arXiv subjects

Alex J. Vernon

Publications and source records attributed to Alex J. Vernon.

13 recordsLinked to original sources

arXiv2026

Time diffraction of optical helicity

If in a classic double-slit interference experiment the light that passes though one slit is in an orthogonal polarisation state to that of the second slit, no visible interference fringes emerge. Interference fringes are instead present in a different observable that relates to the difference in energy carried by two orthogonal polarisation components, causing spatially varying polarisation patterns: the optical helicity density in the case of linearly polarised fields. Here, we develop a generalised treatment of interference in space and time, and experimentally demonstrate the helicity patterns produced by interference of orthogonally polarised pulses, which would be produced by two temporal slits in time diffraction observations. The developed approach may be important for understanding and applications of complex polarisation patterns and polarisation effects in time varying media.

physics.optics↗

arXiv2026

Vortex formation around islands in random waves

Wave vortices are fundamental topological features of interference fields, occurring at nodal points where the wave amplitude vanishes. A distinct class of vortices can instead form around it islands or `holes' in two-dimensional wavefields, where the wave intensity remains finite and may even peak at the boundary. In particular, such vortices occur in M2 ocean tides around New Zealand, Madagascar, Iceland, and Svalbard, yet the conditions governing their appearance have remained elusive. Here we develop a statistical theory of vortices around islands in random two-dimensional wavefields, with and without the Coriolis effect, and test it experimentally. We determine the probabilities of vortices with different topological charges as functions of island size and Coriolis parameter. We find that island-bound vortices emerge with unexpectedly high probability, approaching 50% in non-rotating systems and nearly 100% in rotating systems. Moreover, for a broad range of parameters, the presence of a subwavelength island dramatically enhances vortex formation compared with homogeneous random wavefields. Our results explain the formation of tidal vortices around ocean islands of particular sizes (~0.1 of the characteristic wavelength) and establish a general mechanism for generating localized high-intensity vortices around defects in diverse wave systems, from water waves to nanophotonic structures.

physics.flu-dyn↗

arXiv2026

Acoustic Chirality

We reveal a previously unknown continuous symmetry and conservation law in the equations of linear isotropic elasticity, which describe the chirality of elastic waves. We show that the integral chirality is determined by the population imbalance between right- and left-handed transverse phonons, whereas the local chirality density generally involves both transverse and longitudinal wave components. We also introduce the related concepts of acoustic helicity and ``false chirality''. The theory is illustrated with simple interference fields exhibiting distinct distributions of chirality, spin angular momentum, and false chirality. Our results establish chirality as a fundamental property of elastic waves and provide a general theoretical framework for chiral acoustic phenomena.

physics.class-ph↗

arXiv2026

Dipole light-matter interactions in the bispinor formalism

The conventional formulation of power absorption, optical forces, and torques on dipolar particles involve lenghty and cumbersome expressions that obscure their shared physical origin. We apply a bispinor formalism that unifies these disparate phenomena in a very general case including chiral and nonreciprocal particles. This reveals that force, torque, absorbed power, and absorbed helicity rate can all be concisely expressed in terms of broken symmetries, and leads to the fundamental inequalities that dipolar particles' cross-sections must satisfy. This framework uncovers profound connections normally hidden behind complex algebra -- for instance, pressure forces depend exclusively on the difference in linear momenta of different light components and the corresponding breaking of symmetry by a particle, and optical recoil forces depend exclusively on helicity cross sections -- providing clarity, conciseness, and a powerful predictive tool for arbitrary dipole interactions.

physics.optics↗

arXiv2026

Polarisation Singularities of Gravitational Waves

Departure from idealised plane waves gives rise to intricate geometric structures in wave fields. One such structure is the polarisation singularity, which emerges when multiple monochromatic waves interfere (such as would be the case for stochastic backgrounds), producing loci of purely circular or linear polarisation. In this work, we extend the theory of polarisation singularities to gravitational waves and higher spin fields. Building on the electromagnetic description, we formulate the gravitational analogue of polarisation singularities and show that they are generic features of gravitational waves. Their dimension, however, depends on the spin of the field. We illustrate these results with simulations of plane-wave interference and analyse the resulting singularity densities.

gr-qc↗

arXiv2025

Electric-Magnetic Geometric Phase

Geometric phases play an enormous role in optics and are generally associated with the evolution of light's polarization state on the Poincaré sphere, or its spin on the sphere of spin directions. Here we put forward a new kind of optical geometric phase that appears exclusively in nonparaxial light, resulting from cyclic changes to the relative amplitude and phase between the electric and magnetic fields. This phase is naturally represented on a recently introduced `electric-magnetic' sphere.

physics.optics↗

arXiv2025

Topologies of light in electric-magnetic space

In nonparaxial, monochromatic light the electric and magnetic fields generally have different energy densities, different singularities and different polarisation structures. A topological picture of the electric field or magnetic field in isolation cannot capture the elusive topology of nonparaxial light that exists in the spatially dependent relationship between the two fields: the degree to which light breaks fundamental symmetries (parity, duality, time-reversal). With this work a new ellipse is introduced that resides not in real space, but in electric-magnetic (EM) space, and whose geometry depends on these broken symmetries. The EM ellipse has circular and linear polarisation singularities and may be organised into particle-like textures. These thus-far hidden topologies are present even in rudimentary structured waves, for a second-order EM-space meron is shown to be present in a focussed linearly polarised vortex beam.

