Light-Assisted, Templated Self-Assembly Using a Photonic-CrystalSlabEric Jaquay,† Luis Javier Martínez,† Camilo A. Mejia,‡ and Michelle L. Povinelli*,†

†Ming Hsieh Department of Electrical Engineering and ‡Department of Physics and Astronomy, University of Southern California,Los Angeles, California 90089, United States

*S Supporting Information

ABSTRACT: We experimentally demonstrate the technique of light-assisted,templated self-assembly (LATS). We excite a guided-resonance mode of aphotonic-crystal slab with 1.55 μm laser light to create an array of optical traps.We demonstrate assembly of a square lattice of 520 nm diameter polystyreneparticles spaced by 860 nm. Our results demonstrate how LATS can be used tofabricate reconfigurable structures with symmetries different from traditionalcolloidal self-assembly, which is limited by free energetic constraints.

KEYWORDS: Optical trapping, self-assembly, photonic crystal, nanomanipulation

The force of light on objects provides tremendous flexibilityfor nanoscale manipulation. While conventional optical

tweezers use the optical gradient force of a focused laser,1−3

recent work has leveraged the strong field gradients nearmicrophotonic devices for particle trapping.4−15 However, suchwork has focused on trapping single or few particles. We haveproposed to use optical forces near microphotonic devices for afundamentally different purpose: to assemble periodic arrays ofnanoparticles resembling synthetic, reconfigurable two dimen-sional (2D) crystals.16,17 Our approach, called light-assisted,templated self-assembly (LATS), exploits photonic-crystal slabsto create resonantly enhanced optical forces orders ofmagnitude larger than radiation pressure.16,17 Here we providethe first experimental demonstration of LATS, assembling asquare array of over 100 polystyrene particles near a siliconphotonic-crystal slab. Our method, ideally suited for on-chipintegration, should provide a platform for flow-through, serialfabrication of 2D or 3D-nanostructured materials, all-opticallytunable photonic devices, and lab-on-a-chip applications.The LATS process is shown schematically in Figure 1. Light

is incident from below on a photonic-crystal slab, whichconsists of a silicon device layer patterned with a periodic arrayof air holes. The slab is designed to support guided-resonancemodes, electromagnetic modes for which the light intensitynear the slab is strongly enhanced.18 Our previous work hastheoretically predicted16 that when the incident laser is tuned tothe wavelength of a guided-resonance mode, nanoparticles willbe attracted toward the slab. The attractive, optical force arisesfrom a strong electric-field gradient just above the slab surface.In addition, the nanoparticles will experience lateral opticalforces due to the electromagnetic field structure of the guided-resonance mode, resulting in the assembly of a nanoparticlearray.Unlike traditional colloidal self-assembly for which free

energy minimization results in hexagonal, close-packedstructures, our process is not subject to such constraints. In

this paper, we experimentally demonstrate the formation of asquare lattice as one such example. Indeed, the use of light todrive the system dramatically alters the underlying potentiallandscape, potentially allowing for the formation of a range ofcomplex lattices16,17 and multiparticle clusters.19 Nanoparticlearrays assembled using LATS can be viewed as “programmable

Received: March 12, 2013Revised: April 5, 2013

Figure 1. Schematic of light-assisted, templated self-assembly (LATS).Incident light from below excites a guided-resonance mode of aphotonic-crystal slab, giving rise to optical forces on nanoparticles insolution. Under the influence of the forces, the nanoparticles self-assemble into regular, crystalline patterns.

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optical matter”:20 turning the laser on and off will reversiblyassemble or disassemble the structure. Moreover, excitingdifferent resonance modes of the photonic crystal, by adjustingthe wavelength of the input laser, should allow differentcrystalline structures to be formed.16

Light-driven assembly of multiparticle patterns has previouslybeen achieved using structured light fields generated byinterference fringes, holography, spatial light modulators, orother methods.21−23 Our approach differs crucially fromprevious work in that it exploits near-field, rather than far-field, effects. Rather than generating a structured light beam viafree-space optics, we use a simple, Gaussian input beam. Thestructured light field responsible for trapping is generated bythe interaction of light with the photonic-crystal device. Here,we demonstrate the method using an external laser incident ona photonic-crystal slab. Ultimately, however, LATS could becarried out using a photonic-crystal laser, allowing theintegration of the light source with the trapping device andmaking our approach highly suitable for on-chip integration.We thus expect a wide range of applications from all-opticallytunable photonic devices, to materials assembly, to biologicaltrapping and manipulation.We designed, fabricated, and characterized a photonic-crystal

slab for use in the LATS process. An electron micrograph isshown in Figure 2a. The device was fabricated in silicon usingelectron-beam lithography and reactive ion etching (seeSupporting Information Methods). The dimension and spacingof the holes was designed to support doubly degenerate guided-resonance modes near 1.55 μm. The lattice constant a is 860nm, and the hole radius is 0.174 Å(150 nm). The thickness ofthe silicon device layer is 250 nm. The magnetic field profileresulting from an x-polarized, incident plane wave is shown inFigure 2b. Fields were calculated using the three-dimensional

