Using Au bowtie nanoantennas arrays (BNAs), we demonstrate that the performance and capability of plasmonic nanotweezers is strongly influenced by both the material comprising the thin adhesion layer used to fix Au to a glass substrate and the nanostructure orientation with respect to incident illumination. We find that a Ti adhesion layer provides up to 30% larger trap stiffness and efficiency compared to a Cr layer of equal thickness. Orientation causes the BNAs to operate as either (1) a 2D optical trap capable of efficient trapping and manipulation of particles as small as 300 nm in diameter, or (2) a quasi-3D trap, with the additional capacity for size-dependent particle sorting utilizing axial Rayleigh-Bénard convection currents caused by heat generation. We show that heat generation is not necessarily deleterious to plasmonic nanotweezers and achieve dexterous manipulation of nanoparticles with non-resonant illumination of BNAs.
© 2012 Optical Society of America
Plasmonic nanostructures are of increasing interest to the optical trapping and manipulation community due, in part, to their ability to produce highly enhanced electric fields with sub-diffraction spatial confinement [1–4]. This results in large intensity gradients, producing correspondingly large optical trapping forces that have been utilized for trapping objects ranging from nanoscale metallic and dielectric particles to micron-sized dielectric beads and biological samples [5–7]. A variety of geometries including dipole antennas [7, 8], nanodots , gratings , nanopillars , nano blocks , and bowtie nanoantennas  have been explored as nanotweezers with exciting potential applications in biology [7, 14] and lab-on-a chip technology . While the range of geometries is diverse, a common factor is the use of Au as the material of choice for fabrication. Gold requires an intermediary adhesion layer (AL) in order to adhere to the substrate, and Ti or Cr are the most common AL materials used [16, 17]. The effect of the AL material on the resonant plasmonic properties of nanostructures has been investigated both theoretically  and experimentally , where it was found that increased absorption losses from the AL can damp radiative emission from plasmonic nanostructures. However, to our knowledge the effect of a thin AL on the performance of a given plasmonic nanotweezer system has heretofore not been studied.
Typically in plasmonic optical trapping, nanostructures are illuminated at a wavelength at or near their peak localized surface plasmon resonance in order to generate maximum field enhancement [9,18]. However, resonant illumination can cause significant heat generation due to enhanced optical absorption by the nanostructures, which results in a subsequent release of heat into the surrounding fluid environment. The consequences of plasmonic heating are generally regarded as deleterious to the optical trap, and techniques including integrated heat sinks  or thin sample chambers [19, 20] have been used to mitigate these effects. Additionally, for plasmonic traps based on delocalized plasmon resonances (surface plasmon polaritons), such as those found in extended metal surfaces or gratings, the extended metal surface acts as a heat sink that prevents excessive thermal build-up . As a result, these plasmonic traps are less prone to heating effects compared to isolated nanostructures. However, we have shown previously that plasmonic nanotweezers can take advantage of convective forces resulting from heat generation to achieve efficient, multipurpose particle manipulation . While the excitation wavelength of plasmonic nanotweezers is usually carefully considered, the effect of orientation of the nanostructures with respect to the incident illumination is only marginally acknowledged .
In this work, we demonstrate that both choice of AL material and nanostructure orientation profoundly impact the performance and capabilities of plasmonic nanotweezers. The optical trapping efficiency and trap stiffness are measured for 0.5 and 1.0-μm diameter polystyrene spheres for an array of Au bowtie nanoantennas (BNAs) using both resonant and non-resonant illumination. The BNAs are affixed to the substrate using an AL consisting of 3-nm of Cr or Ti, and we show that the latter is the preferred AL material for trapping, yielding trap stiffness and efficiency values up to 30% larger than a Cr-based nanotweezer. Furthermore, measurements are performed in two different orientations: upright, where the BNAs are illuminated substrate side first and inverted, where the excitation light encounters the particle before the BNAs; we show that nanostructure orientation dramatically influences trapping dyanamics, causing the inverted BNAs to function as a 2D trap, where stable particle trapping can result solely from “pinning” particles to the substrate with the optical scattering force . Here, the nanostructures primarly serve to enhance lateral trapping forces and are not required for stable trapping. Conversely, upright BNAs function as a quasi-3D trap, wherein axial scattering and fluid forces are balanced in 3D by gradient forces derived from the BNAs, yet particles must be close to the surface for trapping to occur. Finally, we show that non-resonant illumination of nanostructures can produce 4x higher stiffness and 3x the efficiency of a resonantly illuminated system.
