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Transcript
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
S
© 2014 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
Published: January 6, 2014
547
dx.doi.org/10.1021/nl403608a | Nano Lett. 2014, 14, 547−552
Nano Letters
Letter
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 ×
548
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Letter
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
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Letter
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
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Letter
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.
■
ASSOCIATED CONTENT
* Supporting Information
S
Additional information, figure, 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: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
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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