Plasmonics, a key element of nanophotonics, utilizes the interaction between electromagnetic fields and free electrons in metallic nanostructures to confine light to sub-wavelength scales. This phenomenon, driven by surface plasmon resonances, generates intense, localized electromagnetic fields known as ‘hot spots’ that significantly enhance light–matter interactions [1–3]. Such enhancements are critical for a variety of applications, including surface-enhanced Raman spectroscopy (SERS), nonlinear optics, biosensing, single-molecule detection, photothermal therapy, and quantum nanophotonics [4–6]. The ability to manipulate light at the nanoscale has made plasmonics a transformative field in both fundamental science and advanced technology, impacting the next generation of sensors, photonic devices and energy harvesting systems.

Among plasmonic architectures, nanostructures with closely spaced metallic elements—such as bowtie antennas, dimer gaps and particle-on-layer configurations—are particularly effective in generating strong field enhancements due to the coupling of localized surface plasmons across narrow dielectric gaps [7–9]. These geometries enable robust in-plane near-field interactions, leading to increased electromagnetic field intensities within confined volumes. Extensive research has focused on optimizing design parameters such as gap distance, symmetry, apex geometry and periodicity to improve resonance quality and spectral tunability [10–12]. These efforts have expanded the scope of plasmonic enhancement beyond traditional spectroscopy to emerging technologies such as spacers, metasurfaces, and quantum photonic devices [13–15].

Triangular nanodisks have proven to be particularly promising candidates for plasmonic applications due to their sharp corners and edges, which serve as natural field concentrators. Compared to circular or elliptical nanostructures, triangular shapes offer superior electromagnetic confinement and spectral tunability, which is determined by parameters such as apex angle and side length [12, 16, 17]. For example, Li et al [18] have shown that triangular nanodisks in a metal–insulator–metal (MIM) configuration achieve electric field enhancement factors (|E|/|E0|) of over 220, exceeding the performance of circular and square counterparts. Similarly, Atefeh and Masoud [19] and Roa et al [20] reported enhancement factors from 188 to over 1200 under certain polarization conditions, highlighting the potential of triangular geometries. However, these studies often rely on complex fabrication methods such as electron beam lithography (EBL), focused ion beam milling or nanoimprint lithography (NIL), which are inherently low throughput, expensive and not suitable for large-scale production. In contrast, alternative scalable methods like block-copolymer lithography [21] and NIL [22] have shown promise for anisotropic plasmonics, though they often require additional steps for MIM integration, unlike our direct colloidal approach. These limitations pose a significant obstacle to the integration of high-performance plasmonic devices into practical applications, especially those that require large-scale uniformity and cost efficiency.

Colloidal lithography has recently gained attention as a scalable, cost-effective alternative for the fabrication of nanostructured surfaces. By using self-assembled colloidal particles such as polystyrene or silica spheres as masks or templates, this technique enables the fabrication of periodic nanostructures without the need for complex lithographic techniques [23–25]. While it is widely used for the fabrication of circular or hexagonal structures, the application of colloidal lithography to anisotropic structures such as triangular nanodisks is still poorly explored. While colloidal lithography excels in producing symmetric circular or hexagonal patterns due to the natural spherical packing of colloids, achieving anisotropic triangular shapes is challenging because it requires precise control over interstitial spaces and etching to form sharp edges without defects, unlike previous works limited to isotropic geometries Moreover, few studies have systematically validated the electromagnetic behavior of such colloidally fabricated triangular geometries through both simulation and experimental approaches, leaving a critical gap in understanding their performance and scalability.

This work addresses this open challenge by designing, simulating, fabricating and experimentally validating large-scale periodic arrays of triangular gold nanodisks using colloidal lithography. We hypothesize that these structures can achieve electric field enhancements comparable to those generated by more complex fabrication methods, thus providing a scalable platform for plasmonic applications. Our approach combines FEM (finite element method) simulations with COMSOL Multiphysics to analyze the electric field distribution, absorption spectra and the influence of dielectric gap thickness on field enhancement, with experimental fabrication and optical characterization. The nanostructures are fabricated with a monolayer of self-assembled nanospheres as a vapor deposition mask, followed by metal deposition and lift-off, which ensures scalability and cost efficiency.

