Enhanced optical trapping by concentrated local fields in metallic semi-continuous films

Abstract

On-chip optical trapping necessitates substrates that generate strong near-field forces while mitigating thermal instability. Here, metallic semi-continuous films are established as a transformative platform for high-efficiency optical manipulation. Through controlled sputter deposition, we engineer gold films across three morphological regimes: discontinuous nanoparticles (NPs), semi-continuous films (SCFs), and continuous films (CFs). Optical trapping experiments with 500-nm polystyrene spheres reveal that SCF substrates achieve a peak stiffness of 0.0955 ± 8.0 × 10^− 4 pN/µm, representing 16.9× and 6.2× enhancements over NP and CF substrates, respectively. The performance arises from sub-12-nm nanogaps within percolated gold networks, which concentrates electromagnetic fields via coupled gap-plasmon modes, intensifying optical gradient forces. Concurrently, SCFs’ interconnected pathways dissipate localized heating that destabilizes trapping in CFs. Electromagnetic simulations and experimental trajectory analysis confirm that SCFs balance field enhancement and thermal effect, overcoming the persistent trade-off in plasmonic optical trapping. This work provides a morphology-driven design principle for scalable lab-on-chip optical manipulation systems.

Supplementary Information

The online version contains supplementary material available at 10.1186/s11671-025-04383-8.

Introduction

Optical trapping has become an indispensable tool in nanotechnology and life sciences since its pioneering development [1–6]. The recent shift toward on-chip manipulation platforms necessitates substrates capable of generating strong optical forces near surfaces [7–9]. Plasmonic nanostructures, particularly gold nanoparticles, enhance trapping efficiency through localized surface plasmon resonance (LSPR), yet their discrete nature limits field uniformity [10–14]. Conversely, continuous metallic films exhibit high optical reflection and significant heat generation under laser illumination, which compromises trapping stability through thermal convection and amplified Brownian motion [15–17]. A promising but unexplored solution lies in metallic semi-continuous films (SCFs)—transitional structures formed during sputter deposition near the percolation threshold [18–21]. These films feature interconnected gold nanostructures separated by sub-12-nm nanogaps, which theoretically support intense electromagnetic field enhancement via coupled LSPR modes [22, 23]. Such nanogap-dominated physics could dramatically amplify optical gradient forces while potentially mitigating thermal constraints through their porous morphology [24–28]. However, experimental validation of SCFs’ trapping performance and its direct correlation with nanogap-induced field effects remains absent.

In this study, we investigate gold film morphologies across three distinct regimes: discontinuous nanoparticles (NPs), semi-continuous films (SCFs), and continuous films (CFs). Through controlled sputtering durations, we fabricate substrates representing these morphological states. Optical trapping experiments using 500-nm polystyrene (PS) spheres reveal that SCFs deliver considerably higher trapping stiffness compared to NP or CF substrates. We attribute this enhancement primarily to electromagnetic field amplification within nanoscale gaps, where coupled plasmon modes concentrate optical energy into sub-diffraction-limited volumes [29–33]. Additional benefits arise from reduced localized heating due to the films’ interconnected pathways for heat dissipation. This work establishes SCFs as a platform for high-efficiency surface-based optical trapping by fundamentally exploiting interparticle nanogap phenomena. Our findings also provide a morphology-dependent framework for designing next-generation optical manipulation devices.

Results and discussion

Experimental setup and optical trapping mechanism

The optical trapping system (Fig. 1a) was designed to quantify near-surface forces on different substrates. A 1064-nm laser beam was expanded and focused through a high-NA objective (NA = 1.4) to form a Gaussian trap above gold-coated glass. Trapped 500-nm PS spheres underwent Brownian motion, recorded at 38 Hz via CCD imaging (FLIR BFS-U3-200S6, Nikon; maximum frame rate: 500 Hz). Trapping stiffness (k) was derived from the power spectral density of displacement fluctuations, calibrated using viscous drag in glycerol-water solutions (viscosity 1.2 mPa·s, 20 °C) under fixed laser power (1.2 mW at sample plane). This approach ensured force sensitivity of ± 0.01 pN/µm. Central to this study is the role of gold film morphology in modulating optical forces. Figures 1b–d schematically demonstrate how structural transitions from discontinuous NPs to SCFs and CFs dictate light-matter interactions:

• In NP substrates (Fig. 1b), sparse gold islands generate isolated plasmonic hotspots [34, 35]. However, interparticle gaps exceeding 49 nm impede efficient field coupling, resulting in shallow optical potential wells that weakly confine particles.

