Near-Field, On-Chip Optical Brownian Ratchets - Nano Letters (ACS

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Near-field, on-chip optical Brownian ratchets Shao-Hua Wu, Ningfeng Huang, Eric Jaquay, and Michelle L. Povinelli Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b02426 • Publication Date (Web): 12 Jul 2016 Downloaded from http://pubs.acs.org on July 13, 2016

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Near-field, on-chip optical Brownian ratchets

By Shao-Hua Wu Ningfeng Huang Eric Jaquay And Michelle L. Povinelli*

KEYWORDS: Optical trapping, photonic crystal, nanomanipulation, Brownian ratchets

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June 14, 2016

All authors are affiliated with the Ming Hsieh Department of Electrical Engineering, Viterbi School of Engineering, University of Southern California, 3737 Watt Way, Los Angeles, CA 90007-0271, USA. *email: [email protected] We acknowledge financial support of this research from Army Research Office PECASE Award under Grant 56801-MS-PCS.

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Near-field, on-chip optical Brownian ratchets Shao-Hua Wu, Ningfeng Huang, Eric Jaquay, and Michelle L. Povinelli∗ *email: [email protected] Ming Hsieh Department of Electrical Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089 KEYWORDS: Optical trapping, photonic crystal, nanomanipulation, Brownian ratchets Abstract: Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25x greater trap stiffness and 10x greater transport speed than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.

Brownian ratchets1, 2 are of fundamental interest, and their understanding yields insight into natural systems from protein motors3-5 to far-from equilibrium statistical physics.6 The realization of Brownian ratchets in engineered systems1,

7-11

opens up the potential to

harness thermal energy for directed motion, and has applications in transport and sorting of


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nanoparticles8, 12 and DNA.13, 14 Optically-driven Brownian ratchets15 offer opportunities for tuning and reconfiguration. By using different laser wavelengths, polarizations, and wave fields, complex optical potential landscapes can be created16 and modulated in time.17 Previous work based on conventional and holographic optical tweezers18,

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has

demonstrated ratchet motion. The on-chip implementation of optical Brownian ratchets would greatly facilitate applications in lab-on-a-chip, microfluidic environments, from particle sorting to directed transport. Optical ratchets20 based on plasmonic traps21-23 have been proposed theoretically but not demonstrated. Here, we experimentally demonstrate an on-chip optical ratchet based on an all-dielectric approach. In dielectric optical traps, the strong electromagnetic field gradient near a patterned dielectric surface attracts particles to desired trapping locations.24-27 In our previous work, we have demonstrated the creation of multiple, periodically spaced trapping sites using a silicon photonic crystal template.28-30 Resonant enhancement of the optical near field of the template strongly enhances the trap stiffness. We show that by breaking the symmetry of an all-dielectric template, we can create asymmetric optical potentials suitable for on-chip ratchets. We fabricate our template design and experimentally demonstrate ultra-stable optical trapping. For 520 nm diameter polystyrene particles, our measured trap stiffness is 53 pN·nm-1·W-1, more than 25 times stiffer than conventional optical tweezers31 and >400 times higher than holographic traps.32 We demonstrate optical ratcheting with transport speeds of approximately ~1 µm/s. These speeds are greater than previous optical Brownian ratchets;7,

15, 18, 19

Refs. [18,19]

demonstrated a transport speed of 0.01 µm/s for 1.53 µm diameter particles, Ref. [15]


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demonstrated a transport speed of 0.095 µm/s for 1.5 µm diameter particles, and Ref. [7] demonstrated a transport speed of 0.2 µm/s for 0.5 µm diameter particles. Brownian Ratchets The basic principle of a Brownian ratchet involves the on-off modulation of a spatially asymmetric potential,1 shown in Figure 1a. The particle probability distribution is shown in grey and the potential in blue. Initially (top panel), the particles are trapped in the potential minima. When the potential is turned off (middle panel), the particles start to diffuse freely. The particle probability distribution becomes a set of broadened Gaussians centered on the potential minima. Particles in the shadowed region of the Gaussian diffuse past the potential maxima of the neighboring trap. When the potential is turned on again (lower panel), these particles are captured by the neighboring trap, resulting in net motion to the right. The asymmetry parameter of the potential is defined as α = 1-lf / (lf + lb), where lf +

