Letter pubs.acs.org/NanoLett
Selective Trapping or Rotation of Isotropic Dielectric Microparticles by Optical Near Field in a Plasmonic Archimedes Spiral Wei-Yi Tsai,† Jer-Shing Huang,‡,§,∥ and Chen-Bin Huang*,† †
Institute of Photonics Technologies, ‡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 S Supporting Information *
ABSTRACT: We demonstrate selective trapping or rotation of optically isotropic dielectric microparticles by plasmonic near field in a single gold plasmonic Archimedes spiral. Depending on the handedness of circularly polarized excitation, plasmonic near fields can be selectively engineered into either a focusing spot for particle trapping or a plasmonic vortex for particle rotation. Our design provides a simple solution for subwavelength optical manipulation and may find applications in micromechanical and microfluidic systems.
KEYWORDS: Plasmonics, optical trapping, optical rotor, optical vortex ince the first demonstration in 1970 showing that a focused laser beam can stably trap microparticles,1 there are many immerging applications of optical trapping.2 In particular, rotation and spin of particles by light have drawn great attention since they may offer more functionality to practical microsystems.3−8 In conventional optical tweezers, the trapping force drops quickly as the radius of particles decreases due to reduced gradient force.9 Increasing the laser power might help but the price to pay is the complex convection flow and sample damage due to laser heating.10,11 Another intrinsic weakness of conventional optical tweezers is the diffraction limited focal volume, which prevents subwavelength optical manipulation of particles. To resolve these problems, plasmonic near fields have recently been applied to particle trapping.12,13 Surface plasmons (SPs) provide giant local field intensity and surmount the conventional diffraction limit, facilitating trapping of very small particles at a much lower intensity level. Various plasmonic trapping schemes utilizing localized surface plasmon resonance or propagating surface plasmon polaritons (SPPs) have been demonstrated to trap and manipulate nanoparticles.10−24 For particle rotation/spin by conventional circularly polarized light, the effect is usually weak and requires the particle to be anisotropic, absorbing, or birefringent.5,25−27 Otherwise, a spin-to-orbital conversion of angular momentum of light is needed.8,28,29 Taking advantage of the resonanceenhanced polarizability of plasmonic nanoparticles, optical rotation and spin have been successfully demonstrated.30−33 However, rotation of optically isotropic dielectric particles by plasmonic fields has not been demonstrated. In addition, most of the plasmonic trapping designs are limited to only one single
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© XXXX American Chemical Society
function, that is, either trapping or rotation of particles. Switching between trapping and rotation in one single plasmonic structure has not been realized so far. In this work, we demonstrate for the first time selective trapping or rotation of dielectric microparticles by a single gold plasmonic Archimedes spiral (PAS). The working principle is based on simultaneous control of angular momentum and intensity distribution of plasmonic near field of a PAS.34−36 Depending on the handedness of the input circularly polarized light, we show selective particle trapping toward the spiral origin by a focusing spot, or particle rotation along the primary ring by a plasmonic vortex field. We analyze the optical forces in our PAS for both trapping and rotation of microparticles. To our best knowledge, this is the first demonstration of selective optical control over the motion of isotropic dielectric microparticles (trapping or rotation) using a single plasmonic device. Our design is simple and the control mechanism is readily achievable by normal microscopes. The ability to selectively perform particle trapping or rotation by one single plasmonic structure is of great interest. We anticipate applications in micromechanical system, for example, as a micromotor, and in microfluidic systems, for example, as a microblender for localized mixing. Our method may also be applied to the analysis of conformational change of DNA or Received: September 27, 2013 Revised: December 18, 2013
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Figure 1. Plasmonic Archimedes spiral for selective optical trapping or rotation. (a) Geometry of a three-turn right-hand PAS. (b) SEM picture of the fabricated PAS. (c) Under left-hand circularly polarized plane wave excitation, the SP field is focusing with no angular momentum and is used to trap microparticles. (d) The time-averaged focusing SP intensity pattern within the area marked by the dotted box in (a). (e) Under right-hand circularly polarized plane wave excitation, the resulting SP vortex can be used to trap microparticles at the primary ring of the vortex while rotating the particles. (f) The time-averaged SP vortex intensity pattern within the area marked by the dotted box in (a).
