Using holographic optical tweezers we create crystal-like structures
over a scale of 10s microns. Real-time calculation of the required holographic
pattern allows us to scale or rotate the structures about arbitrary
axes. Once the desired structure is formed we can make it permanent
by gelling the surrounding fluid.
Optical tweezers work on a very simple principle. They use the gradient
force produced by a light field to trap and hold micron-sized objects.
For a dielectric particle the gradient force acts to attract the particle
to the point of highest intensity. The intensity gradient, the corresponding
gradient force, and consequently the trapping capability of the light
increases with the degree of focussing. Hence, to produce the smallest
possible focus, optical tweezers are usually implemented using a diffraction-limited
laser beam, coupled into a high-magnification microscope objective.
Conveniently, the microscope objective both focuses the laser beam and
images any trapped objects. In general, the particles are suspended
in a fluid that not only offers partial buoyancy but also provides the
damping force essential for a stable trap.
Optical tweezers were first described in the late 1980s by Ashkin ,
who trapped small particles at the focus of a laser beam. Following
their first demonstration, the number of applications of optical tweezers
has grown and a number of commercial systems are available . In biological
fields, optical tweezers have measured the pN-forces necessary to stretch
individual muscle fibres, have uncoiled DNA, and have manipulated individual
cells. In the physical sciences, tweezers have found themselves at the
centre of experiments studying the linear and angular momentum of light
and being used as drives for micromachines .
|Fig. 1. The rotating cube. Eight 2mm
diameter silica spheres trapped at the corners of a cube.
Over the last few years, the commercial availability of spatial light
modulators (SLMs), which act as reconfigurable phase holograms, has
revolutionised optical tweezers. Unlike a data projector, which produces
an image using a pixellated device to selectively attenuate the transmitted
light, a phase-holographic component simply redirects the light to the
desired location. Not only is this inherently more optically efficient,
but it allows the light to be brought to be focussed in different planes.
Within the context of optical tweezers, a spatial light modulator placed
into the beam allows a single laser to be efficiently divided to produce
simultaneous multiple optical traps that can be positioned anywhere
within a 3 dimensional volume . Previous approaches to multiple traps
use scanning mirrors or other beam deflectors, but such systems require
time-multiplexing between traps and can only position the traps within
a single plane. Interference patterns between two or more beams have
also been used to create three-dimensional arrays of traps , but
this approach is limited to relatively simple interference patterns.
This newsletter details our recent research in trapping multiple particles
in three dimensions. By using existing and developing new hologram-design
algorithms, we have created crystal-like structures within optical tweezers.
II. Multiple Trapping and Hologram Design
The key to successful trapping of multiple objects is the hologram design
transferred to the SLM. The ideal result is a design giving multiple
beams without introducing aberrations that enlarge the focus spot and
reduce the trapping strength. Additionally, when two traps come close
together there is a risk that one trap may capture the particle held
in the other. This is a particular problem if the displacement is axial,
in which case great care needs to be taken to avoid unwanted stacking
of the particles. We have used three different algorithms, which offer
different trade-offs between complexity of achievable trap arrangements
and computational effort.
|Fig. 2. Eighteen 2mm diameter silica spheres
trapped at the lattice cites of a diamond unit cell.
The first approach, used for simple, symmetric patterns, is effectively
the summation of familiar optical components. For example, a two-level
phase hologram of a Fresnel lens, combined with two crossed phase gratings,
will produce eight traps positioned at the corners of a cuboid. Figure
1 shows a video sequence of eight, 2µm diameter silica spheres,
trapped at the corners of a cube. This cube can be rotated or scaled
by altering the hologram appropriately. At video resolution, such calculations
can be carried out at video frame rates. In our case, practical limitations
in the design of the microscope objective and to the resolution of the
SLM limit the unit-cell size to 4mm to 20mm. Note that at certain times
in the rotation cycle, spheres are trapped immediately above one another
separated only in the axial direction. Contrary to what one might expect,
the high numerical aperture of the system means that the distant trap
is not influenced by the shadow cast by the object in the
near trap. We have also shown that such structures can be made permanent
by using a suspension fluid that after a fixed time turns into gel.
For more complex, non-symmetric designs we use a direct binary search
algorithm. Here we specify both regions of high (i.e. the trap) and
low intensity (i.e. the trap separation) in the target beam and define
a figure of merit corresponding to the holograms performance at
meeting these criteria. We then use an iterative process to optimise
the design of the hologram, which simply consists of making a random
change and keeping or discarding it depending on whether or not the
holograms performance has improved. Figure 2 is an example of
a structure created using this method. It shows silica spheres trapped
at the lattice sites of a diamond unit cell 18 particles trapped
in 5 planes.
The third approach to hologram design is an extension to the two-dimensional
Fourier transform based Gerchberg-Saxton algorithms. In original form
this allows the general specification of a target intensity distribution
in one plane. Although this plane can be deformed, the trapping of two
axially displaced particles is problematic. By incorporating an additional
beam-propagation steps into the algorithm we can define unrelated trapping
patterns in multiple planes. Although the algorithm is significantly
slower than the original Gerchberg-Saxton algorithm, it is still possible
to calculate video resolution holograms two or three times a second.
Figure 3 shows a video sequence of a general manipulation in 3 dimensions
where the positions of individual particles are independently controlled.
|Fig. 3. Image sequence showing general
manipulation in 3 dimensions where the positions of individual particles
are independently controlled.
III. Optical Tweezers System
As is typical, our tweezers system is based upon an inverted microscope
with a 1.3NA ¥100, oil immersion objective lens. The SLM is introduced
into the beam path and is imaged onto the entrance aperture of the objective
lens such that lateral and axial displacements of the optical trap correspond
to the SLM displaying a diffraction grating and Fresnel lens respectively.
A combination of the spatial resolution of the SLM and the aberrations
within the object lens limit the maximum lateral and axial displacements
to approximately 30 and 20 microns respectively.
We have outlined a technique to create three dimensional crystal-like
structures within optical tweezers that can be scaled or rotated about
arbitrary axes. We anticipate that the generation and control of such
pre-determined three dimensional crystal structures, over length scales
over several 10s of microns will have significant potential in fields
as diverse as photonic crystal construction, creation of metrological
standards within nanotechnology and the seeding of tissue growth. For
example, by organizing one or more cell types into spatially defined
3D arrays, tweezers could perhaps be used to engineer templates for
tissue replacement therapies.
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 J. E. Molloy, M. J. Padgett, Lights, action: optical tweezers,
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 D. G. Grier, A revolution in optical manipulation, Nature,
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 M. P. MacDonald, L. Paterson , K. Volke-Sepulveda, J. Arlt, W. Sibbett,
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