lb is the lattice constant of the potential. With higher asymmetry of the potential (larger α), the rectification efficiency (probability of rightward motion during one cycle) is larger. Design of Asymmetric Optical Potential We consider a silicon PhC slab (n = 3.45) with a square lattice of modified triangular holes. The lattice constant a is 960 nm, and the slab thickness is 250 nm. The slab rests on a silica substrate (n = 1.45) and is covered by water (n = 1.33). The PhC slab is designed to support a guided mode resonance33 near a wavelength of 1550 nm. The guided mode resonance is strongly confined within the silicon PhC slab, and thus the electric field intensity is resonantly enhanced near the slab surface. Figure 2a shows the normalized electric field


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intensity profile (|E|2) on resonance for y-polarized incident light, calculated using a 3D finite-difference time-domain (FDTD) electromagnetic solver (Lumerical Solutions, Inc.). The white dashed line represents the position of the hole. The field profile is clearly asymmetric with respect to the y-axis and mostly concentrated in the hole. The simulated transmission spectrum is shown in Fig. 2b. A resonant wavelength λ0 of 1555 nm and a quality factor Q of ~700 were obtained by fitting the spectrum to a Fano-resonance line shape. We next calculate the optical forces acting on a dielectric nanoparticle due to the guided mode resonance of the PhC slab. We assume a 520 nm diameter polystyrene sphere with n = 1.59. In previous work, we have observed that optical forces tend to pull particles toward the PhC slab, causing the particles to sink slightly into the holes.28, 29 For a particle in contact with the slab, the vertical height can be determined as a function of the in-plane position using the geometrical constraints. The top panel of Fig. 2c shows the height of the bottom edge of the particle (z) as a function of the in-plane x position, where z = 0 is the top edge of the slab. We calculate the optical force on the particle along this (x,z) contact path by numerical integration of the electromagnetic force density over the particle volume.34 The results are shown in Fig. 2c (middle). The optical forces are in dimensionless units of Fc/P, where c is the light speed in vacuum, and P is the incident power. The negative force in the z-direction indicates attraction toward the slab, while the force in the x-direction tends to pull the particle toward the field intensity maxima. The force in the ydirection is zero, as expected due to symmetry.


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To visualize the optical potential experienced by the particle, we perform a line integration of the optical force along the contact path. Figure 2c (lower) shows the optical potential normalized to the room temperature thermal energy and the incident source power flux. For a fixed coupled power flux of 100 µW/µm2, an optical potential energy shift of 57 kBT is achieved. There are two dips in the optical potential. The potential dip with lower potential energy is a more stable trapping position and corresponds to the maximum field intensity. The second dip results from the change in contact height when the particle sinks into the hole. From simulations of the Langevin equation, we have observed that the double dip shape reduces the effective trap stiffness within each unit cell. Using the deeper of the two dips to calculate the asymmetry factor, we find a value of 0.8. Results Device characterization. To experimentally validate our near-field optical Brownian ratchet design, we fabricated the PhC using a silicon on insulator (SOI) wafer with a 250 nm device layer and a 3 µm buried oxide layer (see Methods for detail). A scanning electron microscopy (SEM) image of the device is shown in Fig. 3a. The scale bar is 2 µm, and the lattice constant is 960 nm. To characterize the device, the PhC sample is mounted on an optical characterization setup (see Methods for detail). The parallel-polarization transmission spectrum of the device is shown in Fig. 3b. By fitting the spectrum to a Fano-resonance line shape, the resonant wavelength λ0 and quality factor Q were determined to be 1553 nm and ~570, respectively. The Fabry-Perot fringes visible in the spectrum are due to reflection from the


