Transport and Trapping in Two-Dimensional Nanoscale Plasmonic

Aug 9, 2013 - KEYWORDS: Plasmonics, optical lattice, optical sorting, optical tweezer, Brownian ... Recent advances in optical trapping techniques hav...
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Transport and Trapping in Two-Dimensional Nanoscale Plasmonic Optical Lattice Kuan-Yu Chen,† An-Ting Lee,‡ Chia-Chun Hung,† Jer-Shing Huang,*,‡,§,∥ and Ya-Tang Yang*,† †

Department of Electrical Engineering, ‡Department of Chemistry, §Center for Nanotechnology, Materials Sciences, and Microsystems, and ∥Frontier Research Center on Fundamental and Applied Science of Matters, National Tsing Hua University, Hsinchu 30013, Taiwan, R.O.C. S Supporting Information *

ABSTRACT: We report the transport and trapping behavior of 100 and 500 nm diameter nanospheres in a plasmonenhanced two-dimensional optical lattice. An optical potential is created by a two-dimensional square lattice of gold nanostructures, illuminated by a Gaussian beam to excite plasmon resonance. The nanoparticles can be guided, trapped, and arranged using this optical potential. Stacking of 500 nm nanospheres into a predominantly hexagonal closed pack crystalline structure under such a potential is also reported. KEYWORDS: Plasmonics, optical lattice, optical sorting, optical tweezer, Brownian motion, microfluidics

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such optical potentials. Our experiment has been inspired by the pioneering work conducted by Dholakia’s group7 and is essentially a scaled-down incarnation of their washboard optical potential created by a Bessel-Gaussian beam, albeit through the application of plasmonics. To create our two-dimensional plasmonic array, we pattern metallic nanostructures on an ITO-coated (indium tin oxide) cover glass by electron beam lithography, thermal evaporation of a 40 nm gold layer and the lift-off technique. Adhesion layer is not used in order to minimize the damping of localized surface plasmon resonance. We define our periodic potential by using a lattice and associate each lattice point with a primitive cell. In this experiment, we have chosen a square lattice with period 1 μm, and each primitive cell contains four disks of diameter D = 200 nm. Typically, 7 × 7 arrays are used for the data presented here, as shown in Figure 1a. To excite the plasmonic resonance, we have built a custom optical setup by modifying a commercially available optical trap kit (OTKB, Thorlabs Inc.; for details, see Supporting Information). An infrared diode laser (PL980P330J, Thorlabs) with a wavelength of 980 nm and a fiber output is fed into and only partially overfills the rear aperture of a high numerical aperture oil immersion microscope objective (NA = 1.25, ×100, Nikon) for the beam to be loosely focused on the gold nanostructure array. The objective in conjunction with a dichroic filter set (41001, Chroma Technology) is also used for the imaging of fluorescent polystyrene nanospheres (Invitrogen) using 470 nm LED light (Touchbright) as an excitation source. The

ecent advances in optical trapping techniques have enabled the creation of one-, two-, and three-dimensional periodic potentials (or optical lattices) at the microscale.1−12 These optical potentials have led to numerous interesting fundamental studies and technical applications including the thermal ratchet,6 the washboard potential,7 kinetic lock-in,8 optical sorting of microparticles,9,11 and the optical crystallization and binding of microparticles.12 The optical trapping and manipulation of microscale and nanoscale particles was pioneered by Ashkin et al. in the early 1970s.2 Far-field optical trapping techniques, such as traditional optical traps, face trapping size limitations based on the diffraction limits; in particular, considering an object of radius a, the trapping efficiency drops rapidly (following a ∼a3 law) .13 To overcome these diffraction limits, researchers have developed near-field optical trapping techniques; the optical manipulation of nanoparticles has been demonstrated using waveguides, ring resonators, photonic crystal resonators, and plasmonic metallic nanostructures.14−28 Compared to photonic structures made from dielectric materials,15−19 metallic plasmonic nanostructures allow deep subwavelength concentration of the light20 and resonant enhancement of the optical field intensity.29 Trapping of a wide range of objects such as bacteria, micro- and nanoparticles, and even as small as a single protein molecule has been demonstrated.20−28 Metallic plasmonic structures also present an opportunity for large-scale integration of lab-on-achip applications.30 Recently, optical sorting of metallic nanoparticles based on negative refraction effect of a plasmonic crystal has been reported.31 Here we present a more direct approach to create a periodic potential by simply illuminating a two-dimensional array of plasmonic nanostructures and study the transport and trapping behavior of the nanospheres under © XXXX American Chemical Society