• SCF substrates (Fig. 1c) exhibit a percolated network with sub-12-nm nanogaps. These gaps act as electromagnetic field concentrators, where coupled localized surface plasmons compress light into subwavelength volumes [25]. This significantly strengthens optical potential wells while interconnected gold pathways provide thermal dissipation channels.

• For CF substrates (Fig. 1d), high reflectivity (>80.5% at 1064 nm) redirects incident light away from the particle so that the optical potential wells become broadened [36]. Moreover, residual absorption induces localized heating, weakening optical trapping through thermal convection [37].

This morphological progression—from isolated islands to percolated networks and finally conductive films—is precisely controlled by sputtering duration, as will be quantitatively characterized in the following section. The SCF’s unique topology, balancing field enhancement and heat dispersion, suggests its potential to overcome limitations of both NP and CF substrates.

Fig. 1.

Experimental setup and optical trapping mechanism on gold-film substrates. (a) Schematic of the optical trapping system: A 1064-nm Gaussian laser beam is expanded and focused by a high-NA objective onto gold-sputtered glass substrates. Trapped 500-nm PS spheres undergo Brownian motion, tracked via CCD imaging. (b−d) Morphology-dependent trapping mechanisms. (b) Discontinuous NP substrate, i.e. isolated gold islands, exhibit weak plasmonic coupling (> 49-nm gaps), generating shallow optical potential wells. (c) SCF, i.e. sub-12-nm nanogaps, concentrate electromagnetic fields via coupled localized surface plasmons, creating deep optical potential wells. (d) CF with high reflectivity (> 80.5% at 1064 nm) broadens optical potential wells, while residual absorption induces localized heating effect

Morphological and optical properties of gold films

The morphological progression of gold films—from isolated NPs to percolated networks and ultimately continuous layers—was precisely engineered through sputtering time modulation (see details in Methods), with corresponding structural and optical properties summarized in Fig. 2. Scanning electron microscopy (SEM) imaging reveals different morphologies: discontinuous NPs at 8-nm sputtering thickness exhibit isolated gold islands (diameter: 20–150 nm) separated by wide gaps exceeding 49 nm and a filling ratio of 16.1% (Fig. 2a). Intermediate sputtering (sputtering thickness: 15 nm) generates SCFs, characterized by interconnected gold clusters forming sub-12-nm nanogaps and a filling ratio of 57% that creates intricate charge-transfer pathways (Fig. 2b). To better distinguish between NP and semi-continuous film (SCF) substrates, we have conducted a quantitative morphological analysis to systematically extract key parameters, i.e., average nanogap size, filling ratio, and film thickness, across different sputtering durations (Fig. S1). Extended deposition (34 nm) produces CFs with smooth, fully percolated surfaces devoid of nanoscale porosity (Fig. 2c). The white features in this figure are SEM imaging artifacts induced by minor surface charging effects during measurement. Optical absorption spectra provide insights into plasmonic responses across these morphological transitions (Fig. 2d). NP films display a sharp localized surface plasmon resonance (LSPR) peak centered at 593 nm—characteristic of individual gold nanoparticles—accompanied by an absorption of 28.5% at 1064 nm, which stems from weak interparticle coupling and insufficient metal coverage. In contrast, SCFs exhibit broadband absorption with a pronounced plateau extending into the near-infrared regime, achieving absorption of 34.5% at 1064 nm. This enhancement arises from synergistic light-matter interactions: subwavelength nanogaps concentrate electromagnetic fields through coupled gap-plasmon modes, while the fractal-like gold network facilitates efficient photon trapping via multiple scattering events. Conversely, CFs demonstrate bulk-metal behavior with high reflectivity and minimal absorption (19.5% at 1064 nm), as continuous electron screening extinguishes LSPR activity and promotes specular reflection. The dip in absorption for the Au CF trace arises not only from its high reflectivity within the wavelength range but also from the interband transition of Au [18]. Furthermore, the absorption keeps increasing beyond ~ 700 nm in our experiment, which is primarily attributed to the intraband transition of Au and the enhanced light-matter interactions in the near-infrared (NIR) region [38]. Critically, the maximized 1064-nm absorption in SCFs signifies strong local field gradients—a prerequisite for enhanced optical forces. According to the dipole approximation, gradient forces scale with ∇∣E∣², implying that regions of intense field localization (e.g., nanogaps) generate force magnitudes orders larger than homogeneous fields [39, 40]. The spectral evidence thus anticipates enhanced trapping performance in SCFs, while simultaneously motivating quantitative examination of near-field distributions.

