Alexander B. Stilgoe

Optical tweezers computational toolbox

We describe a toolbox, implemented in Matlab, for the computational modelling of optical tweezers. The toolbox is designed for the calculation of optical forces and torques, and can be used for both spherical and nonspherical particles, in both Gaussian and other beams. The toolbox might also be useful for light scattering using either Lorenz–Mie theory or the T-matrix method.

Angular momentum of a strongly focused Gaussian beam

A circularly polarized paraxial Gaussian laser beam carries ± ¯ h angular momentum per photon as spin, with zero orbital angular momentum. Focusing the beam with a rotationally symmetric lens cannot change this angular momentum flux, yet the focused beam must have spin |Sz| < ¯ h per photon. The remainder of the original spin is converted to orbital angular momentum, manifesting itself as a longitudinal optical vortex at the focus. We investigate the nature of this orbital angular momentum.

The effect of Mie resonances on trapping in optical tweezers

We calculate trapping forces, trap stiffness and interference effects for spherical particles in optical tweezers using electromagnetic theory. We show the dependence of these on relative refractive index and particle size. We investigate resonance effects, especially in high refractive index particles where interference effects are expected to be strongest. We also show how these simulations can be used to assist in the optimal design of traps.

T-matrix method for modelling optical tweezers

We review the use of the T-matrix description of scattering, or the T-matrix method, for the calculation of optical forces and torques, especially for the computational modelling of optical tweezers. We consider both simple particles such as homogeneous isotropic spheres, spherical shells, spheroids, and so on, and complex particles, including anisotropic particles, inhomogenous particles, and geometrically complex particles.

Equilibrium orientations and positions of non-spherical particles in optical traps

Dynamic simulation is a powerful tool to observe the behavior of arbitrary shaped particles trapped in a focused laser beam. Here we develop a method to find equilibrium positions and orientations using dynamic simulation. This general method is applied to micro- and nano-cylinders as a demonstration of its predictive power. Orientation landscapes for particles trapped with beams of differing polarisation are presented. The torque efficiency of micro-cylinders at equilibrium in a plane is also calculated as a function of tilt angle. This systematic investigation elucidates in both the function and properties of micro- and nano-cylinders trapped in optical tweezers.

Roadmap on structured light

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

Constant power optical tweezers with controllable torque

We describe a means for controlling the spin angular-momentum flux of a laser beam at constant power, without introducing any elliptical or linear polarization. This allows a controllable torque, acting to spin the particle uniformly, to be exerted on a birefringent particle in optical tweezers. The constant power means that transverse and axial trapping, and heating due to absorption, are unaffected by changing the torque. The torque can be computer controlled and rapidly changed. In addition, the lateral trapping is kept constant. Very low torques can be obtained such that rotational Brownian motion of birefringent particles can be observed. This has the potential to greatly extend the quantitative applications of the rotation of birefringent objects in optical tweezers.

Calibration of nonspherical particles in optical tweezers using only position measurement

Nonspherical probe particles are an attractive choice for optically-trapped scanning probe microscopy. We show that it is possible to calibrate a trap with a nonspherical particle using only position measurements, without requiring measurement of orientation, using a pseudopotential based on the position occupation probability. It is not necessary to assume the force is linear with displacement.

Determination of motility forces on isolated chromosomes with laser tweezers

Quantitative determination of the motility forces of chromosomes during cell division is fundamental to understanding a process that is universal among eukaryotic organisms. Using an optical tweezers system, isolated mammalian chromosomes were held in a 1064 nm laser trap. The minimum force required to move a single chromosome was determined to be ≈0.8–5 pN. The maximum transverse trapping efficiency of the isolated chromosomes was calculated as ≈0.01–0.02. These results confirm theoretical force calculations of ≈0.1–12 pN to move a chromosome on the mitotic or meiotic spindle. The verification of these results was carried out by calibration of the optical tweezers when trapping microspheres with a diameter of 4.5–15 µm in media with 1–7 cP viscosity. The results of the chromosome and microsphere trapping experiments agree with optical models developed to simulate trapping of cylindrical and spherical specimens.

Optically trapped and driven paddle-wheel

We demonstrate the control and rotation of an optically trapped object, an optical paddle-wheel, with the rotation direction normal to the beam axis. This is in contrast to the usual situation where the rotation is about the beam axis. The paddle-wheel can be optically driven and moved to any position in the field of view of the microscope, which can be of interest for various biological applications where controlled application of a fluid flow is needed in a particular location and in a specific direction. This is of particular interest in signal transduction studies in cells, especially when a cell is flat and spread out on a surface.