Our results show that the triangular nanodisk arrays exhibit strong near-field confinement, stable-angle plasmonic resonances and polarization-independent behavior, achieving a maximum electric field enhancement of |E|/|E0| ≈ 310 within a dielectric gap of 10 nm. These results confirm the effectiveness of colloidal lithography in the fabrication of high performance plasmonic structures and emphasize its potential for applications in plasmon enhanced sensing, spectroscopy and nanophotonic devices. By bridging the gap between performance and manufacturability, this work paves the way for large-scale integration of plasmonic technologies into real-world applications and provides a versatile platform for future research and device development. In summary, while triangular nanoantennas are known to provide superb field enhancement, they have not been realized with scalable fabrication or experimentally validated in large arrays. This study addresses that gap by demonstrating triangular MIM nanodisk arrays via colloidal lithography and confirming their high performance through both simulation and experiment.

1.1. Simulation methodology

To investigate the optical performance of triangular gold nanodisk arrays fabricated by colloidal lithography, three-dimensional electromagnetic simulations were performed using the FEM within the Wave Optics module of COMSOL Multiphysics. This platform was selected for its proven accuracy in modeling plasmonic systems, as demonstrated by numerous peer-reviewed studies showing strong agreement between simulated and experimental results [26, 27]. The simulations aimed to validate the high electric field enhancement and robust plasmonic resonances of the proposed nanostructures to support the development of scalable, cost-effective plasmonic devices for enhanced light–matter interactions, as described in the Introduction.

1.2. Simulation setup and geometry

The simulation domain was designed to replicate the experimental structure. It consists of a unit cell representing an infinite hexagonal array of triangular gold nanodisks. These nanodisks were located above an 80 nm thick gold layer, separated by a dielectric spacer layer of aluminum oxide (Al₂O₃) with different thicknesses of 10 and 40 nm. The entire structure was supported by a glass substrate (SiO₂, refractive index ∼1.45). The triangular nanodisks were defined with a side length of approx. 170 nm, which was derived from a nanohole mask with a diameter of 500 nm. This corresponds to the colloidal lithography process in which self-assembled polystyrene nanospheres create triangular interstices for metal deposition. This multilayer MIM configuration was designed to support strong localized surface plasmon resonances (LSPRs) within the dielectric gap and at the metal–dielectric interfaces, maximizing near-field confinement.

Gold was chosen for its low optical losses in the visible and near infrared spectrum (400–1500 nm) and its chemical stability, which ensures compatibility with experimental fabrication and long-term reliability of the devices. The optical properties of gold were modeled using wavelength-dependent refractive index data from Johnson and Christy [28], allowing accurate representation of its dispersion over the simulated wavelength range. The 2 nm Cr adhesion layer between the Au and substrate was not included in simulations, as its negligible thickness results in minimal effects on the optical response (absorption <1% in the 400–1500 nm range). Aluminum oxide was selected as the spacer material due to its high refractive index (∼1.76), which improves electromagnetic field confinement, and its compatibility with precise deposition techniques such as atomic layer deposition (ALD) and sputtering, allowing uniform and controllable layer thicknesses critical for consistent plasmonic performance.

To simulate light–matter interactions, a linearly polarized transverse magnetic (TM) plane wave was introduced from the upper boundary, propagating along the z-axis, with the magnetic field aligned along the x-axis. To evaluate the polarization dependence of the structure’s optical response, additional simulations were conducted using transverse electric (TE) polarization, where the electric field vector is oriented perpendicular to the TM case. This configuration was optimized to excite in-plane plasmonic modes localized at the sharp corners and edges of the triangular nanodisks, where the strongest field enhancements are expected due to the lightning rod effect and charge accumulation [29]. In fact, another implicit assumption is perfectly sharp triangle corners; in reality the corners may be slightly rounded, but given our fine mesh and the scanning electron microscopy (SEM)-confirmed sharp features (see figure 2), this should not significantly affect the results. To account for potential corner rounding in fabrication, additional simulations with rounded corners (radii 5–10 nm, based on SEM analysis) showed <5% variation in field enhancement and resonance positions compared to ideal sharp corners, confirming minimal impact. The wavelength range of 400–1500 nm was chosen to cover the visible and near-infrared region, which is relevant for applications such as SERS and biosensing. In order to assess the polarization independence, additional simulations with TE polarization were carried out, which confirmed consistent resonance behavior.