Received: May 3, 2013 Revised: July 11, 2013

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simulation, as shown in Figure 1c. The optical lattice has a spatially dense periodic potential from each primitive cell with a spatially slowly varying Gaussian envelope. Single particle trajectories are recorded in our experiment and the images are then processed frame by frame with the Matlab program to extract each particle trajectory. 32 Representative results are displayed in Figure 2a,b for

Figure 1. Microscope setup and optical lattice design. (a) Experimental setup used to excite surface plasmon resonance. A Gaussian beam at a wavelength of 980 nm is used to excite the surface plasmon resonance of the nanostructures through a microscope objective (100× NA = 1.25, Nikon). (b) Simulated time-averaged electric field intensity enhancement |E|2/|Einc|2 distribution recorded at the plane 55, 90, and 290 nm above the substrate. Surface plasmon resonance on a primitive cell is excited by x-polarized light. Each primitive cell consists of four gold nanodisks with thicknesses of 40 nm and diameters of 200 nm, as indicated by the white dashed circles. (c) Representative intensity profiles of the optical lattice under Gaussian illumination with waist w ∼ 7.4 μm at 55, 90, and 290 nm above the substrate. The array consists of a 7 × 7 square lattice of gold nanostructures. The period of this square lattice is 1 μm.

Figure 2. Single particle trajectory. (a) Single 500 nm diameter nanospheres entering the edge of the array are attracted to the central region. Each trajectory is collected separately and compiled into this figure. The frame-by-frame points here are obtained by image processing of the recorded movie at 10 frames per second. (b) Same as (a) but for 100 nm diameter nanospheres. The data are taken and processed at 15 frames per second. (c) The square of distance versus time for 500 nm diameter nanospheres is displayed for the same trajectory as in (a) with the same color codes used. The black dashed line shows the expectation value of the square of the free diffusion distance of a sphere of the same size. (d) Same as (c) but for 100 nm diameter nanospheres. For all data presented here, the total incident laser power is ∼4.75 mW. For clarity of presentation, the trajectory points after the particle reaches the center have been removed.

scattering from the trapping laser is rejected by using a long pass filter (FM01, Thorlabs). Two nanosphere sizes with diameters d1 = 500 nm and d2 = 100 nm are used in our experiments. These nanospheres are dispersed in deionized water and are dispensed on the gold nano array sample. The motion of the nanospheres is then recorded using a chargecoupled device (CCD) camera (DCU224C, Thorlabs Inc.). Our array is illuminated with an expanded Gaussian beam with an intensity profile defined by I = I0 exp(−2r2/w2), where r is the azimuthal radius and the spot size w is ∼7.4 μm. We have performed finite-difference time-domain (FDTD) simulations of the electromagnetic field distribution within a primitive cell. The structure is designed to resonate at a wavelength of 980 nm. The representative optical intensity profiles of a primitive unit cell simulated by FDTD method at 55, 90, and 290 nm above the substrate are shown in Figure 1b. Note that the plasmon modes of each nanodisk within a primitive cell couples with each other due to the small gap (∼48 nm) between the two neighboring nanodisks. Within each cell at 90 nm above the substrate, four pronounced trapping sites are produced under excitation by linearly polarized light. The density of these trapping sites is therefore 4 sites/μm2, which is more than 20 times the density of a previous diffraction-limited twodimensional optical lattice created by a holographic technique that was reported in the literature.9 The center of the Gaussian beam is aligned with the center of the array. With such an illumination profile, the representative optical intensity profiles can be calculated based on the intensity data from the FDTD