Fig. 2.

Morphological and optical properties of gold films across sputtering durations. (a–c) SEM images of the gold films. (a) Au NPs (diameter: 20–150 nm) with interparticle gaps > 49 nm (8-nm sputtering). (b) Au SCF (percolated gold network) with sub-12-nm nanogaps (15-nm sputtering). (c) Au CF with fully percolated surface (34-nm sputtering). (d) Optical absorption spectra for Au NP, SCF, and CF substrates

Electromagnetic field simulations and optical force analysis

To elucidate the mechanistic basis for enhanced optical trapping in semi-continuous films, we performed finite-element electromagnetic simulations (COMSOL Multiphysics 6.1). Figure 3a-c visualizes the normalized electric field intensity (∣E∣²/∣E₀∣²) for a 500-nm PS sphere positioned 200 nm laterally offset from the focal point above NP, SCF, and CF substrates under 1064-nm Gaussian beam illumination. The simulation domain replicated experimental conditions with a focused beam waist of 532 nm and incident power of 1.2 mW. Adaptive meshing resolved nanoscale features (minimum element size 0.5 nm in gap regions), while perfectly matched layer boundaries minimized reflection artifacts. Material properties incorporated Drude-Lorentz model [41, 42] dispersion data for gold and a constant dielectric permittivity (ε = 2.56) for PS. The morphology of the nanoparticles and SCF films in our COMSOL simulations was comparable to the morphology shown in the SEM images (Fig. 2a, b). To ensure this point as much as possible, the designed physical model for the Au NPs substrate with a thickness of 8 nm (Fig. 3a) consisted of hemispherical gold particles with a radius of 8 nm, separated by gaps of approximately 163 nm (>49 nm). For the semi-continuous film (SCF) with a thickness of 15 nm (Fig. 3b), hemispherical gold nanoparticles with a radius of 15 nm were arranged in a close-packed configuration with a center-to-center spacing of 30 nm (interparticle gaps < 12 nm). Field distributions exhibit differences across substrates: Isolated gold NPs (Fig. 3a) generate localized field constrained to small volumes beneath individual islands. The particle experiences moderate field gradients due to limited interparticle coupling. In SCF substrates (Fig. 3b), sub-12-nm nanogaps concentrate electromagnetic energy into spatially extended hotspots, achieving intensity enhancements that permeate the entire PS particle volume. Conversely, CF substrates (Fig. 3c) reflect incident light to form standing wave patterns, resulting in weak, homogeneous fields that fail to penetrate the particle effectively.

Fig. 3.

Electromagnetic field simulations and optical force calculations for PS spheres on gold substrates. (a−c) Cross-sectional views of normalized electric field intensity (∣E∣²/∣E₀∣²) for a 500-nm PS sphere trapped above Au NP (a), SCF (b), and CF (c) substrates. (d) Transverse optical force (F_x) and temperature difference (ΔT) at 200 nm (x = 200 nm) laterally offset from the trap center

Optical forces perpendicular to the beam axis, i.e., transverse optical force (F_x), were computed via the Maxwell stress tensor formalism. The time-averaged force acting on the particle is given by the surface integral [43]:

1

where is the surface normal unit vector and S is the surface of the trapped objective. The time-independent Maxwell stress tensor component is [44]:

2

where and describe the outer product of the electromagnetic fields, is the electric permittivity, is the magnetic permeability, and q represents the unit dyadic.