finite-difference time-domain method (FDTD). The field-profile for a y-polarized incident wave is rotated by 90°. Figure2c shows the measured transmission spectrum of the device.The guided-resonance mode appears as a dip in the

spectrum. The quality factor Q was determined to be ∼170by fitting to a Fano-resonance shape.We carried out the assembly process in a microfluidic

chamber filled with 520 nm diameter polystyrene particles,using a laser power of 64 mW. Figure 3 shows snapshots of theLATS process. The photonic-crystal lattice is visible in thebackground of each frame. When the laser beam is turned on,nanoparticles are attracted to the slab and begin to occupy sitesof the square lattice (Figure 3a). As time progresses, additionalparticles diffuse into the region where the beam intensity is highand begin to form a cluster (Figure 3b). Eventually, a regulararray of particles is formed (Figure 3c). The square symmetryof the assembled particles is evident from the picture. When thelaser beam is turned off, the particles immediately begin todisperse and diffuse away from the slab (Figure 3d). Full videosof the assembly and release processes are included in theSupporting Information. The frames in Figure 3 were recordedwith a dilute particle solution for clarity of imaging andrepresent an elapsed time of approximately 1 h. Faster clusterformation occurs with solutions of higher concentration.We have explored the dependence upon power, wavelength,

and particle diameter. The size of the cluster, that is, thenumber of particles trapped, decreased in a monotonic fashionas the power was decreased, or as the wavelength was tunedaway from resonance. We also attempted to assemble two othersizes of polystyrene particles, 380 nm and 1 μm. We were ableto assemble a square lattice of 380 nm particles. The trappedparticles exhibited more Brownian motion when compared tothe 520 nm particles. We did not observe trapping with 1 μm

Figure 2. Square lattice photonic crystal. (a) SEM image of photonic-crystal slab. The scale bar in the inset is 1 μm. (b) A 3D FDTD simulation ofthe magnetic field (Hz) for a normally incident, x-polarized plane wave. Circles represent the positions of holes; four unit cells are shown. (c)Measured transmission spectrum (log scale).

Figure 3. Light-assisted, templated self-assembly of 520 nm diameter particles above a photonic-crystal slab. The square lattice of the slab is visible inthe background, oriented at 45° with respect to the camera. (a−c) Sequential snapshots taken with the light beam on. (d) Snapshot taken after thebeam is turned off.

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particles. This is likely due to the increased scattering cross-section, which results in a net repulsive force away from theslab.Each site of the square lattice may be viewed as an optical

trap. We used particle-tracking software to analyze particlemotion for fully assembled clusters (see Supporting Informa-tion Methods). Figure 4a shows the recorded particle positions

extracted from a 20 s video. The incident light was polarizedalong the x-direction of the lattice. The figure shows that theparticles tend to stay above the holes in the photonic crystalwith some variation in position over time. Each blue ellipserepresents a fit to the data in a single unit cell. It can be seenthat the variation in particle position increases at the edge ofthe trapping region due to the reduction in power away fromthe center of the beam.The stiffness of each trap can be determined from the

variance in particle position.24 Figure 4b,c shows histograms ofthe in-plane stiffness values extracted from the videos. Thestiffness of each trap was normalized to the local intensity inthat unit cell (see Supporting Information Methods). Weobserve that the power-normalized stiffness over the array oftraps is normally distributed, both for the parallel andperpendicular stiffness. The mean parallel stiffness is lowerthan the perpendicular stiffness, as shown in Table 1 (0° angle).

We observe that the trap stiffness can be tuned by rotatingthe direction of incident light. When the incident light ispolarized at 45° with respect to the lattice directions, thestiffness values are approximately the same in the x- and y-directions (Table 1). This is to be expected, since the incidentlight excites both of the doubly degenerate modes with equalstrength. At 90°, the stiffness in the parallel direction (y) isagain lower than in the perpendicular (x) direction. The abilityto tune the stiffness with incident light indicates the strongoptical nature of our traps. The mean values of stiffness arecomparable to those reported elsewhere in the literature forsingle particle traps.25

Using the Stokes drag method (see Supporting InformationMethods), we experimentally estimated the maximum forceexerted on the particles by the traps to be 0.3 pN.To understand how the optical forces result in the observed

nanoparticle patterns, we calculated the force numerically (seeSupporting Information Methods). Figure 5a shows the forceon a 520 nm diameter particle whose bottom edge is 25 nmabove the surface of the photonic crystal slab for x-polarizedlight. The background color represents the vertical force, wherea negative force indicates attraction toward the slab. There aretwo regions above and below the hole where the force is slightlyrepulsive, but at any other position within the unit cell theparticle is attracted to the slab. The arrows represent the in-plane forces.To determine the equilibrium position of the trapped

particle, we calculate the optical potential. Given the relativesize of the particles (260 nm radius) and holes (150 nm radius)in our experiment, the particle can be partially drawn into thehole by the attractive vertical force. We calculate the opticalpotential as a function of x−y position. For each x−y position,the vertical height of the particle is as small as possible, giventhe geometrical constraints (see inset in Figure 5b). The resultis shown by the blue line (“total potential”) in Figure 5b,c. Itcan be seen that the stable equilibrium position is in the centerof the hole (x = 0, y = 0), which is in agreement withexperiments.The ability of the particle to sink into the hole is a key factor

