arXiv subjects

Kayn A. Forbes

Publications and source records attributed to Kayn A. Forbes.

17 recordsLinked to original sources

arXiv2026

Dual-Symmetrized Construction of Electromagnetic Beams Beyond the Paraxial Approximation with an Explicit Separation of Scalar and Vectorial Corrections

We develop a perturbative framework for constructing the fields of electromagnetic beams beyond the paraxial approximation, in which the vectorial correction is shared symmetrically between the electric and magnetic fields and separated from the isotropic scalar correction. The method is based on a direct iterative derivation from Maxwell equations and combines complementary electric-first and magnetic-first constructions, thereby removing the construction-dependent assignment of the vectorial correction to either the electric or magnetic field. In addition, the scalar envelope correction is obtained independently from the isotropic co-polar contribution to the solutions of the higher-order Helmholtz equation. The resulting corrected fields apply to an arbitrary paraxial envelope and input Jones polarization.

physics.optics↗

arXiv2026

Transversality Locks Longitudinal Gradients in Structured-Light Quadrupole Transitions

Electric quadrupole absorption is driven by optical field gradients, not by field amplitudes alone. This distinction is crucial for structured light, where a paraxially small longitudinal field can generate a leading-order longitudinal gradient. For fully vectorial Laguerre-Gaussian modes, Maxwell transversality locks this longitudinal gradient to the transverse structured gradient of the leading paraxial field. This locking is therefore a general electromagnetic constraint, not a focusing-dependent correction that can be removed independently. Decomposing the symmetric-traceless optical field-gradient tensor into spherical components reveals a strongly channel-selective response: the $\Delta m=0$ transition requires the longitudinal gradient at the retained order, the $\Delta m=\pm1$ channels receive scalar and vectorial nonparaxial corrections on top of the carrier-scale longitudinal derivative of the transverse field, and the $\Delta m=\pm2$ channels remain transverse at the same order. These results show that longitudinal optical structure can enter structured-light quadrupole transitions as an indispensable leading-gradient contribution, even when the longitudinal field amplitude itself is paraxially small.

physics.optics↗

arXiv2026

Topological Control of Chirality and Spin with Structured Light

Structured light beams with engineered topological properties offer a powerful means to control spin angular momentum (SAM) and optical chirality, key quantities shaped by spin-orbit interaction (SOI) in light. Such effects are typically regarded as emerging only through light-matter interactions. Here, we show that higher-order Poincaré modes, carrying a tunable Pancharatnam topological charge $\ell_p$, enable precise control of SOI purely from the intrinsic topology of the light field, without requiring any material interface. In doing so, we reveal a free-space paraxial optical Hall effect, where modulation of $\ell_p$ drives spatial separation of circular polarization states - a direct signature of SOI in a regime previously thought immune to such behaviour. Our analysis identifies two propagation-induced topological mechanisms underlying this effect: differential Gouy phase shifts between orthogonal components, and radial divergence of the beam envelope. These results overturn the common view that spin-orbit effects in free space require non-paraxial conditions, and establish a broadly tunable route to generating and controlling chirality and SAM without tight focusing. This approach provides new opportunities for optical manipulation, chiral sensing, and high-dimensional photonic information processing.

physics.optics↗

arXiv2025

Generalized Polarization Matrix Approach to Near-Field Optical Chirality

For paraxial light beams and electromagnetic fields, the Stokes vector and polarization matrix provide equivalent scalar measures of optical chirality, widely used in linear optics. However, growing interest in non-paraxial fields, with fully three-dimensional polarization components, necessitates an extended framework. Here, we develop a general theory for characterizing optical chirality in arbitrary electromagnetic fields, formulated through extensions of the polarization matrix approach. This framework applies to both near- and far-field optical helicity and chirality. As examples, we demonstrate its relevance to near-zone fields from chiral dipole emission and the focal plane of tightly focused beams.

physics.optics↗

arXiv2024

Generating optical angular momentum through wavefront curvature

Recent developments in the understanding of optical angular momentum have resulted in many demonstrations of unusual optical phenomena, such as optical beams with orbital angular momentum and transverse spinning light. Here we detail novel contributions to spin and orbital angular momentum generated by the gradient of wavefront curvature that becomes relevant in strongly focused beams of light. While circularly polarized beams are shown to develop helicity-dependent transverse spin, a linearly polarized Gaussian beam produces longitudinal spin and orbital angular momenta in the focal region, even if lacking both of these before focusing. Analytical treatment of a nonparaxial electromagnetic field, validated with vectorial diffraction modelling, shows that the terms related to higher orders of a paraxial parameter are responsible for the appearance of non-trivial angular momenta. The obtained dependences relate these quantities to the gradient of the wavefront curvature, showing how it can be used as a novel degree of freedom for applications in optical manipulation and light-matter interactions at subwavelength scales, enabling angular momentum transfer even from a simple Gaussian beam with linear polarization.