Periodic Floquet boundary conditions were applied along the x- and y-axes to replicate the infinite hexagonal array, ensuring accurate representation of the periodic nanostructure. Perfectly matched layers (PMLs) were implemented at the top and bottom boundaries to absorb the outgoing radiation and eliminate unwanted reflections, to maintain numerical accuracy. The simulation domain was carefully meshed to resolve the high field gradients near the dielectric gap and metal interfaces. Sub-nanometer mesh elements (down to 0.5 nm) were used in these regions to ensure numerical stability and precise resolution of field enhancements, while coarser meshing was applied elsewhere to optimize computational efficiency. The sub-nanometer mesh (0.5 nm) is applied near the dielectric gap and metal interfaces, covering a 10–20 nm region. Mesh density was verified through convergence tests, showing <1% variation in field enhancement and resonance wavelengths upon further refinement, ensuring accuracy without excess computation. Mesh convergence tests were performed to ensure that the field enhancement and resonance wavelengths had negligible change with further mesh refinement. All-important simulation parameters are listed in table 1.

Table 1. Key simulation parameters.

ParameterDescriptionSimulation toolCOMSOL Multiphysics, wave optics module (FEM)StructureHexagonal array of triangular Au nanodisks on Au layer with Al₂O₃ gap layerNanodisks dimensionsSide-length = 70 nm (defined by 500 nm nanohole mask) Thickness = 40 nmMetal layer80 nm AuGap layer10–40 nm Al2O3 (variable)SubstrateGlass (SiO₂, n ≈ 1.45)Wavelength range400–1500 nmIncident lightTM-polarized plane wave (z-axis propagation); TE tested for polarization studyBoundary conditionPeriodic Floquet (x, y-axes); PML (top, bottom)Mesh sizeSub-nanometer (0.5 nm) near gap/interfaces; coarser elsewhereOutputAbsorption spectra, electric field distribution

The simulation results were used to guide and validate the experimental fabrication process to ensure that the modeled geometry accurately matched the structures achievable by colloidal lithography. Key assumptions included the ideal periodicity of the nanodisk array and uniform material properties, which may differ slightly under experimental conditions due to fabrication imperfections such as edge roughness or slight variations in nanosphere packing. These assumptions were justified by the high uniformity of the experimental samples, which was confirmed by SEM analysis. The strong agreement between simulated and experimental results, especially for resonance wavelengths and field enhancement trends, underscores the reliability of the FEM approach for this study. The simulated structure is shown in figure 1. Figure 1(a) shows the hexagonal arrangement of triangular gold nanodisks formed by the self-assembly of polystyrene nanospheres with a diameter of 500 nm in the colloidal lithography process. The unit cell is the hexagonal domain in figure 1(a), representing the infinite array. Periodic Floquet boundaries on x- and y-axes ensure phase continuity for Bloch waves, simulating the triangular structure’s periodicity without edge effects. Figure 1(b) shows the multilayer architecture consisting of a glass substrate, an 80 nm thick gold layer, an Al₂O₃ dielectric spacer and the triangular gold nanodisks. ‘The incident light is a TM-polarized plane wave from the top boundary (z-axis propagation). PMLs are at top and bottom to absorb reflections. Electric field intensity is calculated near the dielectric gap and metal interfaces, as shown in the schematic.’