physics.optics↗

arXiv2025

Non-linear bistability in pulsed optical traps

Optical trapping, also known as optical tweezing or optical levitation, is a technique that uses highly focused laser beams to manipulate micro- and nanoscopic particles. In optical traps driven by high-energy pulses, material non-linearity can result in unusual opto-mechanical effects, such as displaced equilibrium points. However, existing theoretical models of non-linear optical force on small particles consider smooth material dependence on the incident field strength alone, and not the feedback between the particle permittivity and internal field strength, which is, in turn, a function of the permittivity. The hysteresis effects of optical bistability in pulsed optical traps therefore elude existing optical force models. Here, we investigate a bistable optical trap, set up by counter-propagating ultrashort pulses, in which the optical force exerted on a particle depends not only on the field at the particle's current location, but on the particle's historic trajectory in the trap. The developed formalism will be important for designing optical traps and nanoparticle manipulation in pulsed field for various applications, including potentially time crystal demonstrations.

physics.optics↗

arXiv2024

Electromagnetic symmetry dislocations

Singular optics aims to understand and manipulate light's topological defects, pioneered by the discovery that phase vortex lines, strands of destructive interference, naturally occur in scalar wave fields. Monochromatic electromagnetic fields, however, are described by complex three-dimensional vectors that make individual scalar phase vortices in their vector components, which depend on the choice of co-ordinate basis, less meaningful. Instead, polarisation singularities can capture the vector texture of complicated, even non-paraxial light, with separate spatial descriptions for the electric $\mathbf{E}$ and magnetic $\mathbf{H}$ fields. But polarisation textures, too, are basis-dependent, because the laws of electromagnetism can be expressed not only by separate $\mathbf{E}$ and $\mathbf{H}$ fields, but by linear combinations of the two. We instead propose fundamental, basis-independent topological features generic in monochromatic electromagnetic fields: one- and two-dimensional structures that relate to time-averaged symmetries, including parity, duality and time-reversal, held locally by the combined electric and magnetic field polarisation geometry.

physics.optics↗

arXiv2024

The electromagnetic symmetry sphere: a framework for energy, momentum, spin and other electromagnetic quantities

Electromagnetic quantities such as energy density, momentum, spin, and helicity bring meaning and intuition to electromagnetism and possess intricate interrelations, particularly prominent in complex non-paraxial near-fields. These quantities are conventionally expressed using electric and magnetic field vectors, yet the electric-magnetic basis is one among other often overlooked alternatives, including parallel-antiparallel and right-left-handed helicity bases, related to the parity and duality symmetries of electromagnetism. Projecting time-harmonic electromagnetic fields into a variety of bases allows re-interpreting established quantities and reveals underlying mathematical structures: a Bloch sphere which describes asymmetries in electromagnetic energy, a systematic path to unify and uncover relations between electromagnetic quantities, and the unlocking of symmetry-driven equations in light-matter interaction.

physics.optics↗

arXiv2024

Non-Diffracting Polarisation Features around Far-Field Zeros of Electromagnetic Radiation

Light from any physical source diffracts over space, as spherical wavefronts grow and energy density is spread out. Diffractive effects pose fundamental limits to light-based technologies, including communications, spectroscopy, and metrology. Polarisation becomes paraxial in the far field limit and, by ignoring longitudinal field components, the rich physics of non-paraxial fields which exist in near-fields or a beam's tight focus are lost. The longitudinal field cannot, however, be ignored when transverse field components vanish (in a transverse field zero) and carry a small non-paraxial region to infinity. We show that a transverse field zero is always accompanied by non-diffracting polarisation structures, whose geometries are independent of the distance to the source, including an enclosing intensity ratio tube, and parallel, non-diverging polarisation singularities. We illustrate these features in multipole radiation and in double slit interference, two examples which have time-fixed transverse field zeros. Non-diffracting structures with changing position are coupled to time-varying zeros, which are present in all far field radiation.

physics.optics↗

arXiv2023

A decomposition of light's spin angular momentum density

Light carries intrinsic spin angular momentum (SAM) when the electric or magnetic field vector rotates over time. A familiar vector equation calculates the direction of light's SAM density using the right hand rule with reference to the electric and magnetic polarisation ellipses. 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.

physics.optics↗

arXiv2023

3D Zeros in Electromagnetic Fields

We present a study of 3D electromagnetic field zeros, uncovering their remarkable characteristic features and propose a classifying framework. These are a special case of general dark spots in optical fields, which sculpt light's spatial structure into matter-moving, information-rich vortices, escape the diffraction limit for single-molecule imaging, and can trap particles for nanoscale manipulation. Conventional dark spots are two-dimensional in two aspects: localised in a plane and having a non-zero out-of-plane field component. We focus on non-paraxial fields, where three-dimensional dark spots can exist non-stably at fully localised points, making distinct imprints in the flux of energy and momentum, and in the light's polarisation texture. With this work, we hope to enhance current dark spot applications, or inspire new ones impossible with lower-dimensional zeros.

physics.optics↗