We analyse the collective behaviours of Escherichia coli (E. coli) active matter. The individual movements of these E. coli can be accurately tracked and examined using a recently developed machine learning software called DeepTrack (Midvedt et al., 2021). This provides greater insight into the chaotic dynamics of E. coli swarms as well as the potential to critically assess current theoretical models. DeepTrack analysis can also be applied in more complex environments including interactions with microstructures made with photolithography. Analysing the movements of E. coli active matter with DeepTrack has promising implications in engineering and biomedical applications.
Sculpted light provides a very flexible tool for the production of configurable and flexible confining potentials at the nano- and micro-scale. Sculpted light has been extensively used in diverse fields ranging from optical micromanipulation to quantum atom optics and quantum communication. It enables the production of complex optical potentials.
Optically driven nano and micromachines hold a promise of vast applications in interdisciplinary fields of science. These machines can be driven by versatile optical landscapes and provide applications ranging from microfluidics, drag delivery systems to complex biological systems.
Sculpted light refers to the generation of custom designed light fields. These light fields can be applied in many diverse fields ranging from interrogating single atoms or atom assembly to using these fields for optical micromanipulation and optical tweezers as well as creating new quantum devices and sensors. We consider here the study and application of light with structured intensity, polarization and phase. These sculpted lights can be used for intricate studies of light -matter interactions in a variety of environments. I will describe their use in transfer of transvers angular momentum of light and in studies of inertia.
Mechanobiology has become an important and ever-growing field of science that combines biology, engineering, chemistry and physics. It provides invaluable tool to studies of how the application of physical forces influences development, cell differentiation, physiology and disease. Many techniques have been developed throughout the time that enable these studies to contribute to our knowledge of complex biological systems. Optical or light technologies on the nano and micro-scale have enabled unprecedented advances in our understanding of mechanobiology. We will review the new developments in this rich field and point at further developments in this area that could lead to use of these nanotools to a further biomedical research community.
The inertial behaviour of a microscopic particle is obscured by its Brownian motion within a fluid. Collisions with fluid molecules give the particle velocity which dissipates on exceedingly short time scales due to the opposing drag forces from the fluid. Studying the motion at these very short time scales provides useful information about dynamic systems. In this work, we detail our approach to measure the angular velocity at these short time scales using Rotational Optical Tweezers enabling novel measurements of rotational dynamics and studying systems that are out of equilibrium.
We study far from equilibrium systems through investigating how groups of bacteria behave when other bacteria are present in the system and when barriers are introduced. For these studies we use structured light to fabricate microscopic structures for optical trapping and cell studies using two photon photopolymerization process. Structured light is created using spatial light modulator and correct for wavefront distortions in-situ providing aberration corrected system. This system is used to enable production of simple holographic optical tweezers apparatus with as many as 50 individual foci to create complex 3D microstructures. These structures can induce the collective behaviour of bacteria.
We overview and further methods for using structured light to fabricate microscopic structures for optical trapping and cell study experiments through two-photon-photopolymerisation (2PP). We utilise a spatial light modulator (SLM) to correct wavefront distortions in-situ from gold nanoparticle reflections, which are shown to offer significant improvements for in-house nanofabrication. Aberration corrected 2PP offers a mechanism for using a simple, modified holographic optical tweezers apparatus to produce complex 3D micro-structures with as many as 50 independent foci. Custom-designed structures are used to induce and study the collective behaviour of bacteria allowing us to test otherwise simulated theories of cell dynamics.
Light can transfer both linear and angular momentum to matter. This constitutes the principle of optical tweezers developed by Arthur Ashkin and can be used for three dimensional trapping and manipulation of objects in a large variety of systems. The optical tweezers can be used in combination with three dimensional structures produced using two photon photopolymerisation process (2PP) in order to provide a source of all optically driven mircomachines that in turn are used for dynamic studies of biological and physical processes. They can also be used to construct heat engines.