physics.optics↗

arXiv2024

Laguerre-Gaussian modes become elegant after an azimuthal phase modulation

Laguerre-Gaussian (LG) modes are solutions of the paraxial Helmholtz equation in cylindrical coordinates and are associated with light fields carrying orbital angular momentum (OAM). It is customary to modulate such beams using phase-only vortex profiles, for example, when increasing (laddering up) or decreasing (laddering down) the OAM content of some given LG mode. However, the resulting beams have been shown to be hypergeometric-Gaussian modes, due to the changing radial amplitudes on propagation. In this work, we show that these beams in fact have the angular spectrum of elegant Laguerre-Gaussian (eLG) modes, and therefore map back to LG-type modes. Accordingly, the fields obtain new OAM and radial quantum numbers that depend on the initial OAM and additional OAM gained during modulation.

physics.optics↗

arXiv2024

Comment on M. Babiker, J. Yuan, K. Koksal, and V. Lembessis, Optics Communications 554, 130185 (2024)

In a recent article Babiker et al. [Optics Communications $\mathbf{554}$, 130185 (2024)] claim that cylindrical vector beams (CVBs), also referred to as higher-order Poincaré (HOP) beams, possess optical chirality densities which exhibit `superchirality'. Here we show that, on the contrary, CVBs possess less optical chirality density than a corresponding circularly polarized scalar vortex beam and that the `superchiral' results are nonphysical. We also identify a number of issues concerning the derivation and general theory presented.

physics.optics↗

arXiv2024

On the orbit-induced spin density of tightly focused optical vortex beams: ellipticity and helicity

It has recently been established that a linearly-polarized optical vortex possesses spin angular momentum density in the direction of propagation (longitudinal spin) under tight-focusing. The helicity of light has long been associated with longitudinal spin angular momentum. Here we show that the longitudinal spin density of linearly-polarized vortices is anomalous because it has no associated helicity. It was also recently determined that the polarization-independent helicity of tightly-focused optical vortices is associated with their transverse spin momentum density. The key finding of this work is the fact that, in general, longitudinal spin can not necessarily be associated with helicity, and transverse spin is in general not associated with a zero helicity, and such extraordinary behaviour manifests most clearly for optical vortices under non-paraxial conditions.

physics.optics↗

arXiv2024

Spin angular momentum and optical chirality of Poincaré vector vortex beams

The optical chirality and spin angular momentum of structured scalar vortex beams has been intensively studied in recent years. The pseudoscalar topological charge $\ell$ of these beams is responsible for their unique properties. Constructed from a superposition of scalar vortex beams with topological charges $\ell_\text{A}$ and $\ell_\text{B}$, cylindrical vector vortex beams are higher-order Poincaré modes which possess a spatially inhomogeneous polarization distribution. Here we highlight the highly tailorable and exotic spatial distributions of the optical spin and chirality densities of these higher-order structured beams under both paraxial (weak focusing) and non-paraxial (tight focusing) conditions. Our analytical theory can yield the spin angular momentum and optical chirality of each point on any higher-order or hybrid-order Poincaré sphere. It is shown that the tunable Pancharatnam topological charge $\ell_{\text{P}} = (\ell_\text{A} + \ell_\text{B})/2$ and polarization index $m = (\ell_\text{B} -\ell_\text{A})/2$ of the vector vortex beam plays a decisive role in customizing their spin and chirality spatial distributions. We also provide the correct analytical equations to describe a focused, non-paraxial scalar Bessel beam.

physics.optics↗

arXiv2024

Topological-charge-dependent dichroism and birefringence of optical vortices

Material anisotropy and chirality produce polarization-dependent light-matter interactions. Absorption leads to linear and circular dichroism, whereas elastic forward scattering produces linear and circular birefringence. Here we highlight a form of dichroism and birefringence whereby ordered generic media display locally different absorption and scattering of a focused vortex beam that depends upon the sign of the topological charge $\ell$. The light-matter interactions described in this work manifest purely through dominant electric-dipole coupling mechanisms and depend on the paraxial parameter to first-order. Previous topological-charge-dependent light-matter interactions required the significantly weaker higher-order multipole moments and are proportional to the paraxial parameter to second-order. The result represents a method of probing the nano-optics of advanced materials and the topological properties of structured light.

physics.optics↗

arXiv2023

Customized optical chirality of vortex structured light through state and degree of polarization control

We show how both the ellipticity $η$ and degree of polarization $\textit{P}$ influences the extraordinary optical chirality properties of non-paraxial vortex beams. We find that, in stark contrast to paraxial optics and non-vortex modes, extremely rich and tuneable spatial distributions of optical chirality density can be produced by an optical vortex beam under tight focussing. We develop a theoretical description of how the optical chirality can be tailored for purpose by altering both the state $η$ and degree of polarization $\textit{P}$ of the input vortex mode, along with the magnitude and sign of optical orbital angular momentum via the pseudoscalar topological charge $\ell$. We expect that the results will have a significant role in both producing novel techniques and improving existing methods in chiral nano-optics and structured light photonics.

