When particles are held in optical tweezers, we assume that they are in thermal equilibrium. Here we show that this condition only holds for high symmetry cases, e.g. perfectly isotropic particles in unaberrated, linearly polarized Gaussian traps. We show both experimentally and theoretically that when a birefringent microsphere is held in a linearly polarised Gaussian optical trap in vacuum, spontaneous oscillations emerge that grow rapidly in amplitude and become increasingly coherent as the air pressure is reduced. Furthermore, when parametrically driven, these self-sustained oscillators exhibit an ultrahigh quality factor exceeding 200 million, which can be highly sensitive to external perturbations.
When particles are held in optical tweezers, we assume that they are in thermal equilibrium, in which the equipartition of energy determines the position variance of optically trapped spheres. Here we show that this condition only holds for very high symmetry cases, e.g. perfectly isotropic particles in unaberrated, linearly polarized Gaussian traps. We report an experimental observation that when a birefringent microsphere is held in a linearly polarised Gaussian optical trap in vacuum, spontaneous oscillations emerge that grow rapidly in amplitude and become increasingly coherent as the air pressure is reduced. Furthermore, when parametrically driven, these self-sustained oscillators exhibit an ultrahigh mechanical quality factor > 2 x 108, which can be highly sensitive to external purtabations.
Optically levitated nanoparticles in vacuum are a promising tool aiming for the extremely sensitive force measurements in reaching up to the order of zN•Hz-1/2 and for the potential investigation in the field of quantum physics. In contrast to other mechanical oscillators, the optically trapped nanoparticle in vacuum has no clamping losses, its motion is influenced only by a laser beam and its potential profle and therefore the mechanical quality factor of such oscillator is very high. In water immersion the optical trap is almost exclusively considered as harmonic but in vacuum the optical potential anharmonicity starts to play an important role. This can be observed in power spectrum density profile where the oscillation peak is asymmetric. Here we demonstrate on the simulated trajectories of the levitated particle how the standard power spectral density method provides strongly biased values of parameters describing the optical trap and its surrounding properties.
Particles held in optical tweezers are commonly thought to be at thermodynamic equilibrium with their environment. Under this assumption the elastic energy of the trap is equal to the thermal energy. As a result the variance of the particle position is completely independent of viscosity and inversely proportional to the optical power in the trap. Here we show that these conditions only hold for very high symmetry cases e.g. perfectly spherical particles in unaberrated, linearly polarized Gaussian traps. Here we show that any reduction in symmetry leads to asymmetrically coupled degrees of freedom. The associated force field is linearly non-conservative and the tweezer is no longer at equilibrium. In overdamped systems the effect is a underlying systematic bias to the Brownian motion. In underdamped systems, this systematic component can accumulate momentum, eventually destabilizing the trap. We illustrate this latter effect with reference to two systems, (i) an isotropic sphere in a circularly polarized trap, and (ii) a birefringent sphere in a linearly polarized trap. In both cases the instability can be approached either by decreasing air pressure or by increasing optical power. Close to instability, the trapped particle executes increasingly coherent motion that is highly sensitive to external perturbations. Potential applications to weak force sensing are discussed.
We theoretically examine the transport properties of non-ideal optical fibres with high numerical aperture. Using a simple spectral method, we derive the modes in perturbed or non-ideal fibres from the numerically evaluated modes of circularly symmetric fibres. We then consider the propagation through the fibre of Gaussian spots, projected onto the distal fibre end. The incident spots are of uniform, arbitrary polarization and positioned at any point on the fibre facet. We then evaluate the effect of propagation through the fibre in terms of various indices. In particular, we consider the motion of the centre of energy, the average polarization state and the average spin and orbital angular momentum. The study includes both step index and graded index optical fibres with symmetric and chiral deformations. We observe a fundamental difference between propagation in step index and graded index optical fibres: in the latter case, the centre of energy converges to the fibre axis as the light propagated along the fibre and in the former it moves erratically about the transverse plane. In addition, we find that circular polarization states are preserved for cylindrically symmetric fibres, of arbitrarily high numerical aperture. However, this property is destroyed by relatively weak deformations of the fibre.
When using multimode fibers as high-resolution endoscopes, advanced adaptive optics is needed to overcome the modal dispersion which scrambles the image. Additionally, for non-linear imaging methods, all the wavelengths of a femtosecond laser pulse must be simultaneously focused at the sample plane, with appropriate dispersion compensation, that might vary across the sample area. We investigate the bandwidth of the focused spot for a graded index fiber used as a point scanning imaging device. We demonstrate that with proper compensation for the dispersion of the spatial light modulator this can be <45 nm. We also measure the spectral phase at the sample plane, and demonstrate that this does not vary substantially with spot position.