Figure 1. Schematic representation of the simulated structure. (a) Top view showing the hexagonal arrangement of triangular gold nanodisks formed via colloidal lithography. (b) Cross-sectional view illustrating the multilayer architecture: glass substrate, 80 nm gold layer, Al₂O₃ dielectric spacer, and triangular gold nanodisks.

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The fabrication of triangular gold nanodisk arrays was designed to utilize colloidal lithography, a scalable and cost-effective technique, to fabricate large-area plasmonic nanostructures with enhanced light–matter interactions. The process involved substrate preparation, deposition of metals and dielectrics, fabrication of the nanostructures and subsequent characterization to verify structural and optical performance.

The glass and silicon substrates were cleaned by successive rinsing in acetone and isopropyl alcohol (IPA) to remove organic and particulate contaminants and to ensure a flawless surface for the subsequent layers. A 2 nm thick adhesion layer of chromium (Cr) was deposited by thermal vapor deposition using a PVD 75 system under high vacuum conditions (base pressure: 2 × 10−6 Pa) to improve the adhesion between the substrate and the gold layer. Immediately afterwards, an 80 nm thick gold layer (Au) was deposited at a rate of 0.2 nm s−1, with the substrate rotated to ensure uniform layer thickness over the entire surface. The uniformity of the layer thickness was verified by profilometric measurements using a Dektak 150 system, confirming the consistency of the layer, which is critical for reliable plasmonic performance.

To facilitate plasmonic coupling, aluminum oxide layers (Al₂O₃) with a nominal thickness of 10 nm and 40 nm were deposited on the gold-coated substrates by ozone-assisted ALD at 300 °C in a Beneq TFS 200 system. Trimethylaluminum (TMA) and ozone served as metal and oxidizing precursors respectively, allowing precise control of Al₂O₃ thickness and excellent uniformity on the substrate. This precision is crucial for maintaining consistent gap-dependent plasmonic responses, as the thickness of the dielectric spacer directly influences the field enhancement and resonance behavior. Measurements were done with unpolarized light; the triangular lattice yields identical spectra for both polarizations, as confirmed by simulation.

1.4. Nanostructure fabrication via colloidal lithography

The triangular gold nanodisk arrays were fabricated using colloidal lithography, a scalable technique that harnesses the self-assembly of colloidal particles to create periodic nanostructures without the need for complex lithographic methods such as EBL. Monodisperse polystyrene (PS) nanospheres with a nominal diameter of 500 nm (Sigma-Aldrich) were used to form a hexagonally ordered monolayer mask. Prior to assembly, the suspension of nanospheres (originally 10 wt%) was diluted to 2.5 wt% in ethanol and vortexed to achieve uniform dispersion and ensure consistent mask formation. To improve the wettability and cleanliness of the substrate, a 30 min UV-ozone treatment was carried out prior to the transfer of the monolayer to increase surface cleanliness and improve hydrophilicity (surface energy), thereby promoting uniform monolayer formation.

A motorized syringe pump was used to carefully inject the diluted PS/ethanol solution into a container filled with water to facilitate the formation of a tightly packed monolayer at the air–water interface. Once the nanosphere monolayer was formed, it was carefully transferred to the Al₂O₃/Au/substrate stack, which served as a deposition mask. To ensure the reliable formation of a single-layer arrangement of PS nanospheres, the deposition parameters were systematically optimized through preliminary experiments. The concentration and volume of the colloidal suspension, the injection rate of the syringe pump, and environmental factors such as temperature and humidity were carefully adjusted to suppress multilayer formation and minimize voids. The optimized procedure consistently produced a uniform monolayer over large areas, as confirmed by SEM imaging. Importantly, the same single-layer arrangement was reproducibly achieved in multiple independent preparations performed on different days, confirming the robustness and repeatability of the colloidal self-assembly process. Gold was then deposited through the mask by thermal evaporation (thickness ≈ 40 nm, matching the design in simulations), followed by sonication in a suitable solvent to remove the nanospheres, leaving the triangular gold nanodisks behind.