physics.optics↗

arXiv2021

Optical helicity of unpolarized light

Recently arXiv:2004.02970 showed that the extraordinary transverse spin momentum density of spatially confined optical fields is largely independent of polarization. Here it is shown that 3D structured optical vortices which possess the phase factor $exp(ilϕ)$ have a contribution to the optical helicity density which is completely independent of polarization. In stark contrast to what is known in classical optics with plane waves and paraxial light, the physical consequence is that unpolarized light can exhibit optical activity and chiral light-matter interactions.

physics.optics↗

arXiv2021

Measures of Helicity and Chirality of Optical Vortex Beams

Analytical forms of the optical helicity and optical chirality of monochromatic Laguerre-Gaussian optical vortex beams are derived up to second order in the paraxial parameter $kw_0$. We show that input linearly polarised optical vortices which possess no optical chirality, helicity or spin densities can acquire them at the focal plane for values of a beam waist $w_0 \approx λ$ via an OAM-SAM conversion which is manifest through longitudinal (with respect to the direction of propagation) fields. We place the results into context with respect to the intrinsic and extrinsic nature of SAM and OAM, respectively; the continuity equation which relates the densities of helicity and spin; and the newly coined term Kelvins chirality which describes the extrinsic, geometrical chirality of structured laser beams. Finally we compare our work (which agrees with previous studies) to the recent article Köksal, et al. Optics Communications 490, 126907 (2021) which shows conflicting results, highlighting the importance of including all relevant terms to a given order in the paraxial parameter.

physics.optics↗

arXiv2021

Optical vortex dichroism in chiral particles

Circular dichroism is the differential rate of absorption of right- and left-handed circularly polarized light by chiral particles. Optical vortices which convey orbital angular momentum (OAM) possess a chirality associated with the clockwise or anti-clockwise twisting of their wavefront. Here it is highlighted that both oriented and randomly oriented chiral particles absorb photons from twisted beams at different rates depending on whether the vortex twists to the right or the left through a dipole coupling scheme. This is in contrast to previous studies that investigated dipole couplings with vortex modes in the paraxial approximation and showed no such chiral sensitivity to the vortex handedness: only in oriented media where electric quadrupole coupling contributes to optical activity effects due to absorption does such a mechanism exist for paraxial vortices. The distinct difference in the scheme highlighted in this work is that longitudinal fields are taken account of and these allow for OAM transfer even during dipole interactions. Due to the vortex dichroism persisting in randomly oriented collections of chiral particles, the mechanism has a distinct advantage in its potential applicability in chemical and biochemical applications where the systems under study are invariably in the liquid phase. Additionally, the result is put into context in terms of the quantifiable optical chirality, highlighting that optical OAM can in fact increase the optical chirality density of an electromagnetic field.

physics.optics↗

arXiv2021

On the transfer of optical orbital angular momentum to matter

The prevailing notion is that the orbital angular momentum (OAM) of an optical vortex can only be transferred to the internal degrees of freedom (i.e. electronic motion) of materials through electric quadrupole and higher-order multipole interactions. Here it is highlighted how this is an artefact of the paraxial approximation and that optical OAM can be transferred to electronic motion via dipole transitions under the correct experimental conditions where non-paraxial, longitudinal fields must be accounted for.

physics.optics↗

arXiv2020

Relevance of Longitudinal Fields of Paraxial Optical Vortices

Longitudinal electromagnetic fields generally become comparable with the usually dominant transverse components in strongly-focussed, non-paraxial beams. For optical vortex modes it is highlighted here how their angular momentum properties produce longitudinal fields that in general must be accounted for, even within the paraxial regime. First-order longitudinal components of quantized Laguerre-Gaussian modes are derived and numerically studied with respect to the paraxial parameter, highlighting light-matter and spin-orbit interactions that stem from longitudinal fields of weakly-focussed, paraxial beams in free space. New restrictions are cast on the validity of the paraxial approximation for optical vortices interacting with atoms, molecules and other nanostructures.

physics.optics↗

arXiv2018

Spin-orbit interactions and chiroptical effects engaging orbital angular momentum of twisted light in chiral and achiral media

There is recurrent interest in the orbital angular momentum (OAM) conveyed by optical vortices, which are structured beams with a helically twisted wavefront. Particular significance is attached to the issue of how, in its interactions with matter, light conveying OAM might prove sensitive to the relative handedness and degree of twist in the associated optical wavefront. As a result of recent experimental and theoretical studies, the supposition that beams with OAM might enable discrimination between oppositely handed forms of matter has become a renewed focus of attention. Some of the tantalizing conclusions that are beginning to emerge from this research have, however, not yet established a definitive basis for a supporting mechanism. To resolve this problem requires the development of theory to support a faithful representation, and a thorough understanding, of the fundamental molecule-photon physics at play in such optical processes, even for processes as basic as absorption. The present analysis establishes mechanisms at play that entail a novel manifestation of optical spin-orbit interactions (SOI), engaging transition electric quadrupole moments. Moreover, powerful symmetry principles prove to render distinctively different criteria governing the exhibition of 2D and 3D chirality. The new results elucidate the operation of such effects, identifying their responsibility for discriminatory optical interactions of various forms in both chiral and achiral media.

physics.optics↗