Microrheology, the study of flow at the microscopic scale, has benefited immensely from a variety of optical micromanipulation techniques developed over the past two decades. However, very few present procedures allow the rapid measurement of the viscoelastic properties of fluid samples with volumes on the order of tens of
picolitres over a wide frequency range. We detail preliminary construction and analysis of an active rotational microrheological method which promises to achieve this. Rotational microrheology was performed by optically trapping a birefringent probe particle in a linearly polarised dual-beam trap and rapidly rotating the polarisation direction through a xed angle. This provides
measurements of the low-frequency fluid response, whilst passive monitoring of thermal motion is used to determine
high-frequency components. Our method is less sensitive to boundary effects and probe particle asphericity than analogous translational microrheological techniques, so will be ideal for microfluidic applications and analysis of fluids which are generally available in volumes which preclude the use of existing experimental techniques.
It is well established that a light beam can carry angular momentum and therefore when using optical tweezers
it is possible to exert torques to twist or rotate microscopic objects. Both spin and orbital angular momentum
can be transferred. This transfer can be achieved using birefringent particles exposed to a Gaussian circularly
polarized beam. In this case, a transfer of spin angular momentum will occur. The change in spin, and hence the
torque, can be readily measured optically. On the other hand, it is much more challenging to measure orbital
angular momentum and torque. Laguerre-Gauss mode decomposition, as used for orbital angular momentum
encoding for quantum communication, and rotational frequency shift can be used, and are effective methods in
a macro-environment. However, the situation becomes more complicated when a measurement is done on microscale,
especially with highly focused laser beams. We review the methods for the measurement of the angular
momentum of light in optical tweezers, and the challenges faced when measuring orbital angular momentum. We
also demonstrate one possible simple method for a quantitative measurement of the orbital angular momentum
in optical tweezers.
Since a light beam can carry angular momentum (AM) it is possible to use optical tweezers to exert torques to twist or
rotate microscopic objects. The alignment torque exerted on an elongated particle in a polarized light field represents a
possible torque mechanism. In this situation, although some exchange of orbital angular momentum occurs, scattering
calculations show that spin dominates, and polarization measurements allow the torque to be measured with good
accuracy. This phenomenon can be explained by considering shape birefringence with an induced polarizability tensor.
Another example of a shape birefringent object is a microsphere with a cylindrical cavity. Its design is based on the fact
that due to its symmetry a sphere does not rotate in an optical trap, but one could break the symmetry by designing an
object with a spherical outer shape with a non spherical cavity inside. The production of such a structure can be achieved
using a two photon photo-polymerization technique. We show that using this technique, hollow spheres with varying
sizes of the cavity can be successfully constructed. We have been able to demonstrate rotation of these spheres with
cylindrical cavities when they are trapped in a laser beam carrying spin angular momentum. The torque efficiency
achievable in this system can be quantified as a function of a cylinder diameter. Because they are biocompatible and
easily functionalized, these structures could be very useful in work involving manipulation, control and probing of
individual biological molecules and molecular motors.
Approximate methods such a Rayleigh scattering and geometric optics have been widely used for the calculation
of forces in optical tweezers. We investigate their applicability and usefulness, comparing results using these
approximate methods with exact calculations.
While a variety of different optically-driven micromachines have been demonstrated by a number of groups
around the world, there is a striking similarity in the designs used. The typical optically-driven rotor consists
of a number of arms attached to a central hub, or elongated stalk in the case of free-floating rotors. This is a
consequence of the relationship between the symmetry of a scattering object and the transfer of optical angular
momentum from a beam to the object.
We use a hybrid discrete-dipole approximation/T-matrix method algorithm to computationally model the
scattering by such optically-driven rotors. We systematically explore the effects of the most important parameters
of rotors, such as the thickness, length, and width of the arms, in order to maximize the torque efficiency.
We show that it is possible to use computational modelling to optimize the design of such devices. We also
compare the computational results with experiment.
As an optically trapped micro-object spins in a fluid, there is a consequent flow in the fluid.. Since a free-floating
optically-driven microrotor can be moved to a desired position, it can allow the controlled application of a directed flow
in a particular location. Here we demonstrate the control and rotation of such a device, an optical paddle-wheel, using a
multiple-beam trap. In contrast to the usual situation where rotation is around the beam axis, here we demonstrate
rotation normal to this axis.
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
systems.
We are exploring a biological application of optical tweezers with fluorescence imaging for microrheometry.
Measurement of the power spectrum of Brownian motion of a trapped probe particle or vesicle provides information on
the viscoelastic properties of the surrounding medium which can change in response to cellular processes or the effect of
drugs.
