title: Aspects of chirality in light and matter
Creators: name: Mackinnon, Neel
Publisher: name: University of Glasgow
Year: 2021
Subjects: subject: Chirality, electromagnetism, light-matter interactions.

description: This thesis presents a series of complementary pieces of work, each related to chirality and handedness in light-matter interactions. There is a particular focus on the electromagnetic helicity – especially when viewed as a pseudoscalar density constructed from the electromagnetic vector potentials which obeys a local continuity equation. A central theme is the ways in which matter (both chiral and achiral) can act as “sources” of helicity, and the circumstances under which helicity is locally conserved. This feature is connected by Noether’s theorem to the duality symmetry of the free-space Maxwell equations – the invariance of the equations under an interchange between electric and magnetic fields. We begin by discussing free fields, and as the thesis progresses introduce various treatments of matter involving both microscopic and macroscopic electrodynamics. The five chapters focusing on original work (3, 5, 6, 7 and 9) are preceded by chapters introducing the necessary background material and concepts. The first piece of work is an examination of the difference between electromagnetic helicity and electromagnetic chirality in polychromatic fields. The two quantities are proportional to one another in monochromatic fields, but not in general. We explicitly calculate the two quantities for some simple field configurations, and the origin and nature of the differences is discussed. This is followed by a discussion of helicity and angular momentum radiated from elementary multipole sources. We examine radiation from the simplest chiral source that can be constructed from point multipoles, consisting of co-located oscillating electric and magnetic dipoles. This is contrasted with the radiation from a rotating dipole, which is an achiral source of circularly polarised light. The former is a net source of helicity, but not of angular momentum, and the latter a net source of angular momentum, but not helicity. We then move on to macroscopic electrodynamics, and consider the generation of helicity at a dielectric interface. We provide and discuss expressions for the helicity fluxes when light is incident on chiral dielectric interfaces, obtained from the Fresnel coefficients for chiral media. Following this, we propose an extension to the definition of the helicity density within chiral media. The standard definition of helicity within a dielectric is found to be unsatisfactory when the medium is chiral – it produces an incorrect helicity-per-photon for left- and right-handed circularly polarised light in the medium, and also is not locally conserved even when the medium is macroscopically dual-symmetric. We present a modification to the definition of the density which yields the correct helicity per circularly polarised photon within the medium, and find by inspection that the new density is indeed locally conserved in a dual-symmetric chiral medium. Our definition is then formally justified by using Noether’s theorem in order to derive the locally conserved quantity associated with macroscopic duality symmetry in chiral media. Finally, we conclude with an extension of a standard semiclassical treatment of molecular light scattering to include higher-order multipole terms. These represent a higher-order correction to the standard results, which should become appreciable when the ratio of scatterer size to the wavelength of the incident light is around 1/10. Expressions for the scattered light from an arbitrary scatterer are presented in terms of its polarisability tensors, with appropriate orientational averaging to describe scattering from an isotropic fluid sample. The transformation of the results under a change in multipolar origin is also examined, and they are found to behave acceptably.