We present a few of our recent theoretical and experimental results related to the behavior of micron-scale particles placed into nonlinear optical potentials. The two-dimensional optical ratchet can rectify motion of Brownian particles in any direction in the plane and unstable cubic optical potential results in noise-induced particle motion. Action of optical spin-force was demonstrated in a novel geometry where it is responsible for particle orbiting.
Optical binding occurs when micron-sized particles interact through the exchange of scattered photons. It has been observed both in systems of colloidal dielectric particles and between metallic nanoparticles, and can result in the formation of clusters and coupled dynamical behaviour. Optical binding between spherical particles has been studied in some detail, but little work has appeared in the literature to describe binding effects in lower symmetry systems. In the present paper we discuss recent theoretical work and computer simulations of optical binding effects operating between dielectric nanowires in counter propagating beams. The reduction in symmetry from simple spheres introduces new opportunities for binding, including different types of orientational ordering and anisotropies in the spatial arrangements that are possible for the bound particles. Various ordered configurations are possible, including ladder-like structures and oriented lattices. The stability of these structures to thermal perturbations will be discussed. Asymmetric arrangements of the nanowires are also possible, as a consequence of interactions between the nanowires and the underlying counter-propagating laser field. These configurations lead to a diversity of non-conservative effects, including uniform translation in linearly polarised beams and synchronous rotations in circularly polarised beams, suggesting potential applications of such bound structures in micro-machines.
We report on an experimental and theoretical study of optical binding of polystyrene sphere pairs illuminated by retro-reflected wide Gaussian beam, so-called "tractor beam". We show that depending on configuration of particle pairs, optically bound structure in the "tractor beam" can be pushed or pulled against the beam propagation. We employ holographic video microscopy to analyse object positions in three dimensions and their time evolution. In such a way, we investigate their dynamics in dependence on the geometrical configuration that is compared with numerical simulations. We observe strong dependence of the particle pair motion on the relative distance of the particles.
Optical binding occurs when systems of both dielectric particles are illuminated by intense light fields, and results in the formation of clusters and coupled dynamical behaviour. Optical binding between spheres has been studied extensively, but little has appeared in the literature describing binding in lower symmetry systems. Here we discuss computer simulations of optical binding between hypothetical knotted nanowires. The knots chosen are drawn from the class of knots known as torus knots which may be represented with n-fold chiral rotational symmetry. We examine the binding properties of the knots in circularly polarised counter propagating beams.
Optical binding occurs in systems of both dielectric and metal particles and results in the formation of clusters
and coupled dynamical behaviour. Optical binding between spherical particles has been long studied, but
comparatively little work has appeared describing binding in lower symmetry systems. In this paper we discuss
recent theoretical work and computer simulations of optical binding between nanowires in linearly polarised
counter propagating beams.
Larger golden nanoparticles grow into several preferred forms. Some of those may be easily approximated by ellipsoids. In this paper we examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio. We study the rotational frequencies and stability of these golden nano-particles theoretically by the means of T-Matrix.
Direct laser writing is a powerful and exible tool with which to create 3D micro-scale structures with nanoscale features. These structures can then be dispersed in aqueous media and dynamically actuated in three dimensions using optical tweezers. The ability to build, actuate and precisely measure the motion of complex microscopic structures heralds a variety of new applications - optically actuated micro-robotics. In this article we describe how these devices are designed, fabricated and controlled. Once trapped, we are able to accurately measure the translational and rotational Brownian motion of the structures in real-time (at up to a few kHz) in three dimensions using high-speed video stereo-microscopy. This enables their motion to be controlled automatically using feedback, transforming the structures into quantitative tools. We discuss a range of applications, including the imaging of surface topography inside a sealed micro- uidic chamber, and work towards the controlled rotation of cells about an arbitrary axis.
Coordinated motion at low Reynolds number is widely observed in biological micro-systems, but the underlying mechanisms are often unclear. A holographic optical tweezers system is used to experimentally study this phenomenon, by employing optical forces to drive a pair of coplanar microspheres in circular orbits with a constant tangential force. In this system synchronisation is caused by hydrodynamic forces arising from the motion of the two spheres. The timescales of their synchronisation from large initial phase differences are explored and found to be dependent on how stiffly the microspheres are confined to their circular orbits. These measured timescales show good agreement with numerical simulations.
The linear Doppler shift forms the basis of various sensor types for the measurement of linear velocity, ranging from speeding cars to fluid flow. Recently, a rotational analogue was demonstrated, enabling the measurement of angular velocity using light carrying orbital angular momentum (OAM). If measurement of the light scattered from a spinning object is restricted to a defined OAM state, then a frequency shift is observed that scales with the rotation rate of the object and the OAM of the scattered photon. In this work we measure the rotational Doppler shift from micron-sized calcite particles spinning in an optical trap at tens of Hz. In this case the signal is complicated by the geometry of the rotating particle, and the effect of Brownian motion. By careful consideration of these influences, we show how the signal is robust to both, representing a new technique with which to probe the rotational motion of micro-scale particles.
