Stephen H. Simpson

The transition from liquid to solid-like behaviour in ultrahigh viscosity aerosol particles

For the first time, a measurement of the viscosity of microparticles composed of Newtonian fluids has been made over a range of 12 orders of magnitude (10−3 to 109 Pa s), extending from dilute aqueous solutions to the solid-like behaviour expected on approaching a glass transition. Using holographic optical tweezers to induce coalescence between two aerosol particles (volume <500 femtolitres), we observe the composite particle relax to a sphere over a timescale from 10−7 to 105 s, dependent on viscosity. The damped oscillations in shape illustrate the interplay of surface capillary forces and bulk fluid flow as the relaxation progresses. Viscosity values estimated from the extrapolation of measurements from macroscopic binary aqueous solutions of sucrose are shown to diverge from the microparticle measurements by as much as five orders of magnitude in the limit of ultrahigh solute supersaturation and viscosity. This is shown to be a consequence of the sensitivity of the viscosity to the composition of the particles, specifically the water content, and the often incorrect compositional dependence on water activity that are assumed to characterise aerosols and amorphous phases under dry conditions. For ternary mixtures of sodium chloride, sucrose and water, the measured viscosities similarly diverge from model predictions by up to three orders of magnitude. The Stokes–Einstein treatment for relating the diffusivity of water in sucrose droplets to the particle viscosity is found to depart from the measured viscosities by more than one order of magnitude when the viscosity exceeds 10 Pa s and up to six orders of magnitude at the highest viscosities accessed. Coalescence is shown to proceed with unit efficiency even up to the highest accessible viscosity. These measurements provide the first comprehensive account of the change in a material property accompanying a transition from a dilute solution to an amorphous semi-solid state using aerosol particles to probe the change in rheological properties.

Optical trapping of spheroidal particles in Gaussian beams

The T matrix method is used to compute equilibrium positions and orientations for spheroidal particles trapped in Gaussian light beams. It is observed that there is a qualitative difference between the behavior of prolate and oblate ellipsoids in linearly polarized Gaussian beams; the former generally orient with the symmetry axis parallel to the beam except at very small particle sizes, while the latter orient with the symmetry axis perpendicular to the beam. In the presence of a circularly polarized beam, it is demonstrated that oblate ellipsoids will experience a torque about the beam axis. However, for a limited range of particle sizes, where the particle dimensions are comparable with the beam waist, the particles are predicted to rotate in a sense counter to the sense of rotation of the circular polarization. This unusual prediction is discussed in some detail.

Application of the discrete dipole approximation to optical trapping calculations of inhomogeneous and anisotropic particles.

The accuracy of the discrete dipole approximation (DDA) for computing forces and torques in optical trapping experiments is discussed in the context of dielectric spheres and a range of low symmetry particles, including particles with geometric anisotropy (spheroids), optical anisotropy (birefringent spheres) and structural inhomogeneity (core-shell spheres). DDA calculations are compared with the results of exact T-matrix theory. In each case excellent agreement is found between the two methods for predictions of optical forces, torques, trap stiffnesses and trapping positions. Since the DDA lends itself to calculations on particles of arbitrary shape, the study is augmented by considering more general systems which have received recent experimental interest. In particular, optical forces and torques on low symmetry letter-shaped colloidal particles, birefringent quartz cylinders and biphasic Janus particles are computed and the trapping behaviour of the particles is discussed. Very good agreement is found with the available experimental data. The efficiency of the DDA algorithm and methods of accelerating the calculations are also discussed.

FDTD simulations of forces on particles during holographic assembly

We present finite-difference time-domain (FDTD) calculations of the forces and torques on dielectric particles of various shapes, held in one or many Gaussian optical traps, as part of a study of the physical limitations involved in the construction of micro- and nanostructures using a dynamic holographic assembler (DHA). We employ a full 3-dimensional FDTD implementation, which includes a complete treatment of optical anisotropy. The Gaussian beams are sourced using a multipole expansion of a fifth order Davis beam. Force and torques are calculated for pairs of silica spheres in adjacent traps, for silica cylinders trapped by multiple beams and for oblate silica spheroids and calcite spheres in both linearly and circularly polarized beams. Comparisons are drawn between the magnitudes of the optical forces and the Van der Waals forces acting on the systems. The paper also considers the limitations of the FDTD approach when applied to optical trapping.

