Measurements of viscoelasticity in the microscopic regime are of interest in polymer solutions as well as in
microscopic structures such as cells. Viscoelasticity can be studied using a localized microrheometer based
on optical tweezers. We rotate a birefringent micron-sized calcium carbonate sphere crystallized in a vaterite
structure. By applying a time-dependent torque or using the time-dependent thermal torque, viscoelasticity can
be measured. The torque can be measured purely optically, by measuring the polarization state of the trapping
beam after passing through the particle. We control the torque by controlling the relative amplitudes of two
orthogonally circularly polarized components of the trapping beam with two acousto-optic modulators. This
allows a wide range of oscillation frequencies to be used. We demonstrate applications of the methods on several
Optical forces and torques acting on microscopic objects trapped in focussed laser beams promise flexible methods of driving micromachines through a microscope cover slip or even a cell wall.
We are endeavouring to engineer special purpose micro-objects for a range of tasks. Colloidal self assembly of calcium carbonate provides birefringent spheres which can exert considerable torque, while two photon polymerisation allows us to fabricate objects of arbitrary shape that can be designed to exchange both spin and orbital angular momentum. Numerical calculations of forces and torques can allow an optimal design, and optical measurements provide us with certain knowledge of the forces and torques which are actually exerted.
Microrheology is the study of fluid flows and material deformations on a microscopic scale. The study of
viscoelasticity of microscopic structures, such as cells, is one application of microrheometry. Another application
is to study biological and medical samples where only a limited volume (microlitres) of fluid is available. This
second application is the focus of our work and we present a suitable microrheometer based on optical tweezers.
Optical tweezers are an optical trap created by a tightly focused laser beam. The gradient force at this focus
acts to trap transparent micron sized particles, which can be manipulated within the surrounding environment.
We use the polarisation of the incident field to transfer angular momentum to a trapped spherical birefringent
particle. This causes the particle to rotate and measuring the polarisation of the forward scattered light allows
the optical torque applied to the sphere to be calculated. From the torque, the viscosity of the surrounding
liquid can be found. We present a technique that allows us to perform these measurements on microlitre volumes
of fluid. By applying a time-dependent torque to the particle, the frequency response of the liquid can also be
determined, which allows viscoelasticity to be measured. This is left as a future direction for this project.
We describe two methods to optically measure the torque applied by the orbital angular momentum of the
trapping beam in an optical tweezers setup. The first decomposes the beam into orbital angular momentum
carrying modes and measures the power in each mode to determine the change in angular momentum of the
beam. The second method is based on a measuring the torque transfer due to spin angular momentum and the
linear relationship between rotation rate and applied torque to determine the orbital angular momentum transfer.
The second method is applied to measuring the transfer efficency for different particle-mode combinations. We
present the results of these experiments and discuss some of the difficulties encountered.
A strongly focused laser beam can be used to trap, manipulate and exert torque on a microparticle. The torque
is the result of transfer of angular momentum from the laser beam. The laser could be used to drive a rotor,
impeller, cog wheel, etc. of a few microns in size, perhaps fabricated from a birefringent material. We review our
methods of computationally simulating the torque and force imparted by a laser beam. We introduce a method
of hybridizing the T-matrix with the finite difference frequency domain (FDFD) method to allow the simulation
of materials that are anisotropic and inhomogeneous, and structures that have complex shapes. We also employ
an alternative discrete dipole approximation method. The high degree of symmetry of a microrotor, such as
rotational periodicity, could be exploited to reduce computational time and memory requirements by orders of
magnitude. This is achieved by performing calculations for only a given segment that is repeated across the
whole structure. This can demonstrated by modeling the optical trapping and rotation of a cube.
Manipulation of micrometer sized particles with optical tweezers can be precisely modeled with electro dynamic theory using Mie's solution for spherical particles or the T-matrix method for more complex objects. We model optical tweezers for a wide range of parameters including size, relative refractive index and objective numerical aperture. We present the resulting landscapes of the trap stiffness and maximum applicable trapping force in the parameter space. These landscapes give a detailed insight into the requirements and possibilities of optical trapping and provide detailed information on trapping of nanometer sized particles or trapping of high index particles like diamond.