We report on the observation of transfer of transverse angular momentum to birefringent vaterite particles (positive uniaxial crystal) several wavelengths in size and trapped with optical tweezers in a transmission optical system and discuss prospects for quantitative measurement of angular momentum that this system poses. Such rotational control of spherical particles are excellent components of optically driven nano and micromachines that generate localised shear flows.
Identifying a particle in an optical trap can be a difficult task, especially for biological samples with low contrast. The relationship of radius and refractive index to the stiffness of optical traps is non-intuitive, motivating a machine learning approach. We demonstrate methods for real-time estimates of the radius and refractive index of particles trapped by optical tweezers. This is achieved by analysing the particle’s position and force with artificial neural networks. Our network achieved binary classification of experimental particles by sampling only milliseconds of force and position values. This demonstrates that real-time particle recognition is achievable with machine learning systems.
Piconewton scale forces can be measured with optical tweezers by monitoring the deflection of the trapping laser transmitted through a particle. This deflection is caused by a momentum transfer from the beam to the particle, measured as a change in voltage at a correctly placed position sensitive detector. To monitor these forces a conversion constant needs to be determined,which provides a mapping between units of voltage and Newtons. We propose, and experimentally verify, a new technique of detector calibration which outperforms previously developed methods. We also provide a quantitative comparison of different calibration techniques and the circumstances in which they are applicable.
Computationally accurate methods for simulating optical tweezers tend to be prohibitively slow, limiting their use to only very simple problems. Simplified models, such as the harmonic model, enable larger simulations by trading off accuracy for speed. In this presentation, I will demonstrate how training an artificial neural network to predict optical force combines the speed of a harmonic model with the accuracy of a semi-analytical method. Artificial neural networks not only enable more extensive and accurate dynamics simulations, but also collaboration through sharing of pre-trained models which can easily be distributed and used on mobile devices and in web browsers, as I will demonstrate.
We use dynamically controlled annular beam optical tweezers to orientate non-spherical swimming E.coli. Typically elliptically shaped particles in a Gaussian optical trap will align themselves with the direction of beam propagation. This orientation makes determining the dynamics of swimming particles difficult, as most optical tweezers systems are only able to capture information in the focal plane, but not the axial direction. We use simulations and experimental measurements to show that we are able to orientate motile E.coli from a vertical to horizontal position with a spatial light modulator in as little as one intermediate step without reduction in trap stiffness.
Vortices can be found in many types of fields, from fluid velocity fields to optical fields. In optical manipulation, we are interested in the optical force field arising from the interaction between the beam and the particle. There are several mechanisms that can lead to circulation of particles around an optical trap including transfer of angular momentum from the beam to the particle or oscillations due to a lack of damping in the dynamical system. Understanding of the creation and behaviour of vortices occurring in optical fields can provide means for creating interesting rotational dynamics for particles held in structured light fields. Here, we describe the mechanisms that can lead to circulation in an optical trap. In particular we describe how the force field vortices can be found in different trapping configurations and we discuss the relationship between force vortices, optical vortices and Brownian vortices.
Simulation of optical tweezers involves the calculation of optical and non-optical forces and torques, modelling the Brownian motion of the particle and combining these components to calculate the overall dynamics of the system. Here we describe two new toolboxes: an improved optical force/torque calculation toolbox and a full dynamics simulation toolbox which combines all the individual parts to simplify the process of calculating particle dynamics. The new toolbox will provide functions for simulating particle dynamics, estimating trap stiffness and calculating trap depths. The toolbox will be able to calculate optical forces/torques in different regimes including the geometric optics limit, Rayleigh limit, and intermediate regime with Vector Spherical Wave Functions/Tmatrix,VSWF/T-matrix, Discrete Dipole Approximation, DDA, and the Final Difference Time Domain method, FDTD. Using these tools, it is possible to model different types of trapping configurations that can be used to study motile particles held in optical tweezers.
