On the differences between helicity and chirality

The optical helicity and the optical chirality are two quantities that are used to describe chiral electromagnetic fields. In a monochromatic field, the two quantities are proportional to one another, and the distinction between the two is therefore largely unimportant. However, in a polychromatic field, no such proportionality holds. This paper explicitly examines both the helicity and chirality densities in various polychromatic fields: the superposition of two circularly polarised plane-waves of different frequencies, a chirped pulse of circularly polarised light, and an "optical centrifuge" consisting of two oppositely chirped circularly polarised beams of opposite handedness. Even in the simplest case there can be significant qualitative differences between the two quantities -- they may have opposite signs, or one may be zero while the other is not. The origin of these differences lies in the different frequency scaling of the two quantities, which is made relevant by the presence of multiple frequency components in the fields

Linear Rayleigh and Raman scattering to the second order: Analytical results for light scattering by any scatterer of size k0d ≤ 1/10

We extend the usual multipolar theory of linear Rayleigh and Raman scattering to include the second-order correction. The new terms promise a wealth of information about the shape of a scatterer and yet are insensitive to the scatterer's chirality. Our extended theory might prove especially useful for analysing samples in which the scatterers have non-trivial shapes but no chiral preference overall, as the zeroth-order theory offers little information about shape and the first-order correction is often quenched for such samples. A basic estimate suggests that our extended theory can be applied to a scatterer as large as k0d ~ 1/10 with less than ~ 0.1% error resulting from the neglect of the third- and higher-order corrections. Our results are entirely analytical

Aspects of chirality in light and matter

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

On the conservation of helicity in a chiral medium

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter β. A form for the helicity density is introduced, valid to first order in β, that produces a helicity of ±\hbar per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmetry condition of a chiral medium with a constant value of ε/μ. Extending the results to arbitrary order in β establishes an exact relationship between the energy and helicity densities in a chiral medium

On the conservation of helicity in a chiral medium

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter β. A form for the helicity density is introduced, valid to first order in β, that produces a helicity of ±\hbar per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmetry condition of a chiral medium with a constant value of ε/μ. Extending the results to arbitrary order in β establishes an exact relationship between the energy and helicity densities in a chiral medium

Optical helicity and chirality: conservation and sources

We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity

Continuous Symmetries and Conservation Laws in Chiral Media

Locally conserved quantities of the electromagnetic field in lossless chiral media are derived from Noether's theorem, including helicity, chirality, momentum, and angular momentum, as well as the separate spin and orbital components of this last quantity. We discuss sources and sinks of each in the presence of current densities within the material, and in some cases, as also generated by inhomogeneity of the medium. A previously obtained result connecting sources of helicity and energy within chiral materials is explored, revealing that association between the two quantities is not restricted to chiral media alone. Rather, it is analogous to the connection between the momentum, and the spin and orbital components of the total angular momentum. The analysis reveals a new quantity, appearing as the "orbital" counterpart of the helicity density in classical electromagnetism

Does Medicine without Evolution Make Sense?

Should evolutionary biology contribute to the education of medical students

Spatial control of 2D nanomaterial electronic properties using chiral light beams

Single-layer two-dimensional (2D) nanomaterials exhibit physical and chemical properties which can be dynamically modulated through out-of-plane deformations. Existing methods rely on intricate micromechanical manipulations (e.g., poking, bending, rumpling), hindering their widespread technological implementation. We address this challenge by proposing an all-optical approach that decouples strain engineering from micromechanical complexities. This method leverages the forces generated by chiral light beams carrying orbital angular momentum (OAM). The inherent sense of twist of these beams enables the exertion of controlled torques on 2D monolayer materials, inducing tailored strain. This approach offers a contactless and dynamically tunable alternative to existing methods. As a proof-of-concept, we demonstrate control over the conductivity of graphene transistors using chiral light beams, showcasing the potential of this approach for manipulating properties in future electronic devices. This optical control mechanism holds promise in enabling the reconfiguration of devices through optically patterned strain. It also allows broader utilization of strain engineering in 2D nanomaterials for advanced functionalities in next-generation optoelectronic devices and sensors