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backside of the sample. The difference in maximum transmission values between the simulated and experimental transmission spectra is due to optical loss in the collection optics (e.g. finite numerical aperture of the collection lens and loss in the fiber to free space coupler). Trapping experiments. Optical trapping and Brownian ratchet experiments were conducted in a sealed microfluidic chamber (~700 nm height) (See Methods for fabrication detail) filled with dilute 520 nm diameter polystyrene particle solution using a laser power of 100 mW. Heavy water (D2O) is used to minimize heating effects in the system; its extinction coefficient k is 5.2×10-6 (unitless) at 1550 nm, in contrast with 1.4×10-4 for water.35 Optical trapping experiments were performed first. Multiple particles were trapped on the sample surface, as shown in Fig. 4a. Taking into account the measured beam radius (see Methods for optical setup detail), the maximum power per trap is ~160 µW. We followed the procedure described in our previous work28-30 to analyze the trap stiffness at each trap site (see Methods for stiffness analysis details). We found that the mean stiffness in the ydirection (ky = 53 pN·nm-1·W-1) is 3 times greater than the stiffness in the x-direction (kx = 18 pN·nm-1·W-1). The standard deviations of the measured values are ± 8 pN·nm-1·W-1 and ± 3 pN·nm-1·W-1, respectively. As mentioned above, the double-dip optical potential tends to reduce trap stiffness along the x-direction. Ratchet motion. To perform Brownian ratcheting, laser power modulation was initiated after tens of particles had been trapped. The modulation frequency was 10 Hz and the duty


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cycle (on time / total time) was 80%. The experiments were recorded and analyzed using microscopy-video analysis. Particle positions were detected in each video image frame, and a nearest neighbor algorithm was applied to link the particle trajectories. Fig. 4a shows four particles with linked trajectories of at least 30 s (dashed circles). Fig. 4b shows the trajectories over a 30 s time period. It is clear that the particles move preferentially to the right as the laser is modulated, with some fluctuation in position. To quantify the ratcheting behavior, we computed the mean displacement of 115 trapped particles from three experiments as a function of time (see Methods for details). Fig. 5(a) shows the mean displacement in the x-direction (red, solid line). The displacement increases linearly as a function of time, with a ratcheting speed of approximately 0.9 µm/s. In contrast, for untrapped, Brownian particles (black, dashed line), the mean displacement fluctuates around zero. Fig. 5(b) shows the mean displacements in the y-direction, which are both close to zero. It is evident that our PhC with triangular holes creates an asymmetric, periodic optical potential that rectifies the particle motion. Transport speed. We further optimize the ratchet speed by varying the laser modulation frequency. Ratcheting behavior is known to depend on the off-time of the laser.1, 7, 15, 20 In a simple theoretical picture, the relation between the forward and backward ratcheting probabilities and toff are1 1 efrc l f 2

4 Dtoff  ,

(1)

1 Pb = efrc l f 2

4 Dtoff  ,

(2)

Pf =


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where Pf (Pb) is the forward (backward) ratcheting probability, erfc is the complementary error function, lf (lb) is the forward (backward) moving distance, and D is the diffusion coefficient. The transport speed can be expressed analytically as V = ( Pf − Pb )( l f + lb ) ( toff + ton ) .

(3)

To determine the diffusion coefficient, we treated our system as an approximate 2D system and analyzed the mean squared displacement of freely-moving Brownian particles as a function of time. A linear, least-squares fit yielded a diffusion coefficient of 0.59 µm2/s. Substituting the experimental value of toff, the estimated diffusion coefficient, and the calculated asymmetry parameter of 0.8 in Equations 1 through 3, we obtain the analytical prediction of the transport speed shown in Fig. 6 (black, dashed line). The optimal average transport speed is 1.0 µm/s and is obtained at a modulation frequency of 10 Hz. At higher frequencies, the speed decreases due to the increased probability that a particle moves neither forward nor backward during one cycle. We repeated the trapping and ratcheting experiment for different modulation frequencies. The average transport speed as a function of modulation frequency is shown in Fig. 6 (red squares). The error bars indicate the standard deviation of the speed. Data was collected down to a frequency of 5 Hz. Below this frequency, too many particles tended to diffuse away into solution. The experimental results agree very well with the analytical prediction. The optimal modulation frequency was 10 Hz, and the average at this value was 0.93 ± 0.14 µm/s (standard deviation).