Using optical tweezers for micro-rheological investigations of a surrounding fluid has been routinely demonstrated. In this work, we will demonstrate that rheological measurements of the bulk and surface properties of aerosol particles can be made directly using optical tweezers, providing important insights into the phase behavior of materials in confined environments and the rate of molecular diffusion in viscous phases. The use of holographic optical tweezers to manipulate aerosol particles has become standard practice in recent years, providing an invaluable tool to investigate particle dynamics, including evaporation/ condensation kinetics, chemical aging and phase transformation. When combined with non-linear Raman spectroscopy, the size and refractive index of a particle can be determined with unprecedented accuracy <+/- 0.05%). Active control of the relative positions of pairs of particles can allow studies of the coalescence of particles, providing a unique opportunity to investigate the bulk and surface properties that govern the hydrodynamic relaxation in particle shape. In particular, we will show how the viscosity and surface tension of particles can be measured directly in the under-damped regime at low viscosity. In the over-damped regime, we will show that viscosity measurements can extend close to the glass transition, allowing measurements over an impressive dynamic range of 12 orders of magnitude in relaxation timescale and viscosity. Indeed, prior to the coalescence event, we will show how the Brownian trajectories of trapped particles can yield important and unique insights into the interactions of aerosol particles.
By moulding optical fields, holographic optical tweezers are able to generate structured force fields with magni- tudes and length scales of great utility for experiments in soft matter and biological physics. Optically induced force fields are determined not only by the incident optical field, but by the shape and composition of the par- ticles involved. Indeed, there are desirable but simple attributes of a force field, such as rotational control, that cannot be introduced by sculpting optical fields alone. In this work we describe techniques for the fabrication, sample preparation, optical manipulation and position and orientation measurement of non-spherical particles. We demonstrate two potential applications: we show how the motion of a non-spherical optically trapped force probe can be used to infer interactions occurring at its tip, and we also demonstrate a structure designed to be controllably rotated about an axis perpendicular to the optical axis of the beam.
We present a computational model for the simulation of optically interacting nano-structures immersed in a viscous fluid. In this scheme, nanostructures are represented by aggregates of small spheres. All optical and hydrodynamic interactions, including thermal fluctuations, are included. As an example, we consider optical binding of dielectric nanowires in counterpropagating plane waves. In particular, the formation of stable, ladder like structures, is demonstrated. In these arrangements, each nanowire lies parallel to the polarization direction of the beams, with their centres of mass colinear.
The motion of a colloidal particle in an optical field depends on a complex interplay between the structure of the field, and
the geometry and composition of the particle. There are two complementary approaches to generating a particular force
field. The first, involving shaping the optical field with e.g. a spatial light modulator, has been extensively developed. A
second method, highlighted recently [J. Gluckstad, Nature Photonics, 5, 7–8 (2011)] involves sculpting of the particles
themselves, and has received less attention. However, as modern two-photon polymerisation methods advance, this avenue
becomes increasingly attractive for micromanipulation. In this paper we will show how computational methods may be
used to optimise particle geometries to produce desirable patterns of forces and torques. In particular, we will examine the
design of a constant force optical spring for use as a passive force clamp, and the effect of particle size on the trapping of
The motion of a particle in an optical field is determined by the interplay between the geometry of the incident optical
field, and the geometry and composition of the object. There are, therefore, two complementary roots to generating
a particular force field. The first, involving sculpting of the optical field with, for example, a spatial light modulator,
has been extensively developed. The second approach, which involves sculpting of the particles themselves, has been
highlighted recently, but has received much less attention [J. Gluckstad, Nature Photonics, 5, 7–8 (2011)]. However, as
modern fabrication methods advance, this avenue becomes increasingly attractive. In the following contribution we show
how computational methods may be used to optimize particle geometries so as to reproduce desirable forms of behaviour.
In particular, we exhibit a constant force optical spring for use as a passive force clamp in force sensing applications and a
high efficiency optical wing.
In this proceedings paper we show describe how a microtool can be assembled, and tracked in three dimensions
such that its full rotational and translational coordinates, q, are recovered. This allows tracking of the motion
of any arbitrary point, d, on the microtool's surface. When the micro-tool is held using multiple optical traps
the motion of such a point investigates the inside of an ellipsoidal volume - we term this a `thermal ellipsoid. We
demonstrate how the shape of this thermal ellipsoid may be controlled by varying the relative trapping power
of the optical traps, and adjusting the angle at which the micro-tool is held relative to the focal plane. Our
experimental results follow the trends derived by Simpson and Hanna.