1.768)]1/2 = 1150 nm. The designed PASs are fabricated with focused-ion beam milling into a thermally evaporated gold film (thickness = 250 nm) on a standard cover glass. The air slot is around 300 nm wide and starts at r0 = 2.5 μm with azimuthal angle ranging from 0 to 6π. Figure 1b shows the SEM picture of our gold PAS. Excited by z-propagating circularly polarized plane waves, the SPPs in the PAS propagate on the spiral plane (x−y plane). Neglecting loss, the resulting z-polarized near field can be analytically expressed as Ê spp(R, θ) ∝ ẑJq(ksppR)exp[jqθ], where (R, θ) denotes an observation point on the spiral plane, and kspp is the SPP wave-vector.35,36 Jq denotes the qth-order Bessel function of the first kind, and the order q simultaneously defines the total topological charge of the SP vortex. The relationship among the total SP topological charge (q), the
protein by providing a controllable trapping or local vortex turbulence.7,37,38 The top view of a right-hand PAS is schematically shown in Figure 1a. The PAS geometry is mathematically defined in the polar coordinate as r(ϕ) = r0 + (ϕλspp)/2π, where r denotes the distance between the spiral slot and the origin O, r0is the starting distance, ϕ is the azimuthal angle, and λspp is the SPP wavelength. In our design, a three-turn PAS (defined with ϕ ranging from 0 to 6π) is to be excited by a continuous-wave laser with vacuum wavelength of 1545 nm while immersed in water. The three-turn is adopted in order to enhance the SPP field strength under the presence of optical damping due to both gold and water. The SPP wavelength at gold/water interface is estimated using λspp = λ0[(Re(εmetal) + εdielectric)/ (Re(εmetal) × εdielectric)]1/2 = 1545[(−92.9 + 1.768)/(−92.9 × B
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Figure 2. Optical trapping force analysis for the SP focusing field. (a) A sphere with 1 μm diameter having a y-offset of −500 nm. The forces exerted onto the sphere by the focusing SP field are shown by arrows. (b) Calculated optical forces Fx and Fy at various y-offsets along the dash-dotted line in (a). The results shows optical force Fy is exerted onto the sphere which attracts the sphere into the origin. (c) Calculated trapping potential in the ydirection verifies the origin (focusing) is a stable trapping location. (d) The sphere having an x-offset of 500 nm. The forces exerted onto the sphere by the focusing SP field are shown by arrows. (e) Calculated optical forces Fx and Fy at various x-offsets along the dash-dotted line in (d). The results shows optical force Fx is exerted onto the sphere which attracts the sphere into the origin. (f) Calculated trapping potential in the x-direction verifies the origin (focusing) is a stable trapping location.
three-dimensional finite-difference time-domain calculations.39 As can be seen from our later analysis and experimental demonstration, the primary ring of the SP vortex provides a stable “track” for the trapped microparticles to rotate along in the counter-clockwise direction. To understand the feasibility in trapping and rotation of microparticles, optical forces provided by the focusing and the vortex plasmonic near fields are numerically analyzed using FEM. The microparticle used in this work is a polystyrene sphere with a diameter of 1 μm. Maxwell stress tensor is used to evaluate the optical force and potential values40 exerted on the microsphere (see Supporting Information). The optical trapping force and potential provided by the focusing SP field is depicted in Figure 2. Figure 2a shows the near-field intensity map of the focusing spot with a microsphere (indicated by a yellow dotted circle) placed at a position 500 nm away from the spiral origin in negative y-direction. The force vectors on the microsphere surface (indicated by white arrows) reveal that the sphere experiences mainly an optical force Fy in the positive ydirection that pulls the microsphere toward the PAS origin. Following the same procedures, optical forces at various y-offset values (indicated by the dash-dotted line in Figure 2a) are calculated. Figure 2b shows the optical forces exerted onto the microsphere in the x-direction (Fx) and y-direction (Fy) as a function of y-offset. For negative (positive) y-offsets, the microsphere experiences positive (negative) Fy. The forces in
geometrical charge (m = 1 for a right-hand PAS), and the spin angular momentum (s = 1 and s = −1 for right- and left-hand circularly polarized plane waves, respectively) is described by q = m + s.35 For a right-hand PAS excited by a left-hand circularly polarized plane wave (Figure 1c), the total topological charge is zero, that is, q = 0. This means that the plasmonic near field exerts zero angular momentum on the particle and the intensity distribution fits a zeroth order Bessel function of the first kind, corresponding to a focusing plasmonic field toward the PAS origin. Figure 1d shows the time-stationary intensity distribution of the plasmonic focusing field, obtained using finite element method (FEM, Comsol Multiphysics). As we will see later, such a focusing near field provides sufficient stiffness of optical potential well to firmly trap a microparticle. On the other hand, if the optical excitation is switched to a right-hand circular polarization plane wave (Figure 1e), plasmonic near field with total topological charge q = 2 is generated around the spiral origin, resulting in a near-field vortex with a donut-shaped field distribution that fits the second order Bessel function of the first kind (Figure 1f). Such a near-field vortex can transfer its angular momentum to microparticle and induce rotation motion of particle. The slight asymmetry of the intensity observed in the annular ring is anticipated when taking into considerations the damping of SPP in both media and the nonequal SPP propagation distance from the spiral slot to the origin over all azimuthal angles. This is also confirmed via C