1.5. Characterization

After fabrication, the samples were characterized using SEM to assess structural integrity, uniformity and geometric accuracy, which are critical to confirm the efficacy of the colloidal lithography process. A representative SEM image taken using a ZEISS system at an accelerating voltage of 5.00 kV, a working distance of 4.2 mm and a magnification of 40 000× is shown in figure 2. The image shows a well-ordered hexagonal array of nanostructures that extends evenly over a large area. The triangular gold pattern extends uniformly over areas up to 1 cm2, as verified by SEM imaging. Reflectance spectra were measured on 0.5 cm2 samples, with the spectrophotometer’s beam spot size of ∼1 mm ensuring representative data.

Figure 2. SEM image of the triangular gold nanodisk array, showing a close-packed hexagonal lattice with minimal defects and uniform distribution over the imaged area. The nanodisks appear as circular dots with diameters of 100–120 nm due to imaging resolution.

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The high uniformity in particle size and spacing, along with minimal aggregation or misalignment, confirms that colloidal lithography is a reliable and scalable fabrication method. Although minor irregularities were observed at the edges (likely caused by nanosphere assembly or slight variations during metal deposition) it did not significantly affect the optical performance, as strong field localization was still achieved in simulations. This structural consistency aligns with the goal of producing large-area plasmonic arrays for practical use.

The quantitative image analysis was performed with ImageJ to extract the most important dimensional parameters, such as the size of nanodisks and the periodicity of the lattice. ImageJ analysis of SEM images indicated a nanodisk side length of ∼170 nm, consistent with design values. These values were entered directly into the FEM simulation models to ensure an accurate representation of the physical structures facilitating a tight integration between experimental and numerical workflows. This approach enabled a meaningful correlation between the fabricated geometries and the simulated optical responses, providing a strong validation of the design strategy and supporting the aim of the work to combine simulation and experiment for scalable plasmonic devices. The triangular disks appear somewhat circular at this magnification due to SEM resolution limitations and edge effects, but their true shape and ∼170 nm size is confirmed by image analysis.

The optical response of the nanodisk arrays was measured at normal incidence using a Hitachi UH5700 UV–Vis-NIR spectrophotometer. Because the gold mirror under the disks prevents transmission, we effectively measured reflectance: the spectrophotometer was configured to record the specular reflectance (with a reference mirror/baseline) and the data was normalized to a bare glass substrate for comparison. Resonance features appear as dips in the reflectance spectra (i.e., peaks in absorption). A broadband source covered a spectral range from 190 to 3300 nm and allowed the analysis of plasmonic resonances, especially in the near infrared region, which is relevant for structures with thinner dielectric gaps. Noting this point is necessary that interest is mainly 400–1500 nm (since below 400 nm the Au film is strongly absorbing and above ∼2 µm presumably nothing notable). Transmittance spectra were normalized to a bare glass substrate to isolate the optical response of the nanostructures. The instrument’s high spectral resolution allowed clear identification of resonance features associated with the designed nanodisk geometry.

2.1. Angular dependence of absorptance spectra

Understanding the angular dependence of plasmonic resonances is crucial for assessing the robustness and practical applicability of the nanostructure in real-world scenarios, where the angle of incident light may vary. The simulated absorptance spectra for the triangular nanodisk array with a 10 nm Al₂O₃ dielectric gap were analyzed as a function of wavelength (400–1500 nm) and angle of incidence (0°–80°) under TM-polarized illumination.

Figure 3 presents a 2D plot of the absorptance spectra, revealing two distinct absorption bands across all angles. The first band, located at wavelengths below 500 nm, is associated with the created LSPR at the upper edges of the nanodisks which is not the main concern in this study. The second, more prominent band occurs in the near-infrared region between 1200 and 1300 nm, with a dominant peak at approximately 1260 nm, exhibiting absorptance values exceeding 0.8. This peak is attributed to the excitation of LSPRs within the nanogap between the triangular nanodisks and the underlying gold layer. The strong confinement within the 10 nm dielectric gap results in significant near-field enhancement and high energy absorption, consistent with the expected behavior of MIM configurations with sharp-edged geometries [10, 30].

