In counter propagating plane waves, spherical beads occupy the interference fringes and optically bind with separations of around a wavelength. The binding strength depends on particle size and refractive index with the particle arrangement also dependent on the polarisation. Some combinations of refractive index and size do not optically bind: instead, the particles experience a force in the propagation direction that leads to a transition to longitudinal binding. These instabilities are assessed computationally with different particle numbers and polarisation states.
Freely propagating, purely optical skyrmions may be generated from combinations of vector beams with orthogonal polarisation states. Through this approach it is possible to create skyrmions of both Néel (hedgehog) and Bloch (spiral) types, using both paraxial [Gao et al. Phys. Rev. A, 102, 053513 (2020)] and focussed Laguerre-Gaussian beams [Gutiérrez-Cuevas and Pisanty, J. Opt. 23, 024004 (2021)]. In this computational study we construct skyrmionic beams with different skyrmion numbers and types with a view to analysing the spin and orbital angular momentum fluxes carried by the beams. The optical forces and torques experienced by dielectric and absorbing particles are calculated and their dynamic behaviour assessed.
In this computational study we examine the behaviour of mixed-refractive index colloidal clusters. The clusters consist of bonded collections of spherical nanospheres with different refractive indices. The behaviour of these clusters in optical traps varies depending on the numbers of particles involved and the overall symmetry of the cluster. The symmetry can be varied by changing the refractive indices. It has been shown that breaking the symmetry of a cluster by, for example, introducing a single high refractive index impurity can produce a pronounced impact on the dynamics of the cluster in an optical trap [Davie et al. Proc. SPIE 12649, 126490E (2023)]. In the present study we will explore the dynamics of mixed refractive index clusters counter propagating plane waves and in different types of optical trap. Optical forces are calculated using the discrete dipole approximation; dynamics are computed using Brownian dynamics, with hydrodynamic interactions in the low Reynolds number regime and particle separations are constrained using the SHAKE-HI algorithm.
Lateral optical forces (LOFs) exerted on metamaterials typically arise from broken mirror symmetry in the system. In previous studies, we have demonstrated that, in addition to asymmetric particle or motif pairs, a periodic array of isosceles triangle motifs with carefully chosen shape can also exert large LOFs under plane wave illumination. In this study, we further explore this phenomenon systematically with consideration of thickness of the triangle motif. Results demonstrate new insight on how LOFs relate to the shape of triangle motifs.
We consider a system of colloidal particles, with two or more different refractive indices, which stick together to form mixed clusters. The behaviour of such clusters in optical traps will vary depending on the numbers of particles involved and the distribution of their refractive indices. Our own recent studies of heterodimers of such beads suggest there is a rich vein of novel behaviour to explore, including unusual dynamics and optical binding [O'Donnell et al. Proc. SPIE 12436, 124360J (2023)]. In the present computational study we will explore the dynamics of mixed refractive index clusters in different types of optical trap, as a function of number and composition of beads as well as their arrangement. In particular, we will highlighting the difference between symmetrical and asymmetrical arrangements of beads in conventional Gaussian beams as well as in OAM beams. The optics model used is based on the discrete dipole approximation and includes low Reynolds number hydrodynamics with bead separations maintained using SHAKE-HI constraints. Further studies will investigate optical binding between arrays of such clusters in different types of structured fields.
Lateral optical forces (LOFs) exerted on metamaterials typically arise from the broken mirror symmetry in the system. It has been reported that a repeated pair of particles or circular motifs with different sizes or refractive indices can generate LOFs. Studies show that an optimised LOF could be large enough to manipulate the structure moving at a macroscopic scale. We demonstrate that this force can also be generated by a repeated single triangle motif. By adjusting the size and shape of the triangle, we can control the magnitude and direction of the LOF. The optimised structure parameters can be found by optimisation routines such as Bayesian optimisation combined with optical force calculation methods such as rigorous coupled-wave analysis.
Optical binding occurs when light scattered from a microscopic particle induces forces on other microscopic particles, which includes attractive, binding, forces. Since the original demonstration using dielectric spheres, there has been much interest in altering the shape and symmetry of the bound particles, leading to complex optically driven behaviour typically involving uniform illumination in a restricted region e.g. an extended or line focus or the axis of a Bessel beam. However, in the present computational study we consider confinement in complex optical landscapes comprising one or many focussed beams. In this survey we will explore the behaviours of systems of spherical beads with various refractive indices, as well as systems of dimers, or dumbbells, consisting of pairs of linked spheres and active janus particles comprising pairs of beads with different refractive indices. The relative importance of optical trapping versus optical trapping between the particles will be assessed.
We present a computational study of the trapping, packing and dynamics of clusters of Rayleigh particles in optical vortices. We examine the effect of OAM on the cylindrical packing arrangements and dynamics of the clusters, drawing comparisons with macroscopic systems of beads in fluid vortices.
The use of a patterned surface to create an optical conveyor for spherical, and near spherical particles is explored. Using a surface constructed of a repeating micron-sized motif, we simulate the effects of moving a particle in the near-field region above the surface, as well as exploring optical force changes in the axis perpendicular to the surface resulting from changes in size of the particles, and the choice of incident wavelength.
In this paper the use of a patterned surface to create an optical conveyor for spherical, and near spherical particles is explored. Using a surface constructed of a repeating micron-sized motif, we simulate the effects of moving a particles in the near micron regime above the surface. To reduce optical calculation overheads, a fluid index matched to the substrate of the meta-surface is used, as this allows use to ignore scattering effects due to the presence of a substrate. We also explore optical force changes in the axis perpendicular to the surface that occur due to changes in size of the particles, and the choice of incident wavelength.