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Figure 3. Optical rotation force analysis for the SP vortex field. (a) A sphere with 1 μm diameter having a y-offset of 250 nm. The forces exerted onto the sphere by the SP vortex field are labeled as arrows. (b) Calculated optical forces Fx and Fy at various y-offsets along the dash-dotted line in (a). The primary ring locations are labeled by the dotted lines. Shaded area denotes sphere offsets within the primary ring. (c) Calculated trapping potential in the y-direction verifies the primary ring is a stable trapping track. (d) A sphere having an x-offset of 250 nm. (e) Calculated optical forces Fx and Fy at various x-offsets along the dash-dotted line in (d). (f) Calculated trapping potential in the x-direction verifies the primary ring is a stable trapping track. Insets in (a,d) show the total optical force exerted on the sphere inside and out of the primary ring.
the x-direction are negligible as compared to the force in the ydirection. The result clearly shows that optical force Fy is accountable in attracting the sphere toward the PAS origin. Figure 2c shows the calculated optical trapping potential from the data shown in Figure 2b by integrating the force component along the corresponding direction (see Supporting Information). Similar results have been obtained for microparticle at various x-offsets, as shown in Figure 2d−f. These analyses confirm that under left-hand circularly polarized excitation, the PAS origin forms a stable near field optical trap for microspheres in the vicinity. Now we switch to a right-hand circularly polarized excitation and analyze the optical force and potential provided by the resulted vortex SP field. Figure 3a shows the near-field intensity map of the plasmonic vortex with a microsphere placed at a position 250 nm away from the spiral origin in the y-direction. The force vectors on the microsphere surface, indicated by white arrows, show that the sphere experiences optical forces both in negative x-direction and positive y-direction. A detailed analysis on the force further reveals a rotational force on the microsphere in counter-clockwise direction. Optical forces on the microsphere for other y-offset values (dash-dotted line in Figure 3a) are calculated following the same procedures. Figure 3b shows the optical forces exerted onto the microsphere in the x-direction (Fx) and y-direction (Fy) as a function of the yoffset. The locations of the primary ring in the y-direction are marked by the two dotted lines. The shaded area in between marks the region when the sphere is within the primary ring. It
is clear that the optical force Fy now attracts the sphere into the primary ring, as is confirmed by the y-direction optical potential (Figure 3c). Different from the case of focusing spot, the force in x-direction (Fx) now has a significant value and plays a role in determining the movement of the sphere. As depicted in Figure 3b, the Fx is negative (positive) when the y-offset is positive (negative), suggesting rotation of the microsphere in counter-clockwise direction. Same analyses have been carried out for particles at various x-offsets and the results are displayed in Figure 3d−f. Again, the analyses suggest that the optical force drags the sphere into the primary ring and rotate the sphere in counter-clockwise direction. Insets in Figure 3a,d depict the trace of the sphere being trapped and rotated by the optical force at regions inside and outside of the primary ring along y- and x-axis, respectively. To experimentally visualize the selective trapping and rotation, we use a commercial microscope (BX51, Olympus) with self-modified optical paths (see Supporting Information for setup details). The motion of the microspheres is recorded using a charge-coupled device (CCD) camera (DCU224, Thorlabs) with white light illumination. The excitation laser source is a continuous-wave laser (vacuum wavelength = 1545 nm, Adjustik E15, NKT) connected to an erbium-doped fiber amplifier (LNHPFA-30, Pritel). The amplified laser output with maximum power of 100 mW is connected to a fiberized collimator (F280FC-1550, Thorlabs) and aligned into the excitation beam path. A linear polarizer (LPMIR050, Thorlabs) and a quarter-wave plate (WPQ05M-1550, Thorlabs) are used D
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Figure 4. Selective trapping or rotation of a single microsphere. (a) Four recorded frames at t = 1 s, t = 2 s, t = 3 s, and t = 4 s extracted from the movie clip are shown when the SP focusing field is excited by left-hand circular plane wave excitation. The sphere is firmly trapped within the PAS origin. (b) When the polarization of the input circular plane wave is switched to right-handed, the trapped sphere is rotated by the SP vortex in counter-clockwise direction. Four frames extracted from the movie clip at t = 1 s, t = 2 s, t = 3 s, and t = 4 s after the polarization switching is provided. The white dotted circles call out the border of the microsphere. The crosses in the rotation frames mark the PAS origin and divide its vicinity into four quadrants. The red-filled circles label the geometric center of the microsphere.