Figure 3. Simulated absorptance spectra of the triangular gold nanodisk array with a 10 nm Al₂O₃ dielectric gap, plotted as a function of wavelength and angle of incidence under TM-polarized illumination, highlighting the angularly robust plasmonic resonance at 1260 nm and additional resonances at higher angles.

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Notably, the resonance at 1260 nm demonstrates minimal sensitivity to the angle of incidence across a wide range (0°–80°), indicating an angularly robust plasmonic mode. This robustness is likely due to the highly localized nature of the gap plasmon mode, which is less dependent on the incident wavevector compared to propagating surface plasmon polaritons (SPPs) [31]. The hexagonal symmetry of the array further contributes to this angular insensitivity, as it supports isotropic in-plane coupling, making the resonance stable regardless of the azimuthal angle. This is particularly advantageous for sensing applications where alignment of the incident beam can vary; an angularly invariant hot spot ensures consistent sensor response.

As the angle of incidence increases beyond 60◦, a pronounced resonance feature is observed at approximately 800 nm, as evidenced by the angular absorptance map (see figure 3). This angular dependence indicates the excitation of additional plasmonic modes, which are less pronounced at normal incidence. The periodic arrangement of triangular nanodisks in a hexagonal lattice likely facilitates grating-assisted coupling of incident light to SPPs. In periodic plasmonic structures, SPP excitation occurs when the in-plane component of the incident wavevector satisfies the phase-matching condition given by:

where kSPP is the SPP wavevector, k0 is the free-space wavevector, θ is the angle of incidence, m is an integer representing the diffraction order, and G is the reciprocal lattice vector of the hexagonal array [10]. Based on the SEM image (see figure 2), the lattice constant of the nanodisk array is approximately Λ ≈ 250 nm. For a hexagonal lattice, the first-order reciprocal lattice vector is:

For the observed resonance at λ ≈ 800 nm and θ = 60◦, the free-space wavevector and its in-plane component are calculated as:

Assuming first-order grating coupling (m = ±1), the SPP wavevector is for m = +1:

For m = −1:

These values deviate significantly from the expected SPP wavevector at a gold-dielectric interface at 800 nm, which is estimated using:

Using approximate dielectric constants for gold and the dielectric medium (, assuming n ≈ 1.77), the SPP wavevector is:

The discrepancy between the calculated kSPP values from equations (4) and (5) and the expected value from equation (7) suggests that first-order coupling (m = ±1) does not fully account for the observed resonance, likely due to the large reciprocal lattice vector arising from the small periodicity. However, an effective grating vector could yield:

Geff represents an effective grating vector for higher-order or symmetry-driven coupling, as first-order G yields mismatch (equations (1)–(7)). Equation (8) uses Geff ≈ 8 × 106 m−1 to align with expected kSPP, indicating the resonance arises from such effects. This value closely matches the expected kSPP, suggesting that the resonance at 800 nm may result from SPP excitation mediated by higher-order or symmetry-driven grating coupling. Alternatively, the feature could arise from higher-order localized or hybridized plasmonic modes, which become more radiative at oblique incidence due to symmetry breaking and enhanced in-plane momentum. This angularly tunable resonance underscores the multi-modal nature of the structure and its potential for angle-sensitive plasmonic applications. The calculated wavevector values for SPP excitation at λ=800 nm and θ=60° are summarized in table 2.

Table 2. Calculated wavevector values for SPP excitation at λ = 800 nm and θ = 60◦.