2. Results and discussion
The experimental configurations along with representative force diagrams for each orientation are given in Fig. 1. In the upright orientation (Fig. 1(a)), 425 x 425-nm-spaced BNAs are illuminated from the substrate side by a 0.6 numerical aperture (NA) objective at either non-resonant (λnr = 685 nm) or resonant (λr = 785 nm) wavelengths with input polarization along the long axis of the bowtie and an input power range of 250 – 700 μW. Details on the BNAs are published elsewhere . In the inverted orientation (Fig. 1(b)), the BNAs are illuminated from the solution side first. In other words, the incident optical field E⃗ encounters the BNA-substrate system before the particle in the upright orientation, whereas in the inverted system, E⃗ illuminates the particle first. The BNAs are immersed in water containing either 0.5 or 1.0-μm diameter colloidal spheres at ∼ 1/3600 dilution from stock in a 200-μm thick sample chamber. Optical absorption results in localized heating of the nanostructures, which in turn gives rise to a Rayleigh-Bénard convection current that is driven by local temperature gradients [2, 20, 22]. This current is represented by the direction of the unlabeled arrows in Fig. 1, and the relative temperature is represented by the arrow color. Note that the figure is qualitative rather than quantitative, but provides insight on the system dynamics.
Trapped particles experience the standard optical scattering (F̂scat) force, which is always directed axially, and the gradient (F̂grad = F̂grad,ax + F̂grad,L) force which is formed predominantly by the near-field intensity gradients of the BNAs and is directed towards the high-intensity region . Additional convective and thermal forces (F̂RB = F̂RB,ax + F̂RB,L) arise as a result of local heating which produces fluid convection and thermophoresis. Here the subscripts L and ax indicate forces directed laterally and axially, respectively. It should be noted that forces associated with thermophoresis are directed along temperature gradients, i.e., away from the illuminated BNAs; for our trapped colloidal spheres, thermophoresis is expected to be outweighed by convection forces [2,23], and is thus “lumped” with the latter into one F̂RB force. In light of this fact, F̂RB is effectively a fluid drag force Fdrag = γν, where γ = 6πηaε (a,h) is the Stoke’s drag coefficient, η is the water viscosity, a is the sphere radius and ε (a,h) is a correction factor accounting for the particle proximity to the substrate . The Rayleigh-Bénard fluid velocity (νRB) is applied to the trapped sphere with directions shown in Fig. 1 and is given by20]. Equation 1 predicts that |FRB| ≈ 0.5–1.0 pN assuming ∇T ∼ 2 K, which is supported by observations of particle advection parallel to the surface with velocities ∼ 8 μm/s for 1-μm spheres (see Fig. 2).
Evidently, the primary force responsible for a stable optical trap in the upright configuration is F̂grad,ax which results from the axial, near-field intensity gradients generated by the BNAs and thus F̂grad is taken to be the gradient force generated by the BNAs alone. While the incident illumination does provide lateral and axial gradient forces, it is insufficient at 0.6 NA to form a stable optical trap. Conversely, F̂scat and F̂RB,ax oppose F̂grad,ax and work to destabilize the trap. This competition places an upper limit on the input power for a single particle trap since F̂scat + F̂RB,ax eventually destabilize the trap by overpowering F̂grad,ax. This phenomenon has been described in terms of “optical trapping phases”, and empirically-obtained trapping phase diagrams have been developed to navigate between three trapping regimes: (1) lateral delocalization where F̂grad,ax > F̂scat + F̂RB,ax yet particles are not trapped laterally due to insufficient F̂grad,L + F̂RB,L to overcome Brownian motion, (2) single-particle trapping, where particles can be trapped and manipulated over the entire BNA surface and (3) multiple-trapping only, where F̂grad,ax < F̂scat + F̂RB,ax and single particles are forced away from the BNAs along the optical axis . However, if several particles enter the trap region simultaneously, they can form hexagonally-packed, particle clusters that remain trapped due to a disruption of the axial flow associated with F̂RB,ax. The critical point of transition from phase (2)–(3) is dependent on input optical power, polarization and wavelength, BNA array spacing and particle diameter (owing to the size dependence of F̂RB). Therefore, the trapping phase behavior exhibited in the upright orientation can also be utilized for particle sorting .