Using absolutely calibrated optical tweezers, we make quantitative measurements of the motility force of Escherichia coli (E. coli) by measuring the change in momentum of the deflected beam. By tracking the position of the particle, in addition to the optical force measurements, it should be possible to simultaneously calculate the motility force and drag. In a simple Gaussian beam optical trap away from the sample chamber E. coli tends to align and swim along the beam axis, which can make tracking the particle position and measuring the force difficult. We use a 3-D optical force detection system to measure the absolute force on the particle, allowing us to measure the motility force of E. coli in a simple Gaussian beam. By using a line-shaped trap, it is possible to align E. coli transverse to the beam axis, facilitating easy particle position measurement. The investigated methods are not specific to E. coli and could be applied to other motile organisms, the study of wall effects and bio-films.
Structured light is readily used to control and investigate microsystems. Dynamic manipulation of microscopic particles of matter has enabled non-contact investigations of a large number of complex physical, biological and chemical systems. In recent years, ever more sophisticated techniques to control microsystems have been developed, shadowing rapid advances in computer technology. This work utilises computational and other signal processing techniques to dynamically control input light fields and modulate the scattered output light fields to improve the specificity of measurements using either optical switching or beam shaping. The aggregate properties of structured light such as linear and angular momentum are changed when scattered from a particle. We present improvements to measurement of signals otherwise hidden in noise or other larger signals by selectively filtering considering the amplitude, phase or wave function symmetry. Measurements are demonstrated using both liquid crystal spatial light modulators and digital micromirror devices. Further challenges that occur in development of these techniques will be discussed as well as their use when applied to specific experiments. We will give an overview of both past successes in measurement of position, force and angular momentum transfer and other current research developments.
Accurate centroid position measurements of a light spot are vital for optical tweezers. To get quantitative measurements we can find the optical force by measuring the change in momentum of the trapping beam and track the position of the trapped particle using its image. We propose to use a filter with a linear transmittance to modulate the amplitude of the input beam in such a way that the transmitted intensity of the light will be proportional to the displacement of the spot. Our method is compared with existing methods and we find that it provides accurate measurements at high bandwidth.
Precise temperature measurements in optical traps are crucial for biological objects as they are highly sensitive to the temperature. We shift the trapped particle from the equilibrium position by moving the stage and record the position and the optical force synchronously. The absolute nature of the force detection method makes it suitable for measuring optical forces in a non-linear region of the optical trap increasing the precision to 0.2K. Moreover, the proposed method does not require a precalibration of the force detector and, therefore, can be used for temperature independent calibration.
Particle–wall interactions are important in biology, micromachining, coagulation studies, and many other areas of science. As a contactless tool, optical tweezers are ideal for measuring these kind of interactions. Here we will present a new method for calculating the non-optical forces acting on a trapped particle using simultaneous position and force detection. Analysis of the particle's Brownian motion when trapped gives a measure of all the forces experienced by the particle. In contrast, measuring only the light's momentum change directly gives the solely optical force. This is achieved measuring the changes in the scattered light. The difference between the forces recorded by the two techniques reveals the external forces acting on the trapped particle. Therefore, by trapping the particle close to a wall, one can study the particle-wall interaction force in details. The simulation were done using the optical tweezer toolbox [1] to find the optical force acting on a particle. The net force was calculated from a Brownian motion’s statistics of a trapped particle in the presence of the exponential external force. By using the proposed method, we were able to successfully reconstruct the external force. The experiment was done on a trapped spherical PMMA particle (d=2.2um) close to the 3D-printed wall. For the particle-wall distance ~0.7um the non-optical force is ~100fN . The experiment and simulation results confirm the efficiency of the proposed method for an external force measurements. [1] Nieminen et al., J. Opt. A 9, S196-S203 (2007).
