Challenges concerning the discriminatory optical force for chiral molecules

In response to arXiv:1506.07423v1 we discuss the authors work, and our own, on proposed schemes aiming to achieve a discriminatory optical force for chiral molecules

A QED framework for nonlinear and singular optics

The theory of quantum electrodynamics is employed in the description of linear and nonlinear optical effects. We study the effects of using a two energy level approximation in simplifying expressions obtained from perturbation theory, equivalent to truncating the completeness relation. However, applying a two-level model with a lack of regard for its domain of validity may deliver misleading results. A new theorem on the expectation values of analytical operator functions imposes additional constraints on any atom or molecule modelled as a two-level system. We introduce measures designed to indicate occasions when the two-level approximation may be valid. Analysis of the optical angular momentum operator delivers a division into spin and orbital parts satisfying electric-magnetic democracy, and determine a new compartmentalisation of the optical angular momentum. An analysis is performed on the recently rediscovered optical chirality, and its corresponding flux, delivering results proportional to the helicity and spin angular momentum in monochromatic beams. A new polarisation basis is introduced to determine the maximum values that an infinite family of optical helicity- and spin- type measures may take, and disproves recent claims of ‘superchiral light’. A theoretical description of recent experiments relate helicity- and spin- type measures to the circular differential response of molecules, and show that nodal enhancements to circular dichroism relate only to photon number-phase uncertainty relation and do not signify ‘superchiral’ regions. The six-wave mixing of optical vortex input, in nonlinear media, demonstrates the quantum entanglement of pairs of optical vortex modes. The probability for each possible output pair displays a combinatorial weighting, associated with Pascal’s triangle. A quantum electrodynamic analysis of the effect of a second body on absorption can be extended by integrating over all possible positions of the mediator molecules, modelling a continuous medium. This provides links with both the molecular and bulk properties of materials

Optical vortex mode generation by nanoarrays with a tailored geometry

Light generated with orbital angular momentum, commonly known as an optical vortex, is widely achieved by modifying the phase structure of a conventional laser beam through the utilization of a suitable optical element. In recent research, a process has been introduced that can produce electromagnetic radiation with a helical wave-front directly from a source. The chirally driven optical emission originates from a hierarchy of tailored nanoscale chromophore arrays arranged with a specific propeller-like geometry and symmetry. In particular, a nanoarray composed of n particles requires each component to be held in a configuration with a rotation and associated phase shift of 2 π/n radians with respect to its neighbor. Following initial electronic excitation, each such array is capable of supporting delocalized doubly degenerate excitons, whose azimuthal phase progression is responsible for the helical wave-front. Under identified conditions, the relaxation of the electronically-excited nanoarray produces structured light in a spontaneous manner. Nanoarrays of escalating order, i.e. those containing an increasing number of components, enable access to a set of topological charges of higher order. Practical considerations for the development of this technique are discussed, and potential new applications are identified. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE)

Expanded horizons for generating and exploring optical angular momentum in vortex structures

Spin provides for a well-known extension to the information capacity of nanometer-scale electronic devices. Spin transfer can be effected with high fidelity between quantum dots, this type of emission being primarily associated with emission dipoles. However, in seeking to extend the more common spectroscopic connection of dipole transitions with orbital angular momentum, it has been shown impossible to securely transmit information on any other multipolar basis – partly because point detectors are confined to polarization measurement. Standard polarization methods in optics provide for only two independent degrees of freedom, such as the circular states of opposing handedness associated with photon spin. Complex light beams with structured wave-fronts or vector polarization do, however, offer a basis for additional degrees of freedom, enabling individual photons to convey far more information content. A familiar example is afforded by Laguerre-Gaussian modes, whose helically twisted wave-front and vortex fields are associated with orbital angular momentum. Each individual photon in such a beam has been shown to carry the entire spatial helical-mode information, supporting an experimental basis for sorting beams of different angular momentum content. One very recent development is a scheme for such optical vortices to be directly generated through electronic relaxation processes in structured molecular chromophore arrays. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE)

Chiral nanoemitter array: A launchpad for optical vortices

A chiral arrangement of molecular nanoemitters is shown to support delocalised exciton states whose spontaneous decay can generate optical vortex radiation. In contrast to techniques in which phase modification is imposed upon conventional optical beams, this exciton method enables radiation with a helical wave-front to be produced directly. To achieve this end, a number of important polarisation and symmetry-based criteria need to be satisfied. It emerges that the phase structure of the optical field produced by degenerate excitons in a propeller-shaped array can exhibit precisely the sought character of an optical vortex – one with unit topological charge. Practical considerations for the further development of this technique are discussed, and potential new applications are identified

Tacit collusion, firm asymmetries and numbers:evidence from EC merger cases

This paper estimates the implicit model, especially the roles of size asymmetries and firm numbers, used by the European Commission to identify mergers with coordinated effects. This subset of cases offers an opportunity to shed empirical light on the conditions where a Competition Authority believes tacit collusion is most likely to arise. We find that, for the Commission, tacit collusion is a rare phenomenon, largely confined to markets of two, more or less symmetric, players. This is consistent with recent experimental literature, but contrasts with the facts on ‘hard-core’ collusion in which firm numbers and asymmetries are often much larger