Optical Trap/ Optical Spanner Instrument Development
An optical trap (or optical
tweezer) is a tool capable of manipulating microscopic particles using the
inherent momentum of light (see Figure 1). This research investigates a means
for building a more sensitive optical trap compared to current designs.
This tool has shown to be a useful tool in fields that
Figure
1: Experimental Setup. A. Power
Meter. B. NanoCube Controller.
C. Position Sensing Amplifier. D.
Position Sensing Photodiode. E.
Laser Shutter Switch.
vary from biology, physics, and chemistry to material
science. For example, optical
traps have been used to study the step size and stall force of the motor
protein kinesin [1,2], and also the elastic properties of DNA [3,4].
In order for these instruments to be used as force transducers, a
position sensor with high spatial resolution is needed for force calibration
and particle manipulation.
One sensor being investigated is an interferometer.
Interferometry for position sensing within an optical trap uses a
microscope that is equipped with DIC imaging capability.
A
circularly polarized laser beam enters the microscope and
is split into two orthogonally polarized beams by a Wollaston prism located in
front of the microscope objective (see figure 2). The distance between the
orthogonal beams is set so that the two beams overlap and act as a single
trap. Both beams are then
recombined in the second Wollaston prism located behind the condenser.
If the bead is centered in the trap, the beam will have the same
polarity as the incoming laser. If
the bead moves from the center of the trap, the light will become elliptically
polarized and therefore can be measured quite accurately and converted to a
displacement. Current designs of this detection scheme are strictly
one-dimensional: only displacements along the Wollaston shear axis are
registered [5,6].
Figure
2: Interferomic position sensing system.
There has also been interest recently in being able to
torque or twist particle at the microscopic level.
This has led to an interest in Laguerre-Gaussian (LG) laser modes,
which have a helical phase structure (see Figure 3). The helical phase
structure transfers orbital angular momentum to trapped particle causing them
to spin [7,8]. Optical traps that are capable of spinning trapped particles
have been dubbed optical spanners.
First LG laser modes must be created in order to torque particles,
which standard lasers are created to avoid.
Two methods of LG mode generation are currently being explored:
holography and mode conversion.
Figure
3: Top: linearly polarized light. Bottom:
Linearly polarized Laguerre-Gaussian mode.
The first method to generate LG laser modes being
explored is to use holograms to convert a Gaussian beams into LG beams.
The holograms used are created by the computer generated interference
pattern between a Gaussian mode and the desired LG mode [7, 9, 10, 11] (see
Figure 4). When the hologram is illuminated by a plane wave, the desired LG
mode results. The image can
either be printed onto a temperature resistant transparent slide or they can
be displayed on an LCD screen, which can be modified in real time to
manipulate the beam. Using an LCD
screen is easier to implement, but the efficiency decreases compared to a
static hologram.
Figure
4: Hologram to convert a Gaussian mode to a Laguerre-Gaussian mode.
The second method of generating LG laser modes is to convert Hermite-Gaussian
(HG) laser modes to LG laser modes by introducing a π/2 phase shift into
the beam [8, 12, 13, 14], in one dimension, but not the other.
However, HG modes must first be created. In order to force a laser into
producing HG modes, a cross-hair made of tungsten wire is placed into the
laser cavity and adjustment of this will result the laser to produce higher
order HG modes. Once the HG modes are generated, the beam is passed through
two cylindrical lenses with matching focal lengths f separated by a
distance of f √2 with the axis of the laser nodes and the
cylindrical lenses rotated at a 45º angle with respect to one another. The
converter adds a π/2 phase shift which converts a HGm,n mode
to an LGpl mode (see Figure 5). In this conversion, m
and n correspond to the number of nodes in the electromagnetic field of
a HG mode, while l gives the number of 2π phase cycles in the
azimuthal direction around the circumference of the mode and p+1 gives
the number of nodes across the radial field distribution [14]. The converter
transforms the modes in such a way that l=|m-n| and p =
min(m,n) [8].
Figure
5. A. Sketch of a mode converter. B.
Transformation of HG to modes to LG modes through the mode converter [14].
The goal of this research is to improve upon current
position sensing techniques and to couple this with feedback control to
improve disturbance rejection making a more sensitive optical trap.
The system will also be adaptable with the capability to manipulate and
spin microscopic particles. Finally
it is the goal of this research to make the system user-friendly with a haptic
control system and adaptable user interface.
References
[1] K. Svoboda, C. F.
Schmidt, B. J. Schnapp, and S. M. Block. Direct observation of kinesin
stepping by optical trapping interferometry. Nature, 365(6448):721–727,
1993.
[2] K. Visscher, M.
J. Schnitzer, and S. M. Block. Single kinesin molecules studied with a
molecular force clamp. Nature, 400(6740):184–189, 1999.
[3] M. D. Wang, H.
Yin, R. Landick, J. Gelles, and S. M. Block. Stretching DNA with optical
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