nanospheres with diameters of 500 and 100 nm, respectively (see also the Supporting Information for movies). Because we can intuitively understand that the particles tend toward the lowest potential energy region in the central region of the maximum optical intensity, we expect them to be attracted to and trapped within the central region of the lattice and this is indeed what we observed. In general, the particles roaming around the optical lattice have a finite probability of being captured by the lattice. The particles, when captured by the lattice, exhibit a running state and are always attracted from the edge toward the central region of the lattice, regardless of the different routes taken, as shown in Figure 2a,b. This is very similar to the behavior that was previously reported for a washboard type potential with a Bessel-Gaussian beam shape.7 Note that the presence of the plasmonic structure enables the trapping of nanospheres at such low optical power. This is especially striking if we estimate the optical potential energy W to be 4 × 10−3 kBT in the absence of the plasmonic structure for the nanospheres of diameter 100 nm (d ≪ λ) in the center of the expanded Gaussian beam (see Supporting Information). Here kBT is the thermal energy at room temperature and as a rule of thumb the optical potential at least ∼10 kBT is needed B

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Figure 3. Multiple particle trapping of nanospheres. (a) Successive fluorescent images of the trapped 500 nm nanospheres are displayed here. The laser illumination is initially turned on at t = 0 s. As time progresses, the particles accumulate in the central region and form predominant (hexagonal) closed pack structures. Finally, at t = 34 s, the laser illumination is turned off and the particles disperse and escape from the array. The total incident laser power is ∼4.75 mW. (b) Same as (a) but for 100 nm diameter nanospheres. At t = 0 s, the laser illumination is turned on. At t = 4 s, the first particle is captured and is trapped in the central region. As time progresses, the particles accumulate in the central regions but are only loosely trapped. When the laser illumination is turned off at t = 46 s, the particles escape from the array. The total incident laser power is ∼3.5 mW (see Supporting Information for movies).

for stable trapping. Such an optical potential is too small to guarantee any observable trapping without plasmonic nanostructures. A control experiment is done on a bare glass without plasmonic nanostructures and with the same Gaussian illumination and no trapping of nanospheres of both sizes is observed because the optical power is too small to create a significant optical gradient fore for trapping. For quantitative comparison of the observed transport process with that of free diffusion, we define the square of the (two-dimensional) distance R2 as R2 = (x − x0)2 + (y − y0)2, where x and y are the frame by frame coordinate points of each trajectory and x0 and y0 are the coordinates of the initial (edge) point of the trajectory. We plot the square of the distance versus time in Figure 2c,d for the same trajectories that were shown in Figure 2a,b. As a comparison, the expectation value of the square of the free diffusion distance versus time, which is given by ⟨R2(t)⟩ = 2Dt, is also plotted with the free diffusion coefficient D0 = kBT/3πηd, where kB, T, η, and d are the Boltzmann constant, the temperature, the viscosity of the medium, and the diameter of the spheres, respectively.33 At T = 298 K, we use η = 8.9 × 10−4 Pa s for the viscosity of the water34 to obtain the diffusion coefficient D1 = 0.98 μm2/s when d = d1 = 500 nm, and D0 = 4.9 μm2/s when d = d2 = 100 nm. The observed transport process is obviously faster than that of free diffusion. For each trajectory displayed in Figure 2a,b, we can define the effective drift velocity veff by veff = R/Tp, where R is the distance from the edge to the center and Tp is the corresponding passage time.35 With such a definition, the observed effective velocity ranges from 3.1 to 5.7 μm/s for nanospheres of diameter 500 nm and from 3.6 to 8.5 μm/s for nanospheres of diameter 100 nm (for details, see Supporting Information). Here, we did not observe significant difference in the velocity of two kinds of spheres. A plausible explanation might be that the stronger optical force experienced by larger spheres is compensated by larger frictional force due to Stoke drag, which is proportional to the particle diameter.34 We point out that a quantitative theoretical analysis involves not only calculating the optical potential from the plasmon electromagnetic field but also solving the problem of a particle in a Gaussian enveloped periodic potential. Although it is beyond the scope of this work, we believe that our single particle trajectory experiment can be best treated and simulated with the path integral formulation of the Fokker−Planck equation.36