ParameterValue (m−1)Free-space wave vector, k07.85 × 106Clean In-plane wavevector, k0sin(θ)6.8 × 106Reciprocal lattice vector, G2.91 × 107SPP wavevector, kSPP (m = +1)3.59 × 107SPP wavevector, kSPP (m = −1)−2.23 × 107Expected SPP wavevector (gold-dielectric)1.49 × 107Effective grating vector, Geff8 × 106SPP wave vector with Geff (m = +1)1.48 × 1072.2. Gap thickness dependence

The influence of the thickness of the dielectric gap layer (tgap) on the plasmonic response was investigated by simulating absorptance spectra for gap thicknesses from 10 to 60 nm under normal incidence (θ = 0°). Figure 4 shows a 2D plot visualizing the evolution of the plasmonic resonances with absorptance values between 0.1 and 0.9. For a 10 nm gap, a strong and sharp resonance peak appears at around 1260 nm with an absorptance of 0.82, which is caused by strong LSPR coupling within the narrow dielectric gap. This high absorptance is due to the intense confinement of the near field, which maximizes the electric field enhancement. As the gap thickness increases to 20 nm, the resonance shifts into the blue to about 1100 nm and the absorptance slightly to 0.84. The resonance jumps from 1260 nm (10 nm gap) to 1100 nm (20 nm) due to rapid decay in near-field coupling strength. For 12–16 nm gaps, resonances are weak or absent, as the structure enters a transitional regime with unbalanced confinement and radiative losses. This shift is attributed to weaker near-field coupling, which changes the local electromagnetic environment and modifies the resonance conditions [5]. The slight increase in absorptance could be due to an improved balance between field confinement and reduced non-radiative losses. At 30 nm, the resonance shifts further to 1050 nm, where the absorptance reaches 0.85. This indicates that the influence of the gap on the coupling decreases and radiative coupling or substrate effects become more important. Beyond 30 nm, up to 40 nm, the resonance wavelength stabilizes around 1050 nm, indicating saturation of the effect of the gap on the primary LSPR mode. At 60 nm, the resonance shifts slightly to 1070 nm and new, weaker resonances appear in the visible region (600–800 nm), probably due to the excitation of multiple plasmonic modes and less vertical field confinement.

Figure 4. Simulated absorptance spectra of the triangular nanodisk array as a function of dielectric gap thickness (10–60 nm) under normal incidence, showing a blue-shift of the primary resonance from 1260 nm to 1050 nm and the emergence of additional visible-range resonances at thicker gaps.

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These trends are consistent with established theories of plasmonic coupling in which the thickness of the dielectric gap controls the strength of the near-field interactions and the effective refractive index. Quantitatively, the shift of the resonance wavelength from 1260 nm (tgap = 10 nm) to 1050 nm (tgap = 30 nm) corresponds to a decrease of 16%, reflecting the sensitivity of the LSPR to the gap thickness. The increase in maximum absorptance from 0.82 to 0.85 (an improvement of 3.7%) illustrates the trade-off between field confinement and radiation efficiency. The 10 nm gap is optimal to maximize field enhancement, making it ideal for applications such as SERS. Thicker gaps (e.g. 60 nm) support broader spectral responses and multiple resonances suitable for multiband photodetection or broadband light harvesting. As the gap increases, the peak at ∼1260 nm shifts to ∼1050 nm (for 60 nm gap) and becomes broader and weaker, while new higher-energy modes appear. This indicates that a thinner gap yields a single, strong resonance with higher field enhancement, whereas a thicker gap produces multiple resonances, potentially narrower, which could be useful for multispectral sensing. Experimentally, we focus on 10 nm vs 40 nm as representatives of these regimes.

2.3. Polarization dependency

To evaluate the versatility of the triangular nanodisk arrays for real-world applications, the polarization dependence of their optical response was investigated by analyzing absorptance spectra and electric field distributions under TE and TM polarized light at normal incidence.

Figure 5(a) shows the simulated absorptance spectra for the triangular nanodisk array with a 10 nm Al₂O₃ dielectric gap under TE and TM polarizations at normal incidence. The spectra reveal three resonant modes at approximately 640 nm, 880 nm, and a dominant peak at 1260 nm, with absorptance exceeding 0.8 (80%) at the latter. The near-identical resonance wavelengths for both polarizations indicate polarization-independent behavior, particularly at the primary resonance of 1260 nm.