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Summary In summary, we have presented the first demonstration of a near-field optical Brownian ratchet device. Our approach uses a silicon PhC slab designed to support an asymmetric optical potential. The optimal transport speed is 0.93 µm/s, which agrees well with analytical prediction. The device can also be used to perform assembly of hundreds particles with ultra-high trap stiffness of 18 pN·nm-1·W-1 and 53 pN·nm-1·W-1 in the x- and y-directions. The ability of our system to perform both steady and dynamic optical

manipulation can allow a variety of dynamic and lab-on-a-chip applications. The sensitivity of the optical potential to particle size and composition opens up a range of possibilities not provided by the flow control alone. We also expect that our system can be extended to batch processing and delivery of biological objects, impacting the field of microfluidic manipulation.

Methods Device Fabrication and Sample Preparation. The device was fabricated using electron beam lithography (30 kV accelerating voltage, 10 µm aperture) and plasma reactive ion etching. We used a silicon-on-insulator wafer (SOITEC) with a 250 nm thick silicon layer on top of a 3 µm silica layer and a 600 µm silicon handle layer. The backside of the wafer was polished to a mirror finish with surface roughness Ra (arithmetic average) < 10 nm. A PDMS microfluidic chamber (4 mm × 4 mm area, ~700 nm thickness) was fabricated on a glass slide using standard photolithography method. The chamber was used to cover the top the PhC device, forming a sealed container for a solution of 520 nm diameter


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polystyrene particles (100 µL Thermo Scientific FluoroMax R520 aqueous particles, diluted in 10 mL of 99.7% heavy water).

Stiffness Analysis. After the assembly of tens of particles, we recorded videos with a fixed exposure time of 33 ms. Typical videos were 600 frames or more in length. For every trapped particle, the measured variances were corrected for motion blur due to finite integration time of the camera and detection error from the camera.36

Optical Setup. To characterize the device, the PhC sample is mounted on a glass slide with a 2 mm circular hole at the center. A tunable laser with a wavelength range from 1500 nm to 1620 nm (Santec TSL-550) and a single-mode fiber (mode diameter 10.4 ± 0.8 µm) were used. An aspherical lens (f = 11 mm and NA = 0.25, Thorlabs C220 TME-C) was incorporated to collimate the beam. An achromatic doublet (f = 30 mm, Thorlabs AC254) was then used to refocus the beam to the back side of the sample. The Gaussian beam diameter incident on the sample was measured by the knife-edge method to be ~27 µm. To identify the guided mode resonance of the device, the transmission spectrum was first measured in cross-polarization (resonance appears as a transmission peak) and then tuned back to parallel-polarization (resonance appears as a transmission dip) and measured.37 The input power for characterization was 0.1 mW while input power for trapping was 100 mW.

Particle Detection and Trajectories. The experiments were recorded using a 20X objective and a CMOS camera. The video was recorded with exposure time of 1/30 s at 30 frames per second. Each pixel of the video represents a 66 nm × 66 nm area of the sample. The particle positions were obtained by detecting the highest brightness pixel for each


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particle.38 The frame-by-frame particle positions were linked to form trajectories using a nearest neighbor algorithm with maximum movement step of 0.7 lattice constants between each frame.

Mean displacement. The experiment was repeated 3 times for a duration of 80 seconds. For each experiment, we saved any particle trajectory lasting longer than 10 s. This yielded 115 particle trajectories in total. They were averaged to obtain Figure 5.

Modulation frequency dependence. The ratcheting experiment was performed several times for each frequency. Trajectories lasting > 10s used. This yielded 27 to 115 trajectories per frequency. The error bars indicate the standard deviation of the measurements.

Acknowledgements This work was funded by an Army Research Office PECASE Award under Grant 56801MS-PCS. Computation was supported by the University of Southern California Center for High Performance Computing and Communication. The authors thank Luis Javier Martínez for contributing to the experimental infrastructure used in this project, Aravind Krishnan for assistance with experiments, and Camilo A. Mejia for input into optical force calculations.


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Author Contributions All authors conceived and designed the experiments, which were carried out by S.-H. W. and N. H. The data were analysed by S.-H. W. M. L. P. laid out the concept and supervised the project. The interpretation of the data and writing of the manuscript were performed by S.-H. W. and M. L. P. All authors commented on the data and on the final version of the manuscript.


