraction pattern, obtained when the structure is artificially illuminated with the detection wavelength. In previous work with a diffraction gold grating, we confirmed that these diffracted harmonics were emitted at the angles predicted by linear diffraction of the generated harmonics⁸. Taking this into account, the FDTD calculations indicate that normal-incidence 263 nm light from our quasi-3D structure is diffracted at an angle of 56. These calculations also provide the intensity ratio of the central spot to the first diffracted spot, which, for our specific hexagonal pattern, is a factor of 2 as shown in Fig. 7c. When the total THG is considered - combining the zero-order specular emission with all diffracted orders - the overall enhancement factor is approximately 400 times greater than that of a bare gold layer.

Fig. 7.

(a) Top-view SEM image of the hexagonal lattice sample (b) Experimental verification of the diffraction pattern of the generated higher harmonic (c) Simulated diffraction pattern of the generated higher harmonic. The amplitude of the central spot is two times the amplitude of the first order diffracted spots.

The successful detection of extremely low-intensity harmonic generation deep in the UV range indicates that further structural optimization could significantly boost process efficiencies. Since the third-order nonlinearity () of gold is an intrinsic bulk property, EM field penetration into the metal is essential to enhance light-matter interactions. In our current structure, however, the electric field is predominantly confined to the metal-air interface, with minimal penetration into the metal. This can be improved by strategically positioning nonlinear material nanoparticles in the nano-gap hotspots of dimers^42–44 or by embedding HHG materials within gold shells or rings as demonstrated in⁴⁵. These configurations achieve efficient THG by ensuring an optimal spatial overlap between the plasmonic enhancement and the nonlinear material. Additionally, such advanced experimental systems enable a detailed analysis of the individual contributions from the polymer and the metal, thereby shedding light on the origins of the enhanced nonlinear response of the hybrid system.

Alternatively, one could explore the ”ultra-thin metal” regime, where the metal thickness is of the order of its skin depth - ensuring that the spectral position of the resonantly excited SP waves aligns with the absorption maximum^46–49. This distinction between thick and ultra-thin metal regimes is pivotal, as it directly affects the structure’s ability to absorb and localize light. In the following section, the quasi-3D structure is remodeled with comparable to or less than the skin depth of the metal (Fig. 8a), in stark contrast to the widely studied configurations of thicker layers. Theoretical predictions for light propagation in a quasi-3D structure with an ultra-thin gold layer reveal an extraordinary absorptivity of up to . While previous studies on grooved structures with thick or semi-infinite metal layers infer SP excitation by monitoring spectral resonances in reflection or transmission, ultra-thin structures exhibit resonantly excited SP waves that coincide with the absorption maximum. This resonant absorption greatly enhances the EM field concentration and light penetration inside and throughout the bulk of the metal layer, and takes advantage of the bulk third-order nonlinearity () of the metal, thus proving to be a very promising source of THG.

Fig. 8.

(a) Quasi-3D structure with ultra-thin gold, as modelled in FDTD simulations (side view) (b) spectral resonances corresponding to the absorption maxima (c) Transmitted and (d) Reflected THG efficiency from the ultra-thin quasi-3D gold structures. The figures represent the resonant THG spectrum and the corresponding enhancement factors with respect to equivalent thickness of unpatterned gold, as simulated from the structures with of 10, 12 and 14 nm.

In structures with ultra-thin layers of gold, nonlinear generation is enhanced through two primary mechanisms. First, a gold nanolayer with a thickness of 10 to 15 nm already yields an order of magnitude larger TH signal than a 50 nm layer, because a 50 nm layer essentially acts as a mirror, reflecting much of the incident light and confining THG to reflection only. In contrast, an ultra-thin layer absorbs light more efficiently, harnessing the enhanced field concentration and penetration throughout its entire bulk to produce THG in both transmission and reflection. Secondly, periodic patterning of these ultra-thin metals shows their corresponding strong plasmonic resonance, which then furthermore boosts the EM field localization in the wavelength of resonant absorption.

The transition from the thick metal to the ultra-thin metal regime is gradual and can be monitored by varying , while keeping the other geometrical parameters of the structure fixed. A sweep of from 5 to 20 nm shows that the plasmonic resonance corresponding to the resonant absorption in the 800 nm range reaches its maximum for of 10, 12 and 14 nm (Fig. 8b). Next we simulate THG from each structure, considering that the structures are illuminated by a pump laser tunable around the structure’s own wavelength of resonance, and the other characteristics of the pump laser fixed as mentioned in section4. Figure 8c and d represent our theoretical predictions of the spectral profile of the resonant THG from the structures in transmission and in reflection respectively, corresponding to the quasi-3D structure with as of 10 nm (green curve), 12 nm (red curve) and 14 nm (blue curve), considering the other geometrical parameters of the structure fixed and considering in this case a transparent substrate. As in ultra-thin metal regime, the structures produce THG in both transmission and reflection, so it is important to fabricate them on a transparent substrate, so that both reflected and transmitted light can be experimentally retrieved to estimate the total THG. Similarly, from the theoretical point of view it is necessary to simulate the generated third harmonic in both reflection and transmission. Figure8c and d represent our theoretical predictions of the spectral profile of the resonant THG from the structures in transmission and in reflection respectively. In each graph, the curves correspond to the quasi-3D structure with as of 10 nm (green curve), 12 nm (red curve) and 14 nm (blue curve). The other geometrical parameters of the structure are kept fixed and the substrate is considered to be transparent. In each graph, the left y-axis respresents the resonant THG enhancement factor with respect to that of a plain gold layer of the corresponding thickness, and the right y-axis represents the THG conversion efficiencies, around the wavelength of resonance.