The laser beam travels in the z direction and hits a target surface in the x–y plane. The beam intensity has a Gaussian profile with a 1/e radius . In the gold substrate, the beam is exponentially attenuated with an absorption coefficient . The target thickness h is assumed to be much thicker than the absorption depth , and heat loss from the surface is assumed to be negligible compared to conduction into the gold substrates. The thermal conductivity K and isobaric heat capacity of the Au are taken to be constant over the temperature range of interest. The time-dependent heat equation is [45]

3

where is the thermal diffusivity. The heat source is

4

    

where P is the power absorbed from the laser beam, is the scanning speed of the laser beam. According to Green’s function, integrating over the spatial coordinates, and integrating from -t₁ to t₂, a general solution for the temperature rise can be expressed as [46]:

5

where , , , , , and . The generalized solution is:

6

where .

Figure 3d quantifies the optical force F_x acting on the PS particle, along with the film-induced temperature difference ΔT, when centered at a lateral offset of 200 nm (x = 200 nm) from the optical trap for all three film types. Critically, the optical force acting on the PS particle increases with the thickness of all three film types. This enhancement primarily stems from two mechanisms: the electric field amplification within sub-12-nm nanogaps in the SCF substrate, and the interference-induced field enhancement in the CF substrate, both of which significantly contribute to the increase in optical force. Meanwhile, photothermal effects also intensify with increasing film thickness. In the case of the CF substrate, thicker films lead to greater laser absorption, generating steeper temperature gradients and resulting in stronger thermal perturbations. Notably, the percolated network of sub-12 nm gaps in the SCF substrate induces only a slight temperature rise, leading to weaker thermal perturbations. The maximal net optical trapping force in SCFs arises from efficient conversion of incident light into gradient forces via nanogap plasmonics, which is consistent with their broadband absorption (Fig. 2d). This computation anticipates the experimental trapping stability hierarchy, where strongest optical force in SCFs enable maximal stiffness by minimizing particle escape probabilities.

Experimental validation of trapping stiffness

Experimental quantification of optical trapping efficiency across structurally evolving gold substrates provides validation of the trapping enhancement hypothesis. Figures 4a–i show two-dimensional trajectory maps of a 500-nm PS sphere recorded over 10 s (interval: 26 ms), visualizing confinement strength evolution with sputtering thickness. The nine trajectories were extracted from the videos of the trapped PS spheres (Video S1−S9), respectively. On bare glass substrates (0 nm, Fig. 4a), the PS sphere undergoes near-diffusive motion with large positional fluctuations (standard deviation σ_x >0.89 μm), indicative of minimal confinement. Early-stage discontinuous NP films (8 nm, Fig. 4b) partially constrain sphere motion (σ_x = 0.71 μm), yet persistent escape events reveal insufficient plasmonic coupling. As sputtering progresses into the SCF regime (11–17 nm), trajectories progressively localize, culminating at 15 nm (Fig. 4e) with dramatically reduced fluctuations (σ_x = 0.19 μm)—a visual testament to efficient particle confinement. Further morphological transition toward CFs (> 17 nm) gradually degrades trapping stability, with CF substrates (34 nm, Fig. 4i) permitting substantial particle excursions (σ_x = 0.57 μm) due to reflective losses and incipient thermal effects.

Fig. 4.

Experimental quantification of trapping stiffness across gold film morphologies. (a-i) Two-dimensional trajectory maps of 500-nm PS spheres over 10-second intervals, demonstrating confinement evolution with sputtering thickness (from bare glass to CFs). (j, k) Trapping stiffness (κ_x and κ_y) and standard deviations derived from equipartition theorem. Directional isotropy (κx ≈ κy) confirms symmetric force fields in SCFs