Multiple particle trapping in the central region of the array is also observed for both particle sizes. Successive images extracted from a representative motion video of the particle are displayed in Figure 3a,b for nanospheres with diameters of 500 and 100 nm, respectively. For the 500 nm diameter nanospheres, the particles are tightly trapped by the plasmonic nanostructures, and stacking of the nanospheres is observed (see Supporting Information for movies). Similar particle stacking has been observed with a three-dimensional optical trap.10 Closer examination actually reveals that the nanospheres form a predominantly closely packed (hexagonal) crystalline structure, which is similar to that observed in the case of surface plasmon excitation.22 This is understandable since the particles tend to smear out the fine feature of the nanoscale potential as shown in Figure 1c for the optical intensity 290 nm above the substrate so the hexagonal phase bears no resemblance in terms of symmetry to the underlying optical potential, which has square crystalline structures. Similar symmetry breaking has also been observed for entropically driven self-assembly of colloidal particles on patterned substrates.37 Also, we observe slight fluorescent intensity fluctuations consistent with the result reported.38 In contrast, nanospheres of diameter 100 nm are more loosely trapped. Because of resolution limit, we can not count exact number of the trapped 100 nm particle nor can we clearly observe particle stacking. In conclusion, we have shown that a plasmonic enhanced optical lattice can be used to guide and arrange nanoparticles. The experiments reported here can be extended to the study of other stochastic transport phenomena, such as the kinetic lockin of nanoparticles,8 and the realization of optical matter crystallization and binding.12 In principle, we can also achieve nanoparticle sorting based on optical fractionation. 9,11 Compared to holographic or interference techniques,9,10 the plasmonic optical lattice has subwavelength spatial features and is considerably easier to set up with less complicated optical components and is therefore more suitable for integration with microfluidic systems for lab-on-a-chip applications.30 Finally, the scaling down of our experiment also has far reaching implications. Recently, several theoretical works have also explored the feasibility of creating plasmon-enhanced singleatom optical traps39−41 and optical field confinement down to the atomic scale has been reported.42 Scaling down of the plasmonic optical lattice certainly requires considerable engineering effort. It will obviously be necessary to lithoC