The upright orientation can be considered a quasi-3D optical trap: the nanostructures are required to balance F̂scat + F̂RB,ax in 3D, but particles must be within ∼ 20 nm of the surface for trapping to occur. In contrast, a standard 3D optical trap can manipulate particles in three spatial dimensions due to an intrinsic balance of F̂grad and F̂scat caused by high NA focusing . The situation is much different in the inverted configuration, where both F̂scat and F̂grad,ax are directed towards the BNAs and opposed by F̂RB,ax. Here, the transition to a multiple-trapping only phase does not occur, but very large single-particle trapping forces can be obtained due to increased input power. Further, removing the nanostructures results only in F̂scat (and the gradient forces associated with 0.6-NA illumination) so that a stable trap is formed by pinning particles to the substrate. Therefore in general, the inverted configuration is simply a 2D optical trap, with trapping forces enhanced by the presence of the nanostructures.
One metric used to quantify the effect of the AL and orientation on the nanotweezer performance is the trap stiffness obtained by fitting position fluctuation signals from the trapped particle to a Lorentzian power spectrum given by27]. Position signals are measured by imaging the forward scattered light from the trapped particle onto a quadrant photodetector with a 0.6-NA condenser . Measuring the trap stiffness in this manner assumes that the particles are bound by a quadratic potential energy well, and thus the particle fluctuations due to Brownian motion within the well should follow a Gaussian distribution. Time signals are collected for 30 seconds at a sampling rate of 8192 Hz, and a Gaussian distribution of the position fluctuations is verified before calculating each trap stiffness.
Here, we use of the the lubrication value of the drag coefficient correction30]. Due to difficulty in measuring the sphere height, it is taken to be 20 nm in all cases. Note that above h = 40 nm, the local intensity drops to that of the 0.6-NA illumination, i.e., a particle at h > 40 nm cannot be trapped . This gives ε (250 nm, 20 nm) = 2.31 and ε (500 nm, 20 nm) = 2.67, and the largest calculated trap stiffnesses are 0.42 ± 0.03 and 6.8 ± 0.75 pN / (μm · mW) for 0.5 and 1.0 - μm diameter spheres, respectively.
Similarly, the trapping efficiency is used in order to assess the maximum trapping force attainable by a given combination of AL, orientation, wavelength and particle size. The efficiency is given by: Q = Fmaxcm/P0 where cm is the speed of light in water, P0 is the input power, and Fmax = γ · νc is measured by the Stokes’ drag force method, wherein the particle is driven sinusoidally at increasing velocity up to the critical velocity (νc = πApp/tπ, where tπ is the half-period particle transit time and App = 5 μm is the peak-to-peak displacement) at which the particle is ejected from the trap . The largest measured trap efficiencies are 0.22 ± 0.02 and 0.55 ± 0.02 for 0.5 and 1.0-μm diameter spheres, respectively, and the full set of stiffness and efficiency results are available in the appendix. Due to the radially-symmetric convection profile near the illumination point, F̂RB,L has components directed opposite to the applied drag force which effectively increase the strength of the trap. In this case, trapping efficiency is increased as a direct result of heat generation within the BNAs.
While the raw trap stiffness and efficiency values provide a quantitative evaluation of the nanotweezer trap strength, comparison of the trapping performance between Cr and Ti is better suited with the use of a difference parameterTable 1 presents the calculated Δ (Λ) for all parameters considered in this study.