Figure 5. (a) Absorptance spectra of the triangular gold nanodisk array under TE and TM polarization, showing polarization-independent peaks at 640, 880, and a dominant peak at 1260 nm (>80% absorptance).(b) TE-polarized electric field in the xy-plane, concentrated at nanodisk tips.(c) TM-polarized field in the xy-plane, enhanced along polarization-aligned tips.(d) TE-polarized field in the xz-plane, showing strong vertical confinement within the 10 nm gap.

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From a quantitative perspective, the absorptance at 1260 nm reaches approximately 0.82, consistent with the high absorptance observed in figure 4 for the 10 nm gap under normal incidence. The secondary peaks at 640 nm and 880 nm exhibit lower absorptance, estimated at 0.5–0.6 based on typical plasmonic spectra trends, suggesting weaker coupling for these higher-energy modes. The polarization independence at 1260 nm is attributed to the hexagonal symmetry of the array and the uniform 10 nm dielectric gap, which allow the structure to support similar LSPR modes regardless of the electric field orientation. This symmetry minimizes polarization-dependent variations in the effective refractive index and charge distribution, ensuring stable resonance conditions [31].

Figures 5(b) and (c) illustrate the electric field distributions in the xy-plane within the 10 nm Al₂O₃ gap layer for TE and TM polarizations, respectively. In both cases, the electric field is strongly concentrated at the corners of the triangular nanodisks, confirming the formation of plasmonic ‘hot spots’ critical for enhancing light–matter interactions. For TM polarization (figure 5(c)), the field is predominantly enhanced along the two corners aligned with the polarization direction, likely due to increased charge accumulation and out-of-plane field components that amplify the local field intensity. In contrast, for TE polarization (figure 5(b)), the field concentrates at the top corners of the triangles, driven by the lightning rod effect, where sharp geometric features enhance the local electric field [4]. Despite these differences in field distribution, the resonance wavelengths remain consistent across polarizations, as evidenced by the identical peak positions in figure 5(a). This suggests that the triangular geometry and gap design effectively couple the incident light to the same LSPR mode, regardless of polarization.

Figure 5(d) depicts the electric field distribution in the xz-plane under TE polarization, highlighting the vertical confinement within the 10 nm dielectric gap between the nanodisks and the underlying gold layer. A highly confined field forms an intense coupling region between the nanodisks and the gold layer, which plays a key role in the enhanced absorptance and localized field strength. This confinement is a sign of the MIM configuration, where the narrow gap enhances plasmonic coupling. The field decay length within the gap can be estimated using the exponential decay model for gap plasmons, (E(z) = E0 e(−z/δ)), where δ is the decay length, typically on the order of the gap thickness (10 nm) for such structures. This suggests a decay length of approximately 10–20 nm, indicating that the field is highly localized within the gap, contributing to the maximum enhancement.

2.4. Electric field enhancement

To evaluate the electric field enhancement capabilities of the proposed nanostructure, we conducted a comparative analysis against recently reported designs, as summarized in table 3. Our design, fabricated via scalable colloidal lithography, achieved a peak simulated electric field enhancement of |E|/|E0| = 310 within a 10 nm Al₂O₃ dielectric gap.

Table 3. Comparison of electric field enhancement factors (|E|/|E0|) for plasmonic nanostructures, highlighting the high performance and scalability of the triangular nanodisk array fabricated via colloidal lithography.

Structure typeSimulation methodMaximum field enhancement (E/E0)RemarksStudyTriangular Au nanodisks over Au layer with Al₂O₃ gap (colloidal lithography)FEM (COMSOL)310High enhancement with scalable fabricationThis workTriangular Au nanodisks over Au layer (vs circular/square)Not specified220Shape comparison showing triangular disks perform bestLi et al [18]Au/Ag nanodisk photonic crystalsFDTD√1200 ≈ 34.6 Reported |E|2/|E0|2; shown here as |E|/|E0|High |E|2/|E0|2; geometry-sensitive photonic crystal design; fabrication complexity not addressedRoa et al [20]MIM with bowtie nanotriangles and nanodisksNot specified188–3