Optical tweezers can be used to trap, move, and rotate or align microscopic particles. Elongated particles are ideal candidates for alignment and controlled rotation; the behaviour of microfibres within an optical trap is investigated

Heckenberg, N. R.

Nieminen, T. A.

Rubinsztein-Dunlop, H.

Nieminen, TA

Rubinsztein-Dunlop, H

Heckenberg, NR

University of Queensland eSpace

Trapping and alignment of a microfibre using the discrete dipole approximation

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This is an e-print of:
T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg
“Trapping and alignment of a microfibre using the discrete dipole approximation”
pp. II-138–II-139 in Technical Digest, CLEO/Pacific Rim 2001, 4th Pacific Rim
Conference on Lasers and Electro-Optics vol. 2, IEEE, Piscataway, NJ (2001)
Trapping and alignment of a microfibre using the
discrete dipole approximation
T. A. Nieminen, H. Rubinsztein-Dunlop,
and N. R. Heckenberg
Centre for Laser Science, Department of Physics,
The University of Queensland, Brisbane QLD 4072, Australia
phone +617-3365 3405, fax +617-3365 1242
timo@physics.uq.edu.au
Abstract
Optical tweezers can be used to trap,
move, and rotate or align microscopic
particles. Elongated particles are ideal
candidates for alignment and controlled
rotation; the behaviour of microfibres
within an optical trap is investigated.
1 Introduction
Optical trapping, which is the trapping
and manipulation of microscopic parti-
cles by a focussed laser beam or beams,
is a widely used and powerful tool. The
most common optical trap, commonly
called optical tweezers, consists of a
laser beam strongly focussed by a lens,
typically a high numerical aperture
microscope objective (see figure 1).
Applications of optical trapping are
microscope slide
viewing system
cover slip
high NA objective
mirror
dichroic
particles suspended in fluid
laser beam
expanded
Figure 1: Schematic diagram of a typical
optical tweezers setup
numerous, and steadily growing in
number and sophistication. The
increasing number of quantitative appli-
cations require accurate calculation of
the optical trapping forces; a calculation
from first principles is important since it
allows absolute calibration.
The force and torque acting on a
particle in a laser trap can be found from
the momentum and angular momentum
of the total electromagnetic field (the
sum of the incident field and the scat-
tered field) [1]. The fields can be found
using electromagnetic scattering theory,
avoiding the common approximations of
geometric optics and Rayleigh approxi-
mations which are only valid in limited
regimes.
2 The discrete dipole
approximation
A number of different methods can
be, and have been, used to calculate
optical forces: finite element (FEM) and
finite difference time domain (FDTD)
methods [2], which are computation-
ally intensive, required the discretisa-
tion of the particle and surrounding
space, and special boundary conditions;
the T-matrix method [1, 3], which is
fast and efficient, but fails for parti-
cles of very large aspect ratio and
cannot be used for anisotropic parti-
cles; and the discrete dipole approxima-
tion (DDA), which allows calculation of
forces on extreme aspect ratio particles
and anisotropic materials, while only
requiring discretisation of the particle.
In the discrete dipole approximation,
the scatterer is represented as a collec-
tion of small polarisable particles, each
much smaller than the wavelength of
the illumination [4, 5]. The response of
each dipole to the surrounding field can
be readily calculated. The field at any
dipole is the sum of the incident field and
the field produced by all other dipoles;
an iterative procedure can be used to
find the total field. Fourier methods can
be used for rapid convergence.
Once the field has been calculated,
and the polarisation in each dipole is
known, the force and torque acting on
each individual dipole can be simply
found – a known dipole moment in an
applied field. Thus, the total force and
torque can be calculated.
The advantages offered by DDA are
that while the particle must be discre-
tised, the surrounding space is not.
Thus, the computational difficulty varies
with the volume of the particle only, and
the method is suitable for large aspect
ratio particles. As an additional benefit,
the stresses within the scatterer can be
readily found.
3 Microfibres
Torques acting to align homogeneous
particles due to their shape are of partic-
ular interest. Extremely elongated parti-
cles – microfibres – provide us with an
ideal test case for investigating these
effects.
The discrete dipole approximation is
ideal for calculating the force and torque
acting on a microfibre, with a relatively
small volume, and extreme aspect ratio.
A very thin fibre can be approximated as
a single chain of dipoles, while a thicker
fibre will have a number of elements
across the width (see figure 2).
Figure 2: Discrete dipole representations
of thin and thick microfibres
We present calculations of the scat-
tered fields and optical force and torque
for microfibres of a wide range of lengths
and widths.
References
[1] T. A. Nieminen, H. Rubinsztein-
Dunlop, and N. R. Heckenberg,
“Calculation and optical measure-
ment of laser trapping forces on
non-spherical particles,” to appear
in J. Quant. Spectr. Radiat. Transfer
(accepted 2000).
[2] D. A. White, Comp. Phys. Comm. 128,
558–564 (2000).
[3] M. I. Mishchenko, J. Opt. Soc. Am. A
8, 871–882 (1991).
[4] B. T. Draine and P. J. Flatau, J. Opt.
Soc. Am. A 11, 1491–1499 (1994).
[5] H. Kimura and I. Mann, J. Quant.
Spectr. Radiat. Transfer 60, 425–438
(1998).


Trapping and Alignment of a Microfibre Using the Discrete Dipole Approximation

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Trapping and Alignment of a Microfibre Using the Discrete Dipole Approximation

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