The advantage of Ti over Cr as an AL material is striking: we see that Δ (Λ) > 0 in almost every combination of orientation, particle size, and wavelength. This indicates that for at least these conditions, Ti forms a stiffer, more efficient trap than Cr. Furthermore, when using an upright orientation off-resonance, forming a stable single-particle trap with Cr is exceedingly difficult, and the trap stiffness (κCr) and efficiency (QCr) for Cr are κCr, QCr ≈ 0, leading to Δ (Λ) = 1. In this case, the use of Cr is limited to inverted orientations, and thus Cr appears to be unfavorable for sorting applications using BNAs.
It is interesting that a thin, 3-nm AL causes the Cr-based nanotweezer to perform so poorly compared to the Ti-based counterpart, particularly in the upright orientation. To explain this behavior, it is necessary to consider the thermal response of the BNAs. The generation of heat by the BNAs is due to optical absorption of the incident radiation, and under steady state conditions the heat generated is given by Eq. (5) reduces simply to Qheat = σabs (λ)I0 (λ0), where I0 is the incident intensity (W m−2) at the input wavelength λ0. The corresponding temperature increase T+ (r) of the BNAs is governed by the Poisson equation Eq. (6) is geometry-dependent, the temperature increase of the metal nanostructures is uniform, regardless of morphology, due to the fact that kAu/kw ≈ 512 ≫ 1 . Moreover, it has been shown that a characteristic nanostructure length ℓc and volume can be defined over which the temperature increase of an arbitrary nanostructure is closely approximated by that of an equivalent sphere with volume  26]. We choose ℓc = 262 nm, corresponding to the total length of a single bowtie with 50-nm thickness, giving an aspect ratio of ∼ 5. Thus, the temperature increase of a single bowtie in the array can be approximated by [2,26]
Figure 3(a) shows the absorption cross-section (σabs,i where i= Cr or Ti) of an upright, single bowtie in a 425 x 425 nm array obtained for both Cr and Ti using Finite-Difference Time-Domain (FDTD) calculations performed with a commercial software package (Lumerical Solutions). A refined mesh of 2 x 2 x 2 nm centered on each bowtie is used to ensure accuracy, and the 425 x 425 bowtie array is illuminated with a 1.4-μm side length source (emulating the 0.6-NA lens) with perfectly matched layers on all sides. We simulated 3 x 3 and 5 x 5 arrays, and find < 1 % difference in absorption cross sections calculated in both cases. Note that identical cross sections are calculated using inverted orientation. For λnr, we find σabs,Cr = 0.028 (μm2) which is ∼ 10 % larger than σabs,Ti. Similary, at λr, σabs,Cr = 0.031 (μm2) which is again ∼ 10 % larger than σabs,Ti at this wavelength. The heat power generated by a single Cr-AL bowtie is Qheat = 4.7 μW and 6.7 μW, whereas a single Ti-AL bowtie generates 4.2 μW and 6.0 μW at λnr, and λr, respectively. The corresponding temperature increase of a single Cr-AL bowtie is ∼ 2–3 K, which is ∼ 10% larger than the Ti-AL counterpart. The 0.6-NA lens illuminates a minimum of 9 (3 x 3) bowties simultaneously, thus the Cr-AL (Ti-AL) BNAs generate a total of 42 μW (37.8 μW) and 60 μW (54 μW) for non-resonant and resonant illumination, respectively. Moreover, placing bowties in an array effectively increases their characteristic size from ℓ = 262 nm to 850 nm (twice the array spacing), and given the quadratic dependence of flow velocity on ℓ calculated by Donner et. al. , we believe that the additional heat input from the Cr-AL BNAs compared to Ti-AL BNAs leads to comparitively poor trapping performance via enhanced F̂RB,ax, particularly at non-resonant wavelengths.
