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

A photonic quantum gate based on electrically controlled strong cavity coupling between a single nanocrystal quantum dot and an ultra-high Q silica micro-cavity

We investigate the use of nanocrystal quantum dots as a versatile quantum bus element for preparing various quantum resources for use in photonic quantum technologies. The ability to Stark tune nanocrystal quantum dots allows an important degree of control over the cavity QED interaction. Using this property along with the bi-exciton transition, we demonstrate a photonic CNOT interaction between two logical photonic qubits comprising two cavity field modes each. We find the CNOT interaction to be a robust generator of photonic Bell states, even with relatively large bi-exciton losses.These results are discussed in light of the current state-ofthe-art of both microcavity fabrication and recent advances in nanocrystal quantum dot technology. Overall, we find that such a scheme should be feasible in the near future with appropriate refinements to both nanocrystal fabrication technology and micro-cavity design. Such a gate could serve as an active element in photonic-based quantum technologies

Optimizing beams with transverse vortices

It is widely known that beams that have optical vortices along the direction of propagation can be easily created in the laboratory. However, it is less well known that it is possible to create beams that have vortices transversely through the beam waist. Despite much work on beams with parabolic trajectories the creation of beams with transverse vortices are not well understood. Recently such beams have been created in the laboratory with computer-generated holograms. Though such beams can be created relatively easily, optimization of the vortex structure requires generation of the correct kinoform for the optical system. Imprecise application of such kinoforms can generate multiple vortices at the beam focus, which may not be optimal in many experimental applications. In this paper, we discuss the properties of such beams and investigate the optimal geometry for creating beams with transverse vortices. Applications for beams with transverse vortices may exist in optical micromanipulation, quantum communications and microscopy

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

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

Energy, momentum and propagation of non-paraxial high-order Gaussian beams in the presence of an aperture

Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre–, Hermite– and Ince–Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light–matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter

Coherent control and feedback cooling in a remotely-coupled hybrid atom-optomechanical system

Cooling to the motional ground state is an important first step in the preparation of nonclassical states of mesoscopic mechanical oscillators. Light-mediated coupling to a remote atomic ensemble has been proposed as a method to reach the ground state for low frequency oscillators. The ground state can also be reached using optical measurement followed by feedback control. Here we investigate the possibility of enhanced cooling by combining these two approaches. The combination, in general, outperforms either individual technique, though atomic ensemble-based cooling and feedback cooling each individually dominate over large regions of parameter space.Comment: 28 pages, 5 figures, 2 tables. Updated to include exemplary experimental parameters and expanded discussion of noise source

Active rotational and translational microrheology beyond the linear spring regime

Active particle tracking microrheometers have the potential to perform accurate broad-band measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here which gives the complex shear modulus when the motion of a spherical particle is driven by non-linear forces. In some scenarios error can be further reduced by applying a variable transformation which linearises the equation of motion. This allows normalisation which eliminates low frequency drift in the particle's equilibrium position. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.Comment: 9 pages, 2 figure