The positional variance data can be directly translated to trapping stiffness metrics via Boltzmann statistics (Fig. 4j–k). We performed 10 independent experimental repetitions for each substrate type and calculated the corresponding standard deviations. Applying the equipartition theorem (κ_x = k_BT/σ_x², T = 293 K), we observe a pronounced stiffness maximum of κ_x = 0.0955 ± 8.0 × 10^− 4 pN/µm and κ_y = 0.0879 ± 6.1 × 10^− 4 pN/µm at 15-nm sputtering thickness. This represents a 16.9-fold enhancement over NP substrates (8 nm: κ_x = 0.00565 ± 1.8 × 10^− 4 pN/µm) and a 6.2-fold improvement over CFs (34 nm: κ_x = 0.0155 ± 3.2 × 10^− 4 pN/µm). The stiffness peak aligns with the SCF morphology identified in Fig. 2b, where sub-12-nm nanogaps maximize plasmonic field enhancement. Directional isotropy (κ_x ≈ κ_y) further confirms symmetric force gradients generated by the percolated gold network. This stiffness maximum integrates three independent experimental and theoretical strands: (i) The broadband near-infrared high absorption in SCFs maximizes optical energy conversion into field gradients; (ii) Electromagnetic simulations demonstrate field amplification within nanogaps, spatially overlapping with trapped PS spheres; (iii) Near-zero residual forces at equilibrium enable stable particle localization. The inverse correlation between positional variance (Fig. 4a–i) and stiffness magnitude (Fig. 4j, k) establishes SCFs as optimal plasmonic substrates for deepening optical potential wells. These results demonstrate that SCFs—engineered at the percolation threshold—optimize the trade-off between plasmonic field enhancement and operational stability, achieving high trapping stiffness through nanogap-dominated light-matter interactions. This morphology-performance relationship provides a framework for designing advanced optical manipulation platforms. Moreover, this morphology-driven strategy is also applicable to the trapping of multiple particles. In our experiments, we demonstrated multiple-particle trapping by organizing 500-nm PS spheres into a 3 × 3 array on Au NP, Au SCF, and Au CF substrates (Video S10−12). Under identical laser power, all nine particles were successfully trapped simultaneously across all substrates, yet with notable differences in trapping quality: the particles on the Au NP substrate exhibited significant Brownian motion, those on the Au CF showed moderate fluctuations, while the trappings on the Au SCF were the most stable with minimal positional deviation. These results provide evidence that parallel multi-particle trapping can be effectively achieved, particularly on the SCF substrate, supporting the potential of our morphology-based approach for scalable lab-on-chip optical manipulation systems.

Since the particle size directly influences both the optical forces and thermal fluctuations, we next study the trapping of PS spheres with different diameters. In the experiments, we investigated the motion trajectories of polystyrene (PS) spheres with diameters of 300 nm, 1 μm, and 3 μm on three distinct substrates, i.e., Au NPs, Au SCF, and Au CF, and quantitatively evaluated the corresponding optical trapping stiffness. Figure 5 displays two-dimensional trajectory maps for each particle size recorded over 10 s (at 5 ms intervals). The results clearly show that for particles of the same size, spatial localization is most pronounced on the Au SCF substrate, where the trapping stiffness also reaches its maximum, consistent with the trends described in Fig. 4. Furthermore, focusing on a specific substrate type (e.g., Au SCF), we observed significantly higher stiffness values for larger particles. For instance, 3 μm PS spheres exhibited a maximum stiffness of k_x = 0.544 pN/µm and k_y = 0.544 pN/µm (with a standard deviation σ = 0.09 μm, Fig. 5h). This represents a 1.52-fold increase compared to 1 μm PS particles (k_x = 0.358 pN/µm, Fig. 5e), and an enhancement of over 600-fold compared to 300 nm PS particles (k_x = 8.8 × 10⁻⁴ pN/µm, Fig. 5b). Together, these findings underscore that trapping stability is effectively enhanced with increasing particle size, further supporting the efficacy of our substrate design across a range of particle dimensions.

Fig. 5.