We present an experimental demonstration of a method using optical tweezers proposed by Fischer and Berg-Sorensen
for measuring viscoelasticity using optical tweezers. It is based on a sinusoidal oscillation of the liquid in combination
with force measurements using optical tweezers. We verify the method by applying it to measurements in water, glycerol
and polyethylene oxide (PEO).
Two-photon polymerization of optically curing resins is a powerful method to fabricate micron sized objects which can be used as tools to measure properties at small scales. These microdevices can be driven by means of externally applied focused laser beams (optical tweezers) through angular momentum exchange, giving rise to a net torque. The advantage of the optical drive is that no contact is required, therefore making the microdevices suited to non-invasive biological applications.
The fabrication method is versatile and allows building objects of any 3D shape.
We discuss the design and modelling of various optically driven rotors. In particular, we consider fabrication of microspheres with an internal shape birefringence in order to obtain rotation in an optical trap. The reason for fabricating this type of object is that they are well-suited for studies of mechanical properties of single biomolecules such as the torsional stiffness of DNA or torque generated by molecular motors.
The microspheres fabricated are able to transduce torques of 2000 pNnm with optical powers of 500 mW and could be rotated with frequencies up to 40 Hz in circularly polarized light.
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.
Building on the ability to exert torques in optical tweezers,
optically-driven rotating micromachines have reached the verge of practical application. Prototype devices have been made, and useful applications are being sought. We outline some general principles that can be applied to the design of optically-rotated devices, and describe a method for rigorous computational modelling that is well-suited to the optimization and engineering of such micromachines. Finally, we describe a method for rapid microfabrication of prototypes for testing, and some results of such tests.
Particles that can be trapped in optical tweezers range in size from tens of nanometres to tens of micrometres.
Notably, this size range includes large single molecules. We show experimentally, in agreement with theoretical
expectations, that optical tweezers can be used to manipulate single molecules of polyethylene oxide suspended in
water. The trapped molecules accumulate without aggregating, so the optical trap offers a method of controlling
the concentration of macromolecules in solution.
Potential applications are the micromanipulation of nanoparticles, nanoassembly, microchemistry, and the
study of biological macromolecules.
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.
This paper examines two controversies arising within classical electromagnetism which are relevant to the optical
trapping and micromanipulation community. First is the Abraham-Minkowski controversy, a debate relating
to the form of the electromagnetic energy-momentum tensor in dielectric materials, with implications for the
momentum of a photon in dielectric media. A wide range of alternatives exist, and experiments are frequently
proposed to attempt to discriminate between them. We explain the resolution of this controversy and show that
regardless of the electromagnetic energy-momentum tensor chosen, when material disturbances are also taken
into account the predicted behaviour will always be the same. The second controversy, known as the plane wave
angular momentum paradox, relates to the distribution of angular momentum within an electromagnetic wave.
The two competing formulations are reviewed, and an experiment is discussed which is capable of distinguishing
between the two.
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.
Recently we have shown that protein crystals could be grown while they were three-dimensionally trapped by optical tweezers. This permitted studies of modifications of single crystals while gradually changing the conditions in the growing solution. Furthermore it allowed the crystals to grow far away from container walls favoring high quality crystal growth. Many protein crystals themselves consist of fairly large molecules, with sizes up to tens of nanometers. Here we present experiments studying the effect of optical trapping potentials on large molecules, with the aim to explore ways to further enhance crystal growth. For this purpose we extended our tweezers setup with a specially developed detection system allowing us to monitor changes in the molecule concentration of a solution. Using polyethylene oxide (PEO) molecule solutions we were able to demonstrate that the trapping potential of an optical trap is sufficient to collect large single molecules. Our results show that the optical trap induces an increase in the molecule concentration in the focal region. As expected only molecules above a certain molecular weight could be manipulated, and the concentration in the focal region depended on the power of the trapping laser. The ability to locally increase the concentration of molecules may be useful in assisting nucleation of crystals.
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 report on a new experimental technique suitable for measurement of light-activated processes, such as fluorophore transport. The usefulness of this technique is derived from its capacity to decouple the imaging and activation processes, allowing fluorescent imaging of fluorophore transport at a convenient activation wavelength. We demonstrate the efficiency of this new technique in determination of the action spectrum of the light mediated transport of rhodamine 123 into the parasitic protozoan Giardia duodenalis.