The ability to exert optical torques to rotationally manipulate microparticles has developed from an interesting curiosity to seeing deployment in practical applications. Is the next step to genuine optically-driven micromachines feasible or possible? We review the progress made towards this goal, and future prospects.
Exposure of optically curing resin with highly focussed femtosecond laser pulses provides excellent means to produce high resolution micron sized structures. We use the process to fabricate micromechanical components for lab-on-a-chip applications. We present here our experimental realization of the microscope system used for
photopolymerization and detail the advantage of our fabrication process. We characterize our structures using scanning electron microscopy, and compare the results with available data. We demonstrate the technique by manufacturing a movable joint and a free floating cross which is three dimensionally trapped. Future applications of this technique will focus on developing optically driven motors and an all optical measurement of applied torques.
We use passive and active techniques to study microrheology of a biopolymer solution. The passive technique is video tracking of tracer particles in the biopolymer, a technique which is well established. The active technique is based on rotating optical tweezers, which is used to study viscosity. A method to actively measure viscoelascity using time varying rotation of a particle trapped in optical tweezers is also presented.
We investigate the dynamics of microscopic flow vortices. We create flow vortices by rotation of birefringent particles in optical tweezers. We then use either highly sensitive drag force measurements or video tracking to map the fluid velocity around that particle. The results obtained from these different methods are compared. Velocity profiles obtained for water agree very well with theoretical predictions. In contrast, we find a strong deviation of velocity profiles in a complex fluid from those predicted by simple theory.
We present a technique to measure the viscosity of microscopic
volumes of liquid using rotating optical tweezers. The technique
can be used when only microlitre (or less) sample volumes are
available, for example biological or medical samples, or to make
local measurements in complicated micro-structures such as cells.
The rotation of the optical tweezers is achieved using the
polarisation of the trapping light to rotate a trapped
birefringent spherical crystal, called vaterite. Transfer of
angular momentum from a circularly polarised beam to the particle
causes the rotation. The transmitted light can then be analysed to
determine the applied torque to the particle and its rotation
rate. The applied torque is determined from the change in the
circular polarisation of the beam caused by the vaterite and the
rotation rate is used to find the viscous drag on the rotating
spherical particle. The viscosity of the surrounding liquid can
then be determined. Using this technique we measured the viscosity
of liquids at room temperature, which agree well with tabulated
values. We also study the local heating effects due to absorption
of the trapping laser beam. We report heating of 50-70 K/W in the
region of liquid surrounding the particle.
Several techniques have been proposed and used for the rotation or
alignment of microparticles in optical tweezers. In every case the
optical torque results from the exchange of angular momentum
between the beam and the particle, and, in principle, can be
measured by purely optical means. Measurement of this torque could
be useful for quantitative measurements in biological systems and
is required to measure properties such as viscosity of liquids in
microlitre (or less) volumes. Although elongated particles will
align with the plane of polarisation, the torque efficiency is
low, typically about 0.05hbar per photon. The use of a beam
with an elongated focal spot can increase this torque by a factor
of 10-20 times, due to the transfer of orbital angular momentum.
We report measurements of the orbital component using an analysing
(Laguerre-Gauss) hologram. As a proof of principle experiment, an
elliptical beam scattered off a glass rod was simulated on a
macroscopic scale. The torque was found to be as much as
0.8hbar per photon. Microscopic elongated objects have been
aligned and rotated in optical tweezers and we plan to make
measurements of the torques involved.
The ability to controllably rotate, align, or freely spin microparticles in optical tweezers greatly enhances the manipulation possible. A variety of different techniques for achieving alignment or rotation have been suggested and demonstrated. Although these methods are diverse, employing specially shaped particles, birefringent particles, multiple trapping beams, complex beam profiles, vortex modes, plane polarised beams, circularly polarised beams, or other methods, the fundamental principle - that optical torque results from the exchange of electromagnetic angular momentum between the trapping beam and the particle - remains the same. The symmetry of both the particle and the beam play a central role in the transfer of angular momentum. We discuss this in detail, with particular attention paid to the special case of optical torque exerted by an incident beam with zero angular momentum.