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(32) Polin, M.; Ladavac, K.; Lee, S.-H.; Roichman, Y.; Grier, D. Opt. Express 2005, 13, 5831-5845. (33) Fan, S.; Joannopoulos, J. D. Phys. Rev. B 2002, 65, 235112. (34) Jackson, J. D., Classical electrodynamics. 1999; Vol. 3rd. (35) Kedenburg, S.; Vieweg, M.; Gissibl, T.; Giessen, H. Opt. Mater. Ex. 2012, 2, 15881611. (36) P.Wong, W.; Halvorsen, K. Opt. Express 2006, 14. (37) Huang, N.; Martínez, L. J.; Povinelli, M. L. Opt. Express 2013, 21, 20675-20682. (38) Crocker, J. C.; Grier, D. G. J. Colloid Interface Sci. 1996, 179.


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Figure 1

Figure 1. Basic operating principle of Brownian ratchets. a, By modulating an asymmetric external potential, the random, Brownian motion can be rectified in the forward direction. Blue line indicates potential; grey lines indicate particle probability distribution. b, A periodic array of optical traps generated by a photonic crystal slab. Light is incident on the slab from below, perpendicular to the slab surface. The asymmetric, triangular-shaped patterns produce an asymmetric field distribution with strong field intensity in the holes. Modulating the incident light results in sideways motion of the particles, or Brownian ratcheting.


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Figure 2

Figure 2. Design of silicon photonic crystal device with asymmetric patterns and FDTD simulation results. a, Simulated electrical field intensity profile (E2) on resonance for ypolarized incident light (polarization direction shown as red arrow). The white dashed line represents the location of the hole. b, Simulated transmission spectrum of the device. c, Contact height, simulated optical forces, and optical potential as a function of lateral position for a particle in contact with the slab.


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Figure 3

Figure 3. Fabricated device characterization. a, SEM image of the device used in experiments. b, Measured transmission spectrum.


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Figure 4

Figure 4. Microscopy-video analysis of ratcheting experiments. a, Snapshot of particle trapping. Colored circles label the initial position of four trapped particles. b, Particle ratcheting due to laser modulation. Trajectories are shown for the four labeled particles over a 30 s time period.


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Figure 5

Figure 5. Mean displacement for ensemble of particles. a. and b. are the mean displacements in the x- and y- directions. The red curve represents the results for Brownian ratchet with 10 Hz modulation frequency, while the black dashed curve represents the results for Brownian particles.


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Figure 6

Figure 6. Average transport speed of the particles.


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Figure 1. Basic operating principle of Brownian ratchets. a, By modulating an asymmetric external potential, the random, Brownian motion can be rectified in the forward direction. Blue line indicates potential; grey lines indicate particle probability distribution. b, A periodic array of optical traps generated by a photonic crystal slab. Light is incident on the slab from below, perpendicular to the slab surface. The asymmetric, triangular-shaped patterns produce an asymmetric field distribution with strong field intensity in the holes. Modulating the incident light results in sideways motion of the particles, or Brownian ratcheting. 211x358mm (300 x 300 DPI)


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Figure 2. Design of silicon photonic crystal device with asymmetric patterns and FDTD simulation results. a, Simulated electrical field intensity profile (E2) on resonance for y-polarized incident light (polarization direction shown as red arrow). The white dashed line represents the location of the hole. b, Simulated transmission spectrum of the device. c, Contact height, simulated optical forces, and optical potential as a function of lateral position for a particle in contact with the slab. 511x390mm (300 x 300 DPI)


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Figure 3. Fabricated device characterization. a, SEM image of the device used in experiments. b, Measured transmission spectrum. 242x381mm (300 x 300 DPI)


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Figure 4. Microscopy-video analysis of ratcheting experiments. a, Snapshot of particle trapping. Colored circles label the initial position of four trapped particles. b, Particle ratcheting due to laser modulation. Trajectories are shown for the four labeled particles over a 30 s time period. 215x405mm (300 x 300 DPI)


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Figure 5. Mean displacement for ensemble of particles. a. and b. are the mean displacements in the x- and y- directions. The red curve represents the results for Brownian ratchet with 10 Hz modulation frequency, while the black dashed curve represents the results for Brownian particles. 245x378mm (300 x 300 DPI)


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Figure 6. Average transport speed of the particles. 231x183mm (300 x 300 DPI)


Near-Field, On-Chip Optical Brownian Ratchets - Nano Letters (ACS

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