Visualisation of Cherenkov Radiation and the Fields of a Moving Charge

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and Cherenkov radiation is a visible consequence of a charged particle travelling through a medium at locally superluminal velocities. The Heaviside--Feynman equations for calculating the magnetic and electric fields of a moving charge have been known for many decades, but it is only recently that the computing power to plot the fields of such a particle has become readily available for student use. This article investigates and illustrates the calculation of Maxwell's D field in homogeneous isotropic media for arbitrary, including superluminal, constant velocity, and uses the results as a basis for discussing energy transfer in the electromagnetic field.Comment: 18 pages, 8 figures, 2 MATLAB listings. Version 2: Corrected display for letter paper format. Added publication info. Version 3: Corrected typos in Eqs. 5, 8, 1

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

Non-steady-state extremely asymmetrical scattering of waves in periodic gratings

Extremely asymmetrical scattering (EAS) is a highly resonant type of Bragg scattering with a strong resonant increase of the scattered wave amplitude inside and outside the grating. EAS is realized when the scattered wave propagates parallel to the grating boundaries. We present a rigorous algorithm for the analysis of non-steady-state EAS, and investigate the relaxation of the incident and scattered wave amplitudes to their steady-state values. Non-steady-state EAS of bulk TE electromagnetic waves is analyzed in narrow and wide, slanted, holographic gratings. Typical relaxation times are determined and compared with previous rough estimations. Physical explanation of the predicted effects is presented.Comment: 7 pages, 3 figures. This paper is freely available online at http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-6-268 which includes multimedia files not included in this preprint versio

Improved Social Interaction by Children With Autism by Training of Peers

Peer-mediated intervention is seen as promising to facilitate development of both social and cognitive skills in children with autism. However, peers have great difficulty in social interaction with children with autism, presumably diminishing the effect of the intervention. This difficulty does not lie with the children with autism alone - the inability of peers to understand social cues and behaviour of children with autism contributes. Therefore, we designed a peer training program to better enable the peers to interact. Typically developing children acted as peer play partners for children with autism. Following initial play sessions to measure the pre-training levels of cognitive play and social interaction, half of the peers underwent the peer training program, and the effect of the training on cognitive play and social interaction were measured, with the untrained peers as controls. No improvement in social interaction was shown by the untrained peers - experience alone was not enough. Trained peers showed large, and statistically significant, improvements. Clearly, such a peer training program could be of great benefit in inclusive education as well as in peer-mediated intervention. Apart from the observation that the program was effective and necessary, motivation of peers is an important, but difficult, issue. Finally, we note that the level of cognitive play shown by children with autism, which is often used as a measure of success of an intervention, appears to be an extremely unreliable metric of performance

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

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