We present a computational study of the trapping, packing and dynamics of clusters of Rayleigh particles in Bessel beams. We examine the effect of beam order on the cylindrical packing arrangements of the clusters. In addition, we explore the influence of the orbital angular momentum of the Bessel beam, on the nature of the packing arrangements formed and draw comparisons with the confining effect of a fluid vortex.
In this paper, the use of a 2D meta-surface for the optical trapping and directed movement of spherical nanoparticles is explored. Using the Discrete Dipole Approximation, we calculate the optical forces that occur when a spherical nanoparticle moves across a surface constructed of tessellated equilateral triangles. We calculate that given sufficient optical power, choice of optical materials, and wavelengths, it is possible to use a meta-surface to guide micron sized particles in a direction dictated by the geometry of the surface. Furthermore, we suggest several experimental methods of verifying the results which are also discussed in detail.
Extremely large forces and torques have been reported when light is scattered by 2-dimensional metamaterial surfaces. Potential applications include force actuators in optically driven micro-machines, and diffractive solar sails. Here we consider refractive-index patterning of a dielectric substrate achieved photo-lithographically and demonstrate, using a computational electromagnetic approach, how a periodic structure may be optimised to maximise the optical forces and torques generated. We will show that enhancements of two orders of magnitude in the optical force are available in specific cases.
We explore a computational, finite element approach to the study of flexible particles in optical tweezers, illustrating the method with optical deformation of membranes and nanowires and an optically driven microscopic swimmer.
Optical binding was first observed between spherical particles around thirty years ago. Optical binding forces can result in various geometric arrangements of colloidal matter into regular, crystalline arrays and can induce complex, non-conservative and quasi-periodic motions. Although most studies of optical binding have focussed on dielectric spheres, recent departures from this trend have included silver bipyramids, nanowires and chiral particles. With reduction of particle symmetry comes extra complexity: torques can be applied to non-spherical objects by the applied beam, as well as by the scattered field from neighbouring particles. Another way to lower the symmetry of the system is if optical binding itself results in the formation of a lower symmetry cluster. The resulting cluster may then interact with the angular momentum of the beam, generating non-conservative, quasi-cyclic motion. When large numbers of particles are present in the optical trap, the precise natures of the motions become hard to predict. In this paper, we present the results of computer simulations used to explore the dynamical behavior of optically bound clusters of spherical nanoparticles, in beams possessing both spin and orbital angular momentum. While some of the behaviour observed has previously been predicted for low-symmetry shaped and chiral nanoparticles, the use of spheres enables a deeper understanding of the processes underlying the dynamics obtained. The diverse complex motion possible will be explored for a variety of homogeneous and heterogeneous optical fields, with sufficiently large numbers of particles to explore the possibilities of optically driven swarms.
The non-conservative nature of optical forces has been explored many times previously. Non-conservative optical forces occur in many guises and include lateral forces due to shape asymmetry, polarisation dependant optical torques and spin-dependant effects. When considering the design of optical force actuators, one recent approach has been to exploit the periodic structure of 2-dimensional metamaterial surfaces. In some cases, extremely large optical forces have been reported (Zhang et al, Optics Letters, 39, 4883 (2014)). Most recently macroscopic forces and torques have been demonstrated (Magallanes and Brasselet, Nature Photonics, 12, 461 (2018)). Here we consider refractive-index patterning of a substrate, achieved through a photo-lithographic approach. In this paper we will explore the use of different types of patterning, and show how the use of a periodic structure can enhance the optical forces and torques that may be generated. Using computational electromagnetic techniques we will demonstrate how enhancements of two orders of magnitude in the optical force are available in specific cases. We will examine the influence of such surface structuring on the resultant forces and torques, with a view to optimising such 2-dimensional materials for applications as light-driven actuators. Further, we will demonstrate the sensitivity of the forces generated to variations in the local environment, opening up possibilities for optical sensing applications.
The non-conservative nature of optical forces has been explored previously, with the initial focus on spherical particles, and latterly on particles with less than spherical symmetry. Non-conservative optical forces occur in many different guises, and include lateral forces arising from shape asymmetry, polarisation dependant optical torques and spin-dependant lateral forces. Photo-induced curing of liquid crystalline polymers is a technique that may be used to generate refractive-index patterning of surfaces. Here, we use computational methods to examine the influence of such surface structuring on optically-generated forces and torques, with a view to optimising such materials for applications as light-driven sensors and actuators.
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.
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.
Hydrodynamic coupling is thought to play a role in the coordinated beating of cilia and flagella, and may inform the future design of artificial swimmers and pumps. In this study, optical tweezers are used to investigate the hydrodynamic coupling between a pair of driven oscillators. The theoretical model of Lenz and Ryskin [P. Lenz and A. Ryskin, Phys. Biol. 3, 285{294 (2006)] is experimentally recreated, in which each oscillator consists of a sphere driven in a circular trajectory. The optical trap position is maintained ahead of the sphere to provide a tangential driving force. The trap is also moved radially to harmonically constrain the sphere to the circular trajectory. Analytically, it has been shown that two oscillators of this type are able to synchronise or phase-lock under certain conditions. We explore the interplay between synchronisation mechanisms and find good agreement between experiment, theory and Brownian dynamics simulations.
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.
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
prolate spheroids.
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 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 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.
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.
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.
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