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(13) Wright, W. H.; Sonek, G. J.; Berns, M. W. Radiation trapping forces on microspheres with optical tweezers. Appl. Phys. Lett. 1993, 63, 715−717. (14) Kawata, S.; Tani, T. Optically driven Mie particles in an evanescent field along a channel waveguide. Opt. Lett. 1996, 21, 1768− 1770. (15) Yang, A. H. J.; Moore, S. D.; Schmit, B. S.; Klug, M.; Lipson, M.; Erickson, D. Optical Manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides. Nature 2009, 457, 71−75. (16) Lin, S.; Schonbrun, E.; Crozier, K. Optical manipulation with planar silicon microring resonators. Nano Lett. 2010, 10, 2408−2411. (17) Lin, S.; Crozier, K. Planar silicon microrings as wavelengthmultiplexed optical traps for storing and sensing particles. Lab Chip 2011, 11, 4047−4051. (18) Mandal, S.; Serey, X.; Erickson, D. Nanomanipulation using silicon photonic crystal resonators. Nano Lett 2010, 10, 99−104. (19) Novotny, L.; Hecht, B. Principle of Nano Optics, 2nd ed.; Cambridge University Press: Cambridge, 2012. (20) Juan, M. L.; Gordon, R.; Pang, Y.; Eftekhari, F.; Quidant, R. Plasmon nano optical tweezer. Nat. Photonics 2009, 5, 915−919. (21) Novotny, L.; Bian, R. X.; Xie, X. S. Theory of nanometric optical tweezers. Phys. Rev. Lett. 1997, 79, 645−648. (22) Garcés-Chávez, V.; Quidant, R.; Reece, P. J.; Badenes, G.; Torner, L.; Dholakia, K. Extended organization of colloidal microparticles by surface plasmon polariton excitation. Phys. Rev. B 2006, 73, 085417. (23) Volpe, G.; Quidant, R.; Badenes, G.; Petrov, D. Surface plasmon radiation forces. Phys. Rev. Lett. 2006, 96, 238101. (24) Righini, M.; Zelenina, A. S.; Girard, C.; Quidant, R. Parallel and selective trapping in a patterned plasmonic landscape. Nat. Phys. 2007, 3, 477−480. (25) Righini, M.; Volpe, G.; Girard, C.; Petrov, D.; Quidant, R. Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range. Phys. Rev. Lett. 2008, 100, 183604. (26) Zhang, W.; Huang, L.; Santschi, C.; Martin, O. J. F. Trapping and sensing 10 nm metal nanoparticles using plasmonic dipole antennas. Nano Lett. 2010, 10, 1006−1011. (27) Pang, Y.; Gordon, R. Optical trapping of 12 nm dielectric spheres using double-nanoholes in a gold film. Nano Lett. 2011, 11, 3763−3767. (28) Pang, Y.; Gordon, R. Optical trapping of single protein. Nano Lett. 2012, 12, 402−406. (29) Stockman, M. L. Spaser action, loss compensation, and stability in plasmonic systems with gain. Phys. Rev. Lett. 2011, 106, 156802. (30) Huang, L.; Maerkl, S. J.; Martin, O. J. F. Integration of plasmonic trapping in a microfluidic environment. Opt. Express 2009, 17, 6018−6024. (31) Cuche, A.; Stein, B.; Canguier-Durand, A.; Devaux, E.; Genet, C.; Ebbesen, T. W. Brownian motion in a designer force field: dynamical effects of negative refraction on nanoparticles. Nano Lett. 2012, 12, 4329−4332. (32) The threshold detection algorithm is used and we locate the pixel maximum intensity to find the position of the particle. The position resolution is ±20 nm, determined by the calibrated dimension of the pixel. For our single particle trajectory, such resolution is sufficient to characterize the transport for our purpose. (33) Note that in the presence of the substrate surface, there is a correction factor to reduce the self-diffusion due to the surface effect. Because we do not know the exact distance between the nanosphere and the substrate surface, this effect cannot be exactly accounted. At best, we can only state that the free self-diffusion coefficient estimate serves an upperbound of the self-diffusion coefficient if we assume the no slip boundary condition. See Dufresne, E. R.; Altman, D.; Grier, D. G. Brownian dynamics of a sphere between parallel walls. Europhys. Lett. 2001, 53, 264−270. (34) (a) Reif, F. Fundamentals of Statistical and Thermal Physics, 1st ed.; McGraw-Hill: New York, 1965. (b) Kestin, J.; Sokolv, M.; Wakeham, W. A. Viscosity of liquid water in the range −8 to 150 °C. J. Phys. Chem. Ref. Data 1978, 7, 941−948.

graphically reduce the feature sizes of the devices. Also, the device surfaces must be passivated to prevent unwanted adsorption of the trapped objects and appropriate thermal management is required to prevent excessive ohmic heating as a result of light illumination.43 However, we believe that the results of these efforts will be very rewarding; these optical lattices will ultimately enable atomic physicists to study collective coherent interactions and explore novel many-body physics problems.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information, figure, tables, and movies. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (J.S.H.) [email protected]; (Y.T.Y.) ytyang@ ee.nthu.edu.tw. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Dr. K. H. Lin for useful discussions. The authors also acknowledge the support of National Tsing Hua University under Grants 101N20448E1 and 102N2042E1 and NSC Grants NSC 99-2113-M-007-020MY2 and NSC 101-2113-M-007-002-MY2.

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