Experimental quantification of trapping stiffness for different particle sizes. Two-dimensional trajectory maps and trapping stiffness (k_x and k_y) of PS spheres with diameters of 300 nm (a−c), 1 μm (d−f), and 3 μm (g−i) on three distinct substrates: Au NPs, Au SCF, and Au CF

Furthermore, to confirm the plasmonic origin of the enhanced trapping effect, we conducted finite-element electromagnetic simulations (COMSOL Multiphysics 6.1) to analyze the electric field distributions and optical forces for substrates coated with a non-plasmonic material. As shown in Fig. 6, we simulated the normalized electric field intensity (|E|²/|E₀|²) for a 500-nm PS sphere placed 200 nm laterally from the focal point above SiO₂ nanoparticle (NP), semi-continuous film (SCF), and continuous film (CF) substrates under a 1064 nm Gaussian beam, using identical simulation parameters as in Figs. 3a–c. The results reveal nearly identical electric field distributions across all three SiO₂ substrate types. Although a slight increasing trend in optical force is observable, the values remain broadly similar across different morphologies. Notably, these force values closely match those experimentally obtained from the 8 nm-thick Au NP substrate (Fig. 3a). This consistency suggests that the moderate electric field enhancement and trapping performance observed with dielectric materials such as SiO₂ are not attributable to plasmonic effects, thereby underscoring the unique role of plasmonic excitation in metallic (e.g., Au) nanostructures for significantly enhancing optical trapping.

Fig. 6.

Electromagnetic field simulations and optical force calculations for PS spheres on SiO₂ substrates. Cross-sectional views of normalized electric field intensity (∣E∣²/∣E₀∣²) and transverse optical force (F_x) for a 500-nm PS sphere trapped above SiO₂ NP (a), SiO₂ SCF (b), and SiO₂ CF (c) substrates

Conclusion

We’ve established metallic SCFs as a transformative platform for high-efficiency optical trapping by fundamentally exploiting nanogap-based optical field concentration. Through controlled sputter deposition, we engineered gold films across three distinct morphological regimes (discontinuous NPs, SCFs, and CFs), demonstrating that the percolation-threshold state (SCFs) optimizes optical force generation. The SCF substrates achieve a peak stiffness of 0.0955 ± 8.0 × 10^− 4 pN/µm for 500-nm PS spheres, attributed to sub-12-nm nanogaps that amplify local fields via coupled plasmon modes. The sputtering thickness directly modulates nanogap density, with peak stiffness occurring at the transition (15 nm) where interconnected gold networks maximize gap-plasmon coupling while maintaining efficient heat dissipation. This eliminates the traditional trade-off between plasmonic enhancement and thermal instability. Unlike lithographically patterned plasmonic structures, SCFs provide intrinsic, large-area field enhancement without nanofabrication, offering immediate scalability for lab-on-chip systems. Future work will explore applications in single-molecule biophysics (e.g., membrane protein manipulation) and extend this design principle to other materials and wavelengths.

Methods

Materials and sample preparation

Au films were prepared by an ion sputtering deposition technique. High-purity Au (99.999%) was used as the sputtering target, and glass slides (Thorlabs) were employed as substrates. Prior to deposition, the Au target was polished with sandpaper to remove surface oxides and impurities. The glass slides were sequentially cleaned with deionized water, acetone, and anhydrous ethanol. Ion sputtering was carried out using a sputter coater (GVC-2000, Beijing Gewei Instruments Co., Ltd.) with argon as the sputtering gas. The sputtering conditions were maintained at a pressure of 4 Pa and a current of 3 mA. The longer the sputtering time, the thicker the thickness of the gold nanostructure film substrate. Taking the deposition times of 30, 40, 53, and 120 s as examples, the produced thicknesses of the single-layer gold nanostructured films were measured as 8, 11, 15, and 34 nm, respectively. Their surface morphology was then characterized by scanning electron microscopy (JSM-IT800, JEOL, Japan). The optical properties were examined using a UV-vis-NIR spectrophotometer (V-770, JASCO, Japan).

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

H.L., F.N. and Y.Z. supervised the project. H.L., F.N. and Y.Z. conceived and designed the research; C.L. and Z.H. performed the experiments and carried out the theoretical modelling and calculations; C.L., Y.Z. and H.L. wrote the paper. All authors discussed the results.

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 12404361, 12474431, 12374299, and 11974435) and Guangdong Basic and Applied Basic Research Foundation (No. 2024A1515011756).

Data availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

Code availability

Not applicable.

Declarations

Ethics approval and consent to participate

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Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.