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.

This paper develops, in precise quantum electrodynamic terms, photonic attributes of the ``optical chirality density,'' one of several measures long known to be conserved quantities for a vacuum electromagnetic field. The analysis lends insights into some recent interpretations of chiroptical experiments, in which this measure, and an associated chirality flux, have been treated as representing physically distinctive ``superchiral'' phenomena. In the fully quantized formalism the chirality density is promoted to operator status, whose exploration with reference to an arbitrary polarization basis reveals relationships to optical angular momentum and helicity operators. Analyzing multimode beams with complex wave-front structures, notably Laguerre-Gaussian modes, affords a deeper understanding of the interplay between optical chirality and optical angular momentum. By developing theory with due cognizance of the photonic character of light, it emerges that only the spin-angular momentum of light is engaged in such observations. Furthermore, it is shown that these prominent measures of the helicity of chiral electromagnetic radiation have a common basis in differences between the populations of optical modes associated with angular momenta of opposite sign. Using a calculation of the rate of circular dichroism as an example, with coherent states to model the electromagnetic field, it is discovered that two terms contribute to the differential effect. The primary contribution relates to the difference in left- and right-handed photon populations; the only other contribution, which displays a sinusoidal distance dependence corresponding to the claim of nodal enhancements, is connected with the quantum photon number-phase uncertainty relation. From the full analysis, it appears that the term ``superchiral'' can be considered redundant.

Optical activity is conventionally understood as a natural difference in the optical responses of chiral materials with opposite handedness. It stems from the quantised spin angular momentum ±ħ per photon, with the ± representing either left- or right-handed circular polarisations. Less well known, until recently, was the possibility that matter might also respond in a similar, discriminatory way to the handedness of twisted light, or ‘optical vortices’, whose orbital angular momentum (OAM) is quantised as ℓ ℏ per photon, where ℓ is the topological charge whose sign determines a wavefront twist to the left or right. Initial studies focusing on whether, in spectroscopic applications, chiral matter might respond differently to the vortex handedness of + ℓ and − ℓ beams, failed to identify any viable mechanism. However, in the last few years, theory and experiment have both supplied ample evidence that, under certain conditions, such forms of interaction do exist—and as a result, the field of chirality and optical OAM is beginning to flourish at a pace. This topical review presents a survey of this new field, working up from a description of those initial studies to the cutting-edge experiments now taking place. Analysing the fundamental mechanisms provides for a revision of previous precepts, broadening their scope in the light of recent advances in understanding, and highlighting a vibrant synergy between the fields of optical activity and twisted light.

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

In pursuit of a better understanding of how electronic excitation migrates within complex structures, the concept of resonance energy transfer is being extended and deployed in a wide range of applications. Utilizing knowledge of the quantum interactions that operate in natural photosynthetic systems, wide‐ranging molecular and solid‐state materials are explored in the cause of more efficient solar energy harvesting, while advances in theory are paving the way for the development and application of fundamentally new mechanisms. In this review, an introduction to the underlying processes that cause singlet‐singlet and triplet‐triplet energy transfer leads into a discussion of how a new conception of these fundamental processes has emerged over recent years. Illustrative examples relevant to laser science and photonics are described, including photosynthetic light‐harvesting, light‐activated sensors, processes of cooperative and accretive energy pooling and quantum cutting in rare earth‐doped crystals, and incoherent triplet‐triplet energy upconversion in molecular solutions.