A study of zeros in optical fields and the origins of spin in wave fields

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When lots of plane waves interfere, it is possible for point-like nodes to exist in the interference pattern. By point-like nodes we mean zeros in the electric field, confined in all three dimensions, so that the intensity of the field rises in all outward directions. Just like in the centre of a doughnut beam, the canonical momentum (provided by the electric field) vanishes in a 3D electric field zero, creating a vortex-like circulation of momentum. A traditional vortex in a doughnut beam is two dimensional and can be characterised by the winding of the phase of the transverse field components. 3D zeros are largely unstudied - it is not known how polarisation singularities (C/L-lines which are continuous and should pass through the zero in some way) are arranged by the 3D zero, and there is no formal way to characterise the different types of 3D zero that exist - we are trying to provide answers to these statements. In far-field radiation, zeros can impart non-diffractive properties into the nearby field.Light carries intrinsic spin angular momentum (SAM) when the electric or magnetic field vector rotates over time. Using Maxwell's equations, this vector equation can be decomposed into a sum of two distinct terms, akin to the well-known Poynting vector decomposition into orbital and spin currents. We present the first general study of this spin decomposition, showing that the two terms, which we call canonical and Poynting spin, are chiral analogies to the canonical and spin momenta of light in its interaction with matter. Both canonical and Poynting spin incorporate spatial variation of the electric and magnetic fields and are influenced by optical orbital angular momentum (OAM). The decomposition allows us to show that the OAM of a linearly polarised vortex beam can impart a first-order preferential force to chiral matter in the absence of spin.