Optical angular momentum transfer by Laguerre-Gaussian beams

It is well known that Laguerre-Gaussian beams carry angular momentum and that this angular momentum has a mechanical effect when such beams are incident on particles whose refractive indices differ from those of the background medium. Under conditions of tight focusing, intensity gradients arise that are sufficiently large to trap micrometer-sized particles, permitting these mechanical effects to be observed directly. In particular, when the particles are spherical and absorbing, they rotate steadily at a rate that is directly proportional to the theoretical angular momentum flux of the incident beam. We note that this behavior is peculiar to absorbing spheres. For arbitrary, axially placed particles the induced torque for rotation angle zeta is shown to be Gammaz=Asin(2zeta+delta)+B, where A, B, and delta are constants that are determined by the mechanisms coupling optical and mechanical angular momentum. The resulting behavior need not be directly related to the total angular momentum in the beam but can, nonetheless, be understood in terms of an appropriate torque density. This observation is illustrated by calculations of the torque induced in optically and geometrically anisotropic particles using a T-matrix approach.

Constructing 3D crystal templates for photonic band gap materials using holographic optical tweezers.

A simple and robust method is presented for the construction of 3-dimensional crystals from silica and polystyrene microspheres. The crystals are suitable for use as templates in the production of three-dimensional photonic band gap (PBG) materials. Manipulation of the microspheres was achieved using a dynamic holographic assembler (DHA) consisting of computer controlled holographic optical tweezers. Attachment of the microspheres was achieved by adjusting their colloidal interactions during assembly. The method is demonstrated by constructing a variety of 3-dimensional crystals using spheres ranging in size from 3 microm down to 800 nm. A major advantage of the technique is that it may be used to build structures that cannot be made using self-assembly. This is illustrated through the construction of crystals in which line defects have been deliberately included, and by building simple cubic structures.

Optimizing the optical trapping stiffness of holographically trapped microrods using high-speed video tracking

Dielectric microrods can be trapped horizontally in pairs of holographically controlled optical traps. External forces acting on these microrods are registered via the rotational and translational displacement of the microrod relative to the traps. In the following paper we demonstrate accurate, real-time tracking of this displacement in two dimensions. The precision of the method is estimated and the translational and rotational stiffness coefficients of the trapped microrod are evaluated by analysing the thermal motion and the Stokes drag. The variation of these stiffness coefficients relative to the displacement of the traps from the ends of the microrods is measured, and optimal trapping conditions are located.

Numerical calculation of interparticle forces arising in association with holographic assembly

Recent advances in dynamic holography have resulted in spatial light modulators capable of producing an almost limitless variety of field distributions from a single incident beam. Holographic assembly is a technique that exploits this capability to generate and control multiple foci that can be used to trap and manipulate nanoparticles. Although the forces associated with conventional optical tweezers are well understood, the effects arising from the more complicated interactions associated with holographic assembly are not. We present a general and flexible method, based on T matrix theory, for investigating these effects and use it to calculate the forces between particles in a variety of optical environments.

Rotation of absorbing spheres in Laguerre-Gaussian beams

It is well known that optical vortex beams carry orbital as well as spin angular momentum. This optical angular momentum can manifest itself mechanically, for example in tightly focused Laguerre-Gaussian beams, where trapped, weakly absorbing spheres rotate at a rate proportional to the total angular momentum carried by the beam. In the present paper we subject this system to a rigorous analysis involving expansions in vector spherical wave functions that culminates in a simple expression for the torque on the sphere. It is seen that, for large weakly absorbing spheres, the induced torque per unit power is independent of the detailed structure of the incident field, being a simple function of two indices that describe the helicity and polarization state of the beam, the relative refractive indices of the sphere and ambient medium, the absorption index of the sphere, and its radius. A number of relationships between the coefficients of these expansions are also developed.

Optical lift from dielectric semicylinders

A wave optics numerical analysis of the force and torque on a semicylindrical optical wing is presented. Comparisons with a recently reported ray optics analysis indicate good agreement when the radius is large compared with the wavelength of light, as expected. Surprisingly, we find that the dominant rotationally stable angle of attack at α≈-15° is relatively invariant to changes in radius and refractive index. However, the torsional stiffness at the equilibrium point is found to increase, approximately, as the cubic power of the radius. Quasi-resonant internal modes of light produce complex size-dependent variations of the angle and magnitude of the optical lift force.