Optical tweezers use highly focussed beams to trap microscopic particles in three dimensions. It is possible to carry out quantitative force measurements, on the order of piconewtons, if calibration of the system is done first. This requires finding the optical force for a given trapping power and position in the trap. Two tools commonly used for calibration are the camera and position-sensitive detector (PSD). Both are commonly used to track trapped particles, but they give complementary information. The camera gives the position of the particle. The PSD measures the defection of the beam, which is the force exerted on the particle. Since these data are obtained on different instruments, usually at vastly different rates, there is difficulty in synchronising the force and position data. Here we look at a force calibration method, without synchronising the data, by mapping force and position measurements. If the force-position relation is monotonic, then the median of the force distribution corresponds to the median of the position distribution; in general, the nth percentile of one corresponds to the (100-n)th percentile of the other. This intuitively works for traps whose force-position relations are monotonic, which includes Hookean traps like a single round symmetric trap. We discuss the limits at which this method can be applied to non-Hookean trapping arrangements, such as independent or coherent double-well traps.
Boundary walls have a strong influence on the drag force on optically trapped object near surface. Faxen’s correction has shown how a flat surface modifies the hydrodynamic drag. However, to date, the effect of curved walls at microscopic scale on both translational and rotational movement of micro-objects has not been studied. Here we describe our experiments which aim to study the drag force on optically trapped particles moving near walls with different curvatures.
The curved walls were made using 3D laser nano-printing (Nanoscribe), and optical tweezers were used to trap micro-objects near the walls. The translational and rotational motion of the optically trapped particle is related to the drag coefficients. By monitoring the change in the motion of particle, we determined the increase in drag force for particles translating or rotating at different distances from surfaces with different curvatures.
These results are essential for calibrating the drag force on particles, and thus enable accurate rheology at the micron-scale. This opens the potential for microrheology under different conditions, such as within microdevices, biological cells and studies of biological processes
We have estimated the mitotic forces exerted on individual isolated mammalian chromosomes using optical trapping. The chromosomes were trapped by an optical tweezers system created by a continuous wave ytterbium laser at 1064 nm. Individual chromosomes were trapped at different in situ powers in the range of ≈20-50 mW. The corresponding trapping forces were determined by a viscous drag method. In the range of laser powers used, the preliminary data show a linear relationship between the chromosome trapping forces and in situ powers. We have calculated the dimensionless trapping efficiency coefficient (Q) of the chromosomes at 1064 nm and the corresponding effects of trapping power on Q. The value of Q in our experiments was determined to be ≈0.01. The results of this study validate optical tweezers as a non-invasive and precise technique to determine intracellular forces in general, and specifically, the spindle forces exerted on the chromosomes during cell division.
Microrheology, the study of the behavior of fluids on the microscopic scale, has been and continues to be one of the most important subjects that can be applied to characterize the behavior of biological fluids. It is extremely difficult to make rapid measurement of the viscoelastic properties of the interior of living cells. Liposomes are widely used as model system for studying different aspects of cell biology. We propose to develop a microrheometer, based on real-time control of optical tweezers, in order to investigate the viscoelastic properties of the fluid inside liposomes. This will give greater understanding of the viscoelastic properties of the fluids inside cells. In our experiment, the liposomes are prepared by different methods to find out both a better way to make GUVs and achieve efficient encapsulation of particle. By rotating the vaterite inside a liposome via spin angular momentum, the optical torque can be measured by measuring the change of polarization of the transmitted light, which allows the direct measurement of viscous drag torque since the optical torque is balanced by the viscous drag. We present an initial feasibility demonstration of trapping and manipulation of a microscopic vaterite inside the liposome. The applied method is simple and can be extended to sensing within the living cells.
With suitable calibration, optical tweezers can be used to measure forces. If the maximum force that can be exerted is of interest, calibration can be performed using viscous drag to remove a particle from the trap, typically by moving the stage. The stage velocity required to remove the particle then gives the escape force. However, the escape force can vary by up to 30% or more, depending on the particle trajectory. This can have significant quantitative impact on measurements. We describe the variation of escape force and escape trajectory, using both experimental measurements and simulations, and discuss implications for experimental measurement of forces.