The additional heat dissipation by the fluid in the Cr case results in enhanced Rayleigh-Bénard currents that, in the upright orientation, directly destabilize the single-particle trap by producing a larger F̂RB,ax force component. We suspect that this is the mechanism behind the inability of upright, Cr, non-resonant configurations to trap. Figure 3(b) shows the spatial intensity distribution of the BNAs with non-resonant (left panel) and resonant (right panel) illumination at 20 nm above the BNA surface. Resonant illumination produces a local intensity enhancement (Imax/I0) of 19x (18x) for Ti (Cr), whereas non-resonant illumination produces Imax/I0 ≈ 10x for both Ti and Cr. It is this additional intensity enhancement on-resonance that produces a larger F̂grad,ax component which compensates for convection forces, and allows for a stable, albeit less stiff trap using Cr in the upright orientation.
Typically, nanotweezers are excited using wavelengths at or near their peak plasmon resonance in an effort to maximize intensity enhancement and therefore optical forces. However, we find that the peak stiffness and efficiency values measured at λnr on Cr-AL (Ti-AL) BNAs are κ = 4.4x (3.9x) and Q = 2.5x (3.8x) those measured at λr, despite λnr producing ∼ 50% the maximum intensity enhancement. Moreover, κ and Q are greater for λnr in all cases investigated. This counter intuitive result is likely caused by an optimization between optical and thermally-induced forces, whereas λnr produces a lower F̂grad than λr, the heat generated is ∼ 15 % lower at λnr for both Ti and Cr. The net effect is that the axial Rayleigh-Bénard force and Brownian motion, which act to weaken the trap, are reduced off-resonance.
Clearly, the orientation of the nanostructures is an important consideration in their use as nanotweezers. To quantify the effect of orientation, we define another difference parameterTable 2 summarizes the orientation difference for all parameters in this study.
Again, the most prominent result is the inability of upright, Cr-BNAs to trap at λnr due to a combination of insufficient field enhancement and excessive heat generation at this wavelength. Further, we find that inverted Cr-AL BNAs are advantageous in almost every category compared to upright, which suggests that weakening of the trap in the presence of excessive heat generation in a nanotweezer can be compensated by forcing trapped particles against the substrate, viz., using an inverted orientation. Indeed, the maximum trapping efficiency measured for inverted Cr-AL BNAs is 0.38 ± 0.02 for 1.0-μm spheres with λnr, whereas the corresponding upright value is Q ≈ 0. Therefore, in order to achieve large trapping forces using a nanotweezer, an inverted orientation may circumvent the need to actively limit convection using heat sinks or confined sample chambers.
It is useful to compare the performance of the BNA nanotweezer system with respect to other nanotweezers as well as conventional optical tweezers. Figure 4 provides a comparison of trapping efficiency and stiffness across different trapping platforms [9, 10, 27–29]. Conventional stiffness data for 0.5 and 1.0-μm spheres are taken from Ref and Ref, respectively, whereas conventional efficiency data for 0.5 and 1.0-μm spheres are taken from Ref. The represented efficiency and stiffness data from this study are taken to be the largest values measured in each category, as a function of sample orientation — a clear advantage of the BNA system over conventional tweezers in both stiffness and efficiency is evident. The two nanotweezer systems used for comparison are both inverted systems, one being a gold grating excited resonantly at low NA (0.6 NA) with 15 mW input power  and the other discrete nanodot antennas excited resonantly at high NA (1.3 NA) with a high input power of 440 mW . They are specifically chosen due to the fact the particle size and material investigated closely match those used in the current study. However, the particles used in Ref. 10. are 20% smaller than those used in this study (400 nm in diameter instead of 500 nm). The relation between the trap stiffness and particle mean-squared displacement (xm2) can be written as γκ = (6πηε (a,h)a)κ = xm2/D, where D is the particle diffusion coefficient and a is the particle radius. Thus, by decreasing the particle size by 20%, the trap stiffness must increase by ∼ 25 % to maintain a constant xm2 . As a result, the stiffness data for Ref.  may be up to 25% larger than the value given in Fig. 4. We see that non-resonant excitation of BNAs provides comparable, if not larger, stiffness and efficiency than other, resonant plasmonic nanotweezer systems. Whereas many plasmonic nanotweezers employ discrete antennas or nanostructures, creating isolated trap sites [5–7, 9, 11, 12], an added advantage of BNAs is the capability of highly efficient, dexterous manipulation of particles over the full array.