in determining the equilibrium positions. For comparison, thered, dashed line (“in-plane potential”) in Figure 5b shows theoptical potential calculated at a constant z-height (bottom edgeof particle 25 nm above the slab surface). Two local minima areobserved at the edges of the hole, which are indicated by green,dashed lines. From inspection of Figure 5a, it can be seen thatthese points correspond to locations where the in-plane forcesare zero. However, these two minima are not stable equilibriumpositions of the total potential (Figure 5b).From our experiments, we determined that the threshold

intensity for trapping was 134 μW per unit cell (see SupportingInformation Methods). For this intensity, the calculatedpotential depth is 4.5 kBT.In summary, we have experimentally demonstrated the

technique of light-assisted, templated self-assembly (LATS).Our technique uses the resonantly enhanced near field of aphotonic-crystal slab to create periodically spaced optical traps.Nanoparticles in solution are attracted to the slab and formordered arrays. We have observed the assembly of 100polystyrene particles with 520 nm diameter in a square latticeusing 64 mW of incident power. We have measured thetrapping stiffness as a function of incident polarization, and wehave shown that the equilibrium trapping positions can bepredicted via calculation of the optical forces.Our technique can be extended to assemble larger numbers

of particles by designing the photonic-crystal slab to reduce theinput power per area required for trapping. The input beam canthen be spread over a larger area, resulting in a larger cluster.One approach to reducing the required power per area is to usea mode with a higher quality factor, resulting in higher near-field intensity. Another approach is to use slot-confinementeffects to strongly localize the field in the trapping regions, aswe have previously studied theoretically.17

The LATS approach can be used to assemble complexstructures with symmetries not constrained by the typical freeenergetic constraints; here we have demonstrated just one. We

Figure 4. Trap stiffness for incident, x-polarized light. (a) Particlepositions (red dots) extracted from a 20 s video. Blue ellipsesrepresent two standard deviations in position. (b) Histogram ofstiffness values in the direction parallel to the polarization of theincident light. (c) Stiffness in the direction perpendicular to theincident polarization.

Table 1. Polarization Dependence of Trap Stiffness

angle κx (pN nm−1 W−1) σx κy (pN nm−1 W−1) σy

0° 1.48 0.35 2.25 0.4845° 1.88 0.52 1.79 0.4690° 2.08 0.40 1.39 0.29

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envision that judicious template design will allow the assemblyof a variety of lattice types with complex unit cells. Moreover,changing the wavelength of the incident beam to excite adifferent resonance can be used to reconfigure the particlearrangement.14 The use of metal nanoparticles or quantum dotsis also an area for future exploration. While in the currentexperiment with polystyrene particles we did not observeevidence of optical binding26 or self-induced back-action,27

such effects may yield rich assembly behavior in alternateparticle systems.We anticipate that our technique will find applications in the

fabrication of metamaterials and other photonic devices. Forexample, postassembly polymerization could be used to transfer2D nanoparticle arrays to another substrate. Our preliminaryresults indicate that it is also possible to assemble 3D arrays insitu.LATS should also allow a variety of dynamic, real-time

applications. One example is the use of the assembled,reconfigurable “photonic matter” as an all-optically tunabletransmission filter. Other applications, based on particledynamics in the 2D optical potential, include particlesorting28,29 and ratchet behavior.30 We also expect that LATSmay be extended for batch processing of biological objects,providing a novel tool for reconfigurable control over spatiallymediated biological interactions.Finally, LATS naturally lends itself to compact integration

on-chip. By fabricating the photonic-crystal device in an activematerial, the light source could be integrated with the trappingdevice, allowing for system miniaturization.

■ ASSOCIATED CONTENT*S Supporting InformationMethods and Supplementary Videos 1 and 2. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: povinell@usc.edu.NotesThe authors declare no competing financial interests.

■ ACKNOWLEDGMENTSThe authors thank Mia Ferrera Wiesenthal for rendering theschematic in Figure 1. This project was funded by an ArmyResearch Office PECASE Award under Grant 56801-MS-PCS.

Computation for work described in this paper was supportedby the University of Southern California Center for High-Performance Computing and Communications. The authorsthank Ningfeng Huang, Jing Ma, and Chenxi Lin for fruitfuldiscussions.

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Figure 5. Calculated optical forces and potentials. (a) Force map in one unit cell. The black circle represents the position of a hole, and the color barrepresents the vertical optical force in dimensionless units of Fc/P, where c is the speed of light and and P is the incident optical power. A negativeforce indicates attraction toward the slab. The arrows represent the magnitude of the lateral optical force. The length of the white arrow at thebottom center of the figure corresponds to the maximum in-plane value of 1.6. (b) The potential through the center of the hole along the x-direction. The green dashed lines indicate the position of the hole. (c) The potential through the center of the hole along the y-direction.

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