We use highly a focused laser beam incident on a carbon coated coverslip to create microcavitation. Full
optical control of the radii of the bubbles is attained. Multiple bubbles can also be created and their size
changed independently. The dynamics of such multi-bubble systems are studied. These bubble systems
generate strong flows such as Marangoni convection and also large thermal gradients. Since the size of the
micro-bubbles is highly dependent on the temperature, we anticipate that these systems can be used for
precise temperature control of samples. These methods are of use when the knowledge of exact and local
temperature profiles are of importance. Furthermore, since bubble expansion can generate orders of
magnitude more force than conventional optical tweezers, systems have application in manipulation of
particles where large forces are required. We present methods based on optical tweezers for using the
generated bubbles as thermal sensors and as opto-mechanical transducers.
We have combined a laser scissors and a laser tweezers to study, (1) the response of nerve fiber growth cones to laser-induced damage on single axons, and (2) localized microfluidic flow generated by laser-driven spinning birefringent
particles. In the laser scissors study, sub-axotomy damage elicits a growth cone response whether damage is on the same
or an adjacent axon. In laser tweezers study, the axon growth cones turn in response to the optically driven microfluidic
flow. In summary, both the laser scissors and the laser tweezers studies elicit growth cone turning responses.o
Computational tasks such as the calculation and characterization of the optical force acting on a sphere are relatively straightforward in a Gaussian beam trap. Resulting properties of the trap such as the trap strength, spring constants, and equilibrium position can be easily determined. More complex systems with non-spherical particles or multiple particles add many more degrees of freedom to the problem. Extension of the simple methods used for single spherical particles could result in required computational time of months or years. Thus, alternative methods must be used. One powerful tool is to use dynamic simulation: model the dynamics and motion of a particle or particles within the trap. We demonstrate the use of dynamic simulation for non-spherical particles and multi-particle systems. Using a hybrid discrete dipole approximation (DDA) and T-matrix method, we find plausible equilibrium positions and orientations of cylinders of varying size and aspect ratio. Orientation landscapes revealing different regimes of behaviour for micro-cylinders and nanowires with different refractive indices trapped with beams of differing polarization are also presented. This investigation provides a solid background in both the function and properties of micro-cylinders and nanowires trapped in optical tweezers. This method can also be applied to particles with other shapes. We also investigate multiple-particle trapping, which is quite different from single particle systems, as they can include effects such as optical binding. We show that equilibrium positions, and the strength of interactions between particles can be found in systems of two and more particles.
Numerical computation of optical tweezers is one path to understanding the subtleties of their underlying
mechanism—electromagnetic scattering. Electromagnetic scattering models of optical trapping can be used
to find the properties of the optical forces and torques acting on trapped particles. These kinds of calculations
can assist in predicting the outcomes of particular trapping configurations. Experimentally, looking at the parameter
space is time consuming and in most cases unfruitful. Theoretically, the same limitations exist but
are easier to troubleshoot and manage. Towards this end a new more usable optical tweezers toolbox has been
written. Understanding of the underlying theory has been improved, as well as the regimes of applicability of the
methods available to the toolbox. Here we discus the physical principles and carry out numerical comparisons
of performance of the old toolbox with the new one and the reduced (but portable) code.
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.
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.
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.
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.
The cell nucleus is the dominant optical scatterer in the cell. Neoplastic cells are characterized by cell nucleus polymorphism and polychromism-i.e., the nuclei exhibits an increase in the distribution of both size and refractive index. The relative size parameter, and its distribution, is proportional to the product of the nucleus size and its relative refractive index and is a useful discriminant between normal and abnormal (cancerous) cells. We demonstrate a recently introduced holographic technique, digital Fourier microscopy (DFM), to provide a sensitive measure of this relative size parameter. Fourier holograms were recorded and optical scatter of individual scatterers were extracted and modeled with Mie theory to determine the relative size parameter. The relative size parameter of individual melanocyte cell nuclei were found to be 16.5±0.2, which gives a cell nucleus refractive index of 1.38±0.01 and is in good agreement with previously reported data. The relative size parameters of individual malignant melanocyte cell nuclei are expected to be greater than 16.5.
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 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.
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.
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.
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 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 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 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.
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.
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.
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.
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