To further demonstrate the utility of the BNAs as a plasmonic nanotweezer, experiments are performed using 300-nm diameter fluorescent spheres with Ti-AL BNAs in both upright and inverted orientations and non-resonant illumination. Figure 5 shows dark-field microscopy images of the nanoparticle manipulation in which we drag a 300-nm fluorescent sphere in a 5-μm diameter circle at ∼ 8 μm/s by scanning the input beam using a galvonometer-based scanner. This is accomplished using as little as 700 μW of input power. The associated trapping efficiency is ∼ 0.04, and overall this demonstrates a high level of dexterity in nanoparticle manipulation with BNAs that would be difficult using isolated plasmonic structures; note that the corner frequency of the Lorentzian fit is too low to provide a reliable stiffness value.
In this work, we demonstrate the strong influence of a thin, 3-nm adhesion layer and nanostructure orientation on the trapping behavior and performance of plasmonic nanotweezers. We specifically investigate Cr and Ti ALs due to their widespread use in Au nanostructure fabrication, and the results herein can serve as a benchmark for investigating alternate AL materials for plasmonic nanotweezers. Particularly, Ti-AL BNAs yield up to 30% larger stiffness and efficiency than Cr-AL BNAs due to increased heat generation by the latter, which furthermore leads to the inability of Cr-AL BNAs to trap in an upright orientaion. In this configuration, increased heat generation due either to AL material or increased input power strengthens Rayleigh-Bénard convenction, with axial force components that work to destabilize the single-particle trap. While excessive heat generation weakens the Cr-AL BNAs, preventing non-resonant, upright Cr-AL BNAs from trapping, it also brings about beneficial trapping phase behavior in Ti-AL BNAs that can be utilized for multi-purpose particle manipulation and size-dependent particle sorting. Moreover, convection forces can increase lateral trapping efficiency by balancing applied forces, allowing for higher particle manipulation velocities. As such, heat generation in plasmonic nanotweezers is not necesarily deleterious to the trap.
In the inverted orientation, the plasmonic nanotweezer functions as a 2D optical trap in which pinning of trapped particles to the substrate via the scattering force and the axial gradient force can compensate for axial Rayleigh-Bénard forces. This allows access to larger single-particle trapping forces (by virtue of larger available input powers) which may be preferable for trapping nanoparticles, at the expense of eliminating plasmonic trapping phase behavior. Overall, the dramatic influence of nanostructure orientation on trapping behavior justifies the distinction between upright and inverted nanotweezers.
Non-resonant excitation of the BNAs produces up to 4.4x the stiffness and 3.9x the efficiency as resonant excitation, which can be attributed to a trade off between optical and thermally-induced forces. This result is especially important for biological applications — it offers high trapping efficiencies while reducing the local intensity, thereby mitigating potential phototoxic effects. Furthermore, it suggests existence of an optimum excitation wavelength for a given nanotweezer, which will be the subject of a future study. We also demonstrate dexterous manipulation of 300-nm fluorescent particles in a plasmonic optical trap. Tanaka et. al. achieved strong trapping of 350-nm particles using nanoblocks with a 5-nm gap, which suggests that the stiffness and efficiency of BNA-based nanotweezers can be increased by reducing the current 20-nm gap size . Indeed, FDTD calculations show that the local intensity enhancement can be increased ∼ 5x by reducing the gap to 5 nm (with an associated ∼ 100-nm resonance peak shift). Thus, decreasing the gap size is a promising method to achieve better trapping performance with plasmonic nanotweezers.
Tables 3 and 4 summarize the experimentally measured trap stiffness and efficiency values, respectively, for all parameters investigated in this study. The error in stiffness measurements lies in the range ∼ 5– 20% and is likely a result of the low-corner frequencies measured.
This work is supported by the National Science Foundation (NSF ECCS 10-25868).
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