We report here on the use of optical tweezers in the growth and manipulation of protein and inorganic crystals. Sodium chloride and hen egg-white lysozyme crystals were grown in a batch process, and then seeds from the solution were introduced into the optical tweezers. The regular and controllable shape and the known optical birefringence in these structures allowed a detailed study of the orientation effects in the beam due to both polarization and gradient forces. Additionally, we determined that the laser tweezers could be used to suspend a crystal for three-dimensional growth under varying conditions. Studies included increasing the protein concentration, thermal cycling, and a diffusion-induced increase in precipitant concentration. Preliminary studies on the use of the tweezers to create a localized seed for growth from polyethylene oxide solutions are also reported.
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.
Several methods to rotate and align microscopic particles controllably have been developed. Control of the orientation of a trapped particle allows full three dimensional manipulation, whereas rotating particles are tools for the development of optically-driven micromachines. It has been shown that the orientation of an object in the laser trap depends on its birefringence as well as on its shape. The effect of shape is often referred to as form-birefringence. We report on the trapping, rotation, and in-situ growth of birefringent tetragonal lysozyme crystals in optical tweezers operating at a wavelength of 1064 nm. Variation of the temperature, pH and lysozyme concentration of the solution during growth was used to alter the size, as well as the length to width ratio of the crystals, and hence their orientation in the tweezers. Thus this system serves as a model to study the relative importance of birefringence versus form-birefringence for particle orientation. Crystals with the optical axis skewed or perpendicular to the trapping-beam axis could be rotated by changing the orientation of linearly polarized light. We observed spontaneous spinning of some asymmetric crystals in the presence of linearly polarized light, due to radiation pressure effects. Addition of protein to the solution in the tweezers permitted real-time observation of crystal growth.
We describe the production of BECs on a new type of atom chip based on silver foil. Our atom chip is fabricated with thick wires capable of carrying currents of several amperes without overheating. The silver surface is highly reflective to light resonant with optical transitions used for Rb. The pattern on the chip consists of two parallel Z-trap wires, capable of producing two-wire guide, and two additional endcap wires for varying the axial confinement. Condensates are produced in magnetic microtraps formed within 1 mm of surface of the chip. We have observed the fragmentation of cold atom clouds when brought close to the chip surface. This results from a perturbed trapping potential caused by nanometer deviations of the current path through the wires on the chip. We present results of fragmentation of cold clouds at distances below 100 μm from the wires and investigate the origin of the deviating current. The fragmentation has different characteristics to those seen with copper conductors. The dynamics of atoms in these microtraps is also investigated.
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.
Computational modelling of optical tweezers offers opportunities for
the study of a wide range of parameters such as particle shape and
composition and beam profile on the performance of the optical trap,
both of which are of particular importance when applying this technique to arbitrarily shaped biological entities. In addition,
models offer insight into processes that can be difficult to experimentally measure with sufficient accuracy. This can be invaluable for the proper understanding of novel effects within optical tweezers. In general, we can separate methods for computational modelling of optical tweezers into two groups: approximate methods such as geometric optics or Rayleigh scattering, and exact methods, in which the Maxwell equations are solved. We discuss the regimes of applicability of approximate methods, and consider the relative merits of various exact methods. The T-matrix method, in particular, is an attractive technique due to its efficiency for repeated calculations, and the simplicity of determining the optical force and torque. Some example numerical results are presented.
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.
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.
We are investigating the formation of a tissue capsule around a foreign body. This tissue capsule can be used as an autologous graft for the replacement of diseased blood vessels or for bypass surgery. The graft is grown in the peritoneal cavity of the recipient and the formation starts with the adhesion of cells to the foreign body. We identify the cell type and measure the adhesion of these cells to foreign materials using optical tweezers. Cell adhesion to macroscopic samples and microspheres is investigated. No difference in the adhesion force was measurable for polyethylene, silicon and Tygon on a scale accessible to optical tweezers. The density of adherent cells was found to vary strongly, being highest on polyethylene. The mean rupture forces for cell-microsphere adhesion ranged from 24 to 39 pN and changed upon preadsorption of bovine serum albumin. For plain microspheres, the highest mean rupture force was found for PMMA, which also showed the highest adhesion probability for the cell-microsphere interaction.
It has been shown previously that it is possible to two- dimensionally trap a microscopic absorbing particle against a substrate using a focused doughnut beam. Beam angular momentum associated with the phase singularity is transferred to the particle, causing it to rotate. A detailed consideration of the optical forces acting on a particle shows the importance of wavefront curvature for stable trapping and lead to a quantitative description of the motion of the particle in single and multiple beam traps.
Phase singularities in laser beams carry angular momentum due to the associated helical wavefront structure. This angular momentum can be transferred to absorbing particles trapped in the beam, setting them into rotation.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.