Angular momentum of a strongly focussed Gaussian beam

A circularly polarized rotationally symmetric paraxial laser beams carries hbar angular momentum per photon as spin. Focussing the beam with a rotationally symmetric lens cannot change this angular momentum flux, yet the focussed beam must have spin less than hbar per photon. The remainder of the original spin is converted to orbital angular momentum, manifesting itself as a longitudinal optical vortex at the focus. This demonstrates that optical orbital angular momentum can be generated by a rotationally symmetric optical system which preserves the total angular momentum of the beam.Comment: 4 pages, 3 figure

Two controversies in classical electromagnetism

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

Measurement of the total optical angular momentum transfer in optical tweezers

We describe a way to determine the total angular momentum, both spin and orbital, transferred to a particle trapped in optical tweezers. As an example an LG02 mode of a laser beam with varying degrees of circular polarisation is used to trap and rotate an elongated particle with a well defined geometry. The method successfully estimates the total optical torque applied to the particle. For this technique, there is no need to measure the viscous drag on the particle, as it is an optical measurement. Therefore, knowledge of the particle's size and shape, as well as the fluid's viscosity, is not required.Comment: 7 pages, 3 figure

Orientation of optically trapped nonspherical birefringent particles

While the alignment and rotation of microparticles in optical traps have received increased attention recently, one of the earliest examples has been almost totally neglected the alignment of particles relative to the beam axis, as opposed to about the beam axis. However, since the alignment torques determine how particles align in a trap, they are directly relevant to practical applications. Lysozyme crystals are an ideal model system to study factors determining the orientation of nonspherical birefringent particles in a trap. Both their size and their aspect ratio can be controlled by the growth parameters, and their regular shape makes computational modeling feasible. We show that both external shape and internal birefringence anisotropy contribute to the alignment torque. Three-dimensionally trapped elongated objects either align with their long axis parallel or perpendicular to the beam axis depending on their size. The shape-dependent torque can exceed the torque due to birefringence, and can align negative uniaxial particles with their optic axis parallel to the electric field, allowing an application of optical torque about the beam axis.Comment: 5 pages, 5 figure

Measurement of Rotation Speed of Birefringent Material and Optical Torque from Polarisation of Transmitted Light

The rotation speed of, and optical torque acting on, an optically trapped birefringent particle can be determined from the polarisation of the transmitted light. This can be used to determine, for example, viscous drag torque

Computational modeling of optical tweezers

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

Modelling optical micro-machines

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 by scattering of the laser beam. The laser could be used to drive a rotor, impeller, cog wheel or some other microdevice 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 modelling of materials that are anisotropic and inhomogeneous, and structures that have complex shapes. The high degree of symmetry of a microrotor, such as discrete or continuous rotational symmetry, can be exploited to reduce computational time and memory requirements by orders of magnitude. This is achieved by performing calculations for only a given segment or plane that is repeated across the whole structure. This can be demonstrated by modelling the optical trapping and rotation of a cube.Comment: 4 pages, 3 figure

Use of shape induced birefringence for rotation in optical tweezers

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

Approximate and exact modeling of optical trapping

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. © 2010 SPIE

Not just energy, but momentum and angular momentum too: Mechanical effects in scattering

We review the transport and transfer of momentum and angular momentum by electromagnetic waves, and applications of the mechanical effects of scattering