to generate a circularly polarized beam, which is then focused onto the spiral sample using an aspherical double-convex focusing lens (focal length = 5 cm, LB1471-C-N-BK7, Thorlabs). Under such soft focusing condition, the illumination spot (1/e2 diameter of 20 μm) fully covers one single PAS (diameter of 11.325 μm) and the circularly polarized light can be safely considered as a plane wave at the sample plane. Figure 4a shows four recorded frames at t = 1, 2, 3, and 4 s extracted from the movie clip when the PAS is excited by lefthanded circular plane wave to generate the focusing near field. Because the size of our spirals is very large (diameter >10 μm), we only excite one PAS at a time. It is clear that the microsphere is stably trapped within the PAS origin up to 120 s. We observed stable particle trapping over the optical powers ranging from 40 to 80 mW. On the same PAS, as the polarization of the circular plane wave is changed to righthanded, the microsphere is rotated by the SP vortex along the primary ring. Figure 4b shows four frames extracted from the movie at t = 1 s, t = 2 s, t = 3 s, and t = 4 s after the polarization switching. The crosses shown in Figure 4b mark the PAS origin and divide its vicinity into four quadrants. The white dotted rings and the red-filled circles call out the border and the geometric center of the sphere on each frame, respectively. It can be clearly seen that the microsphere sequentially appears in the third, fourth, first, and second quadrants, evidently making rotations in the counter-clockwise direction (see Supporting Information for movies). In addition to single sphere rotation, we have also observed similar trapping and rotation behavior for clusters containing about five spheres, suggesting that the optical force in our PAS is sufficiently large for moving heavy particles (see Supporting Information for movies of cluster trapping).
In summary, we present selective trapping or rotation of microparticles using a single gold plasmonic Archimedes spiral and circularly polarized excitation. We show that the SP focusing field provides stable optical potential at the PAS origin and can be used to trap microparticles. On the other hand, the primary ring of the SP vortex can be used to trap and rotate microparticles. Our design is simple and the selective particle manipulation can be easily achieved by changing the handedness of the circularly polarized excitation. In the current work, qualitative demonstrations of this novel working principle are presented. Interesting future outlooks include quantitative and statistical investigations over the ability to maneuver the trapping stability, the rotational speed, as well as the dependence over the particle size. These additional controls could be approached through the variations in optical excitation power, number of spiral turns, and interestingly the surface roughness of the gold film. Our method is of great interest for various microsystems, where local particle manipulation is needed. For example, using our design one can trap microparticles and rotate them to induce vortex of the fluid for local mixing purpose in microfluidic channels. One may also use the focusing and vortex fields to apply external force or torque to protein or DNA to study their properties and conformational change in solution. We anticipate various interesting applications of PAS for particle manipulation in microsystems.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information, figure, and movies. This material is available free of charge via the Internet at http://pubs.acs.org. E
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
The authors thank the support from the National Science Council of Taiwan under Grants NSC 100-2112-M-007-007MY3, NSC 101-2113-M-007-002-MY2, and the National Tsing Hua University under Grant 102N2081E1.
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