Conclusion

In this paper, we present and study resonant THG from a quasi-3D gold hybrid plasmonic metasurface. We performed a set of simulations to understand and tune the linear and nonlinear resonant properties of the structure at or near zero angle of incidence, as well as a series of experiments to corroborate those results regarding the shape, spectral width, and peak amplitude of the spectral response. Our sophisticated detection system and calibration procedures enable accurate experimental verification of the THG efficiencies emitted from the resonant quasi-3D gold structure, as well as its enhancement with respect to simple plain layer of gold. When the total THG efficiency - defined as the sum of the zeroth and first diffraction orders - is scaled to the THG reference signal from an unpatterned region of the same gold sample (measured under identical conditions), an enhancement factor of is obtained. Numerical modeling quantitatively captures the observed optical properties of these architectures and reveals the complex EM field distributions around their multilevel nanostructured features, which in turn drive the enhanced nonlinear interactions at the metal surface. It is important to note that unlike convensional observations, we are measuring the real efficiencies of conversion from the pump to the third harmonic, directly in terms of incident and generated power. Secondly, our hybrid quasi-3D metasurface already proves to be more efficient in light conversion than more complicated structures, such as¹⁰ and¹³, each of which is technologically challenging to fabricate, however show only one order of magnitude enhancement. We note that while the enhancement factor of reported here is lower than the extreme values achievable in optimized periodic gold gratings, where enhancements exceeding three orders of magnitude have been demonstrated experimentally, and more than four orders of magnitude predicted with minor geometric adjustments (Ref.⁸), it is exceptionally large within the class of quasi-3D plasmonic structures. The present result therefore represents a significant improvement over existing volumetric or vertically structured metasurfaces, while simultaneously offering polarization independent operation, which is not attainable in typical planar 1D or 2D geometries.

Substituting our 50 nm thick Au layer by ultra-thin gold layers would open the door to exploiting THG emission in transmission and its further enhancement. To achieve this, the hybrid structure must be fabricated on a substrate that is transparent to both the pump wavelength and the THG wavelength. However, finding a suitable substrate is challenging because most optical components/materials are highly absorptive in the deep UV range and is part of future work.

This study challenges the notion that a more complex metasurface inherently produces higher nonlinearity. In reality, the successful generation and detection of higher-order harmonics depend on a detailed understanding of the plasmonic structure, its resonant properties, and the nonlinear electron dynamics at the nanoscale. Such insights are fundamental for developing coherent and efficient nanoscale UV/DUV/EUV light sources that facilitate miniaturization and integration into portable devices. Moreover, many photonic devices require operation at small angles of incidence. The precise engineering of metasurface geometry, combined with modern fabrication methods, promises highly tailored plasmonic structures capable of producing compact high-frequency light sources. These structures can be embedded with nonlinear components to achieve beam deflection, metalensing, meta-holography, and even the generation of orbital-angular-momentum beams.

Our experimental findings, corroborated by rigorous EM field simulations, establish this volumetric metasurface as a robust, real-world platform for deep-UV light sources, nonlinear sensors, and emerging quantum photonic applications. This genuinely three-dimensional architecture paves the way for reconfigurable, multi-polarization nanophotonic devices that fully leverage the spatial richness of light–matter interactions at the nanoscale. Ultimately, multifunctional plasmonic materials that enable dynamic manipulation of light properties-such as amplitude and polarization-at the nanoscale are critical for the advancement of future all-optical nanotechnologies based on active photonics.

Author contributions

All authors contributed to the sample design. A.C.R. and A.M. fabricated the samples. S.M., C.C. and J.T. conducted the experiment(s) and analyzed the results. S. M. performed the numerical simulation(s) with supervision of all authors. C.C. and A.M. supervised and led the scientific collaboration. All authors contributed to the writing and review of the manuscript.

Funding

SM, JT, and CC acknowledge the Spanish Agencia Estatal de Investigación from Ministerio de Ciencia, Investigación y Universidades (project PID2023-148620NB-I00 granted by MICIU/AEI/10.13039/501100011033 and FEDER, UE) and US Army Research Laboratory Cooperative Agreement N◦ W911NF-22-2-0236 issued by US ARMY ACC-APG-RTP. S. M. acknowledges predoctoral grant FPI-UPC 2022, funded by Universitat Politècnica de Catalunya (Government of Catalunya). M. A. V. thanks NATO SPS Grant no. G5984 - RESPONDER for financial support. This work has received funding from the Spanish Agencia Estatal de Investigación/ Spanish Ministry of Science and Innovation (AEI/MCIN) through grants PID2022-141956NB-I00 MCIN/AEI/10.13039/501100011033 (OUTLIGHT), and CEX2023-001263-S (MATRANS42, Spanish Severo Ochoa Centre of Excellence program) and from the Generalitat de Catalunya (2021-SGR-00444). A.C.R. acknowledges support from the postdoctoral fellowship program Beatriu de Pinós 2022 BP 00083, funded by the Secretary of Universities and Research (Government of Catalonia).

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-39260-6.