Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications.

This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.

Optical chirality of vortex beams at the nanoscale.

In this work we undertake a systematic study of the optical chirality density of Laguerre-Gaussian and Bessel laser beams tightly focused into nanoscale volumes. In particular we highlight the unique contributions to optical chirality from longitudinal electromagnetic fields, i.e. light that is polarised in the direction of propagation. The influence that polarisation, spin and orbital angular momentum, radial index, degree of focusing, and diffraction has on the optical chirality is studied. The results show that the optical chirality of structured light beams at the nanoscale is significantly richer than that of the well-known circularly polarised propagating plane wave. The work lays the foundation for chiral nanophotonics, and chiral quantum optics based on structured light illumination.

Influence of chirality on fluorescence and resonance energy transfer.

Electronically excited molecules frequently exhibit two distinctive decay mechanisms that rapidly generate optical emission: one is direct fluorescence and the other is energy transfer to a neighboring component. In the latter, the process leading to the ensuing "indirect" fluorescence is known as FRET, or fluorescence resonance energy transfer. For chiral molecules, both fluorescence and FRET exhibit discriminatory behavior with respect to optical and material handedness. While chiral effects such as circular dichroism are well known, as too is chiral discrimination for FRET in isolation, this article presents a study on a stepwise mechanism that involves both. Chirally sensitive processes follow excitation through the absorption of circularly polarized light and are manifest in either direct or indirect fluorescence. Following recent studies setting down the symmetry principles, this analysis provides a rigorous, quantum outlook that complements and expands on these works. Circumventing expressions that contain complicated tensorial components, our results are amenable for determining representative numerical values for the relative importance of the various coupling processes. We discover that circular dichroism exerts a major influence on both fluorescence and FRET, and resolving the engagement of chirality in each component reveals the distinct roles of absorption and emission by, and between, donor and acceptor pairs. It emerges that chiral discrimination in the FRET stage is not, as might have been expected, the main arbiter in the stepwise mechanism. In the concluding discussion on various concepts, attention is focused on the validity of helicity transfer in FRET.

Raman Optical Activity Using Twisted Photons.

Raman optical activity underpins a powerful vibrational spectroscopic technique for obtaining detailed structural information about chiral molecular species. The effect centers on the discriminatory interplay between the handedness of material chirality with that of circularly polarized light. Twisted light possessing an optical orbital angular momentum carries helical phase fronts that screw either clockwise or anticlockwise and, thus, possess a handedness that is completely distinct from the polarization. Here a novel form of Raman optical activity that is sensitive to the handedness of the incident twisted photons through a spin-orbit interaction of light is identified, representing a new chiroptical spectroscopic technique.

Quantum features in the orthogonality of optical modes for structured and plane-wave light.

A fundamental photon creation-annihilation commutation relation underpins the familiar quantum formulation of optics. However, an internal inconsistency becomes apparent in the pursuit of structured light applications. This requires the relationship between operator commutation and mode orthogonality to be recast in a form ensuring full consistency with the precepts of quantum theory. A suitable reformulation, shown to register correctly an intrinsic quantum uncertainty in the associated interactions, has special relevance to optical vortex physics-particularly with regard to information content-through its connection to the degrees of freedom in the associated radiation modes.

Optical orbital angular momentum: twisted light and chirality.

The question of how the orbital angular momentum of structured light might engage with chiral matter is a topic of resurgent interest. By taking account of electric quadrupole transition moments, it is shown that the handedness of the beam can indeed be exhibited in local chiral effects, being dependent on the sign of the topological charge. In the specific case of absorption, a significant interplay of wavefront structure and polarization is resolved, and clear differences in behavior are identified for systems possessing a degree of orientational order and for those that are randomly oriented.

Nonlocalized Generation of Correlated Photon Pairs in Degenerate Down-Conversion.

The achievement of optimum conversion efficiency in conventional spontaneous parametric down-conversion requires consideration of quantum processes that entail multisite electrodynamic coupling, actively taking place within the conversion material. The physical mechanism, which operates through virtual photon propagation, provides for photon pairs to be emitted from spatially separated sites of photon interaction; occasionally pairs are produced in which each photon emerges from a different point in space. The extent of such nonlocalized generation is influenced by individual variations in both distance and phase correlation. Mathematical analysis of the global contributions from this mechanism provides a quantitative measure for a degree of positional uncertainty in the origin of down-converted emission.