The ability to hold and manipulate nanowires using optical beams opens up a range of applications from force sensing
to directed assembly. For this reason, optical trapping of nanowires has received much recent interest. In the following
article we present a detailed computational investigation of the stability and general behaviour of these systems. It is found
that relatively high index wires can be trapped. Furthermore, the properties of the trap vary with the parameters of the
nanowire in characteristic ways. For example, the trap stiffness in the direction parallel to the axes of the beam and the
wire falls off with increasing length, and can be made arbitrarily small. At the same time the other translational stiffness
coefficients attain a limit in which the stiffness perpendicular to the polarization direction is approximately one half of
that in the parallel direction. Rotational stiffness coefficients are seen, conversely, to increase steadily with length. These
observations are explained in terms of a simple analytical model that supports the numerical calculations.
In a recent article [Swartzlander et al. Nature Photonics, 5, 4851 (2010)], the optical analogue of conventional, aerodynamic
lift was experimentally demonstrated. When exposed to quasi-plane wave illumination, a dielectric hemicylinder rotates
into a stable configuration in which its cylindrical axis is perpendicular to the direction of propagation and its flat surface
angled to it. In this configuration the body forces experienced by the particle contain a component perpendicular to the
momentum flux of the incident field. This phenomenon can be meaningfully termed "optical lift", and the hemicylinder acts
as a "light foil". Here, we present rigorous, full wave vector simulations of this effect for light foils of varying dimensions
and composition. We investigate the general form of the forces and torques experienced by light foils, as a function of their
orientation. The influence of the linear dimensions and the refractive indices of the hemicylinders is also investigated.
Having three distinct radii, ellipsoidal particles can be rigidly bound in Gaussian traps. The elongated intensity profile
of the beam exerts forces that both confine, and orient the particle whilst the polarization of the beam provides a further
orientational constraint. Consequently, the longest axis of the ellipsoid tends to align itself with the beam axis and the
next longest with the polarization direction. In this article we examine the optical force fields experienced by ellipsoidal
particles in Gaussian beams. The relationship between the general properties of these traps, especially their stability and
stiffness, with particle shape is investigated.
The force field experienced by a sphere, trapped in a tightly focused Gaussian beam, is approximately conservative for
small displacements. For lower symmetry systems, this is not generally the case. Even when very tightly trapped, a
particle in such a system displays the effects of the non-conservative force field to which it is exposed. It does not come to
thermal equilibrium, but reaches a steady state in which its stochastic motion is subject to a deterministic, cyclic bias. Here,
we examine the dynamics of such a system, and show that the non-conservative nature of the force field manifests itself in
both the covariance and the spectral density of the generalized coordinates of the particle. In addition, we show that the
coupling between different types of thermal motion of such particles, i.e. rotational and translational, is asymmetric, which
leads to the periodic bias to the motion. These points are illustrated through computational simulations of the Brownian
dynamics of a trapped silica disk.
By using multiple optical traps suitably sized complex bodies can be bound with respect to their positions and orientations.
One recent application of this involves the use of an elongated object, equipped with a probe (a "nanotool"), to measure
and apply pico-Newton sized forces to, for example, the surface of a cell. This application has been described as an optical
atomic force microscope (AFM). Calculations of the mechanical susceptibility of trapped probes, and their hydrodynamic
resistance are presented. These quantities are used to assess the subsequent thermal motion of an optically trapped nanotool
in the context of the Orstein-Uhlenbeck process. Implications for the resolution and general behavior of the optical AFM
referred to above are discussed.
Holographic optical tweezers permit the simultaneous control of multiple optical traps. In this paper we examine the use
of such systems for the purposes of micromanipulation and assembly of microstructured materials. To this end, optically
induced forces and torques on a variety of objects are evaluated using numerical and semi-analytical methods. In the
following paper we describe implementations of these methods (the finite difference time domain and T-matrix methods
respectively) and present some salient results before concentrating on a particular application that involves the use of
entropic forces to promote aggregation between microspheres.
In suspensions containing microspheres and a sub-micron species, such as nanoparticles or a polymer, an attractive force
can result between the microspheres. This attraction arises due to an entropic interaction, often referred to as a depletion
force. In this work we demonstrate an application of the depletion force to the controlled assembly of crystalline templates
for the production of photonic band gap (PBG) materials. The method makes use of holographic optical tweezers to
assemble crystalline arrays of silica or polystyrene microspheres, in which depletion interactions are used to stabilise the
structures being built. In addition, we use the holographic optical tweezers to characterise the attraction between pairs of
microspheres in the system.