Scalar axion field of toroidal electromagnetic pulses

Abstract: Axion electrodynamics extends Maxwell's theory by postulating a hypothetical pseudoscalar axion field sourced by a scalar product of electric and magnetic fields. In this work, we demonstrate that a superposition of toroidal electromagnetic pulses propagating in free space naturally exhibits localized regions, where $\bm{E}\cdot\bm{B}\ne0$. As a consequence of axion electrodynamics, these structured light pulses generate a space-time localized pseudoscalar field co-propagating with the pulses. This result should not be interpreted as a mechanism for generating axion particles by light, but rather as a consequence of adopting the axion electrodynamics extension to Maxwell's equations.

• The paper shows that superposing toroidal TE and TM pulses produces localized nonzero E·B regions that drive axion field excitations.
• It employs an analytic axion electrodynamics framework to reveal explicit, stable solutions for propagating pseudoscalar field packets.
• Implications include potential applications in engineered photonic axion insulators and topological magnetoelectric systems for probing axion-like effects.

Scalar Axion Field Excitations by Toroidal Electromagnetic Pulses

Introduction

The paper "Scalar axion field of toroidal electromagnetic pulses" (2604.05791) investigates the generation of space-time localized pseudoscalar field excitations driven by the structured light field configurations arising from the superposition of toroidal electromagnetic pulses in free space. By adopting axion electrodynamics—an extension of classical Maxwellian theory to include a hypothetical pseudoscalar axion field sourced by the electromagnetic invariant $\mathbf{E} \cdot \mathbf{B}$—this work demonstrates how specialized optical field structures produce propagating, localized sources for the axion field, offering new perspectives on the interaction between structured light and axion-like fields in both fundamental physics and engineered media.

Axion Electrodynamics Formalism

Axion electrodynamics supplements Maxwell's equations with an additional pseudoscalar axion field $a(\mathbf{r}, t)$, coupled via the term $\mathbf{E} \cdot \mathbf{B}$. The equations of motion, as formulated by Wilczek, incorporate the axion-photon coupling constant $K$ and include both standard electromagnetic terms and axionic contributions. Most notably, the axion field obeys a Klein-Gordon-type equation with the coupling to the electromagnetic fields entering as a source:

$$\ddot{a} - \nabla^2 a + m^2 a = -K \mathbf{E} \cdot \mathbf{B}$$

where $m$ is the axion mass. Conventionally, electromagnetic plane waves in vacuum yield $\mathbf{E} \cdot \mathbf{B} = 0$, and thus do not excite the axion field. The challenge addressed is identifying physically realizable electromagnetic configurations in free space giving rise to localized, propagating nonzero values of $\mathbf{E} \cdot \mathbf{B}$.

Toroidal Electromagnetic Pulses and Structured Light

The study focuses on non-transverse, space-time non-separable electromagnetic pulses with toroidal topology, known as "flying doughnuts" (FDs), as introduced by Hellwarth and Nouchi. These pulses possess complex spatial and polarization structures, including both transverse and longitudinal components. Pure TE and TM toroidal pulses, while individually not producing nonzero $\mathbf{E} \cdot \mathbf{B}$, enable the generation of finite, localized excitations of $\mathbf{E} \cdot \mathbf{B}$ when suitably superposed. Their analytic representations facilitate a rigorous theoretical treatment of the fields and their interaction within the axion electrodynamics framework.

Generation of Localized Axion Field Perturbations

By constructing a superposition of TE and TM toroidal pulses with tunable relative phase, the authors realize a self-dual electromagnetic configuration where localized regions with nonzero $a(\mathbf{r}, t)$0 emerge and propagate with the light pulses themselves. The $a(\mathbf{r}, t)$1 invariant serves as an effective, spacetime-localized source term in the pseudoscalar field equation. In the weak-coupling regime and neglecting backreaction, explicit solutions for the driven axion field $a(\mathbf{r}, t)$2 demonstrate that the pseudoscalar field packet remains localized in both space and time and is stable during propagation, directly tracking the motion of the composite light pulse.

The study systematically examines the dependence of the axion field excitation on the relative phase between the TE and TM components, highlighting tunable symmetry and amplitude properties of the resulting pseudoscalar field. The field configurations used are based on well-established analytic solutions for toroidal pulses, ensuring experimental feasibility.

Implications and Future Directions

The principal implication is the explicit demonstration that axion electrodynamics predicts the generation of real, co-propagating, localized scalar field excitations in vacuum using controllable, experimentally accessible optical field configurations. This result is conceptually significant: it bridges the gap between abstract axion-photon interactions and their instantiation in structured light fields, without reliance on material interfaces, strong-field regimes, or high-energy scattering. While the results do not constitute evidence for actual axion particle production from photons, they represent a classical field prediction within axion-extended electrodynamics.

Beyond fundamental theoretical insight, the formalism is generic and could extend to engineered axion electrodynamic materials such as photonic axion insulators and topological magnetoelectric systems. Additionally, propagating $a(\mathbf{r}, t)$3 structures offer new degrees of freedom for examining axion-like effects in laboratory platforms and may be harnessed for probing axion-electrodynamics signatures in optical and condensed matter settings.

Anticipated developments include:

• Exploration of nonlinear and backreaction effects in regimes beyond weak coupling
• Experimentally resolved measurements of light-driven axion field excitations in structured photonic materials
• Theoretical extension to axion-like media with dynamical or tunable coupling constants
• Application to topological photonics, quantum materials, and analog gravity models

Conclusion

This study provides a rigorous framework and explicit example of how the superposition of toroidal TE and TM pulses yields propagating, localized sources for the axion field in free space, as formulated by axion electrodynamics. The analysis establishes a clear link between structured light in vacuum and scalar (pseudoscalar) field generation, with implications for both theoretical physics and the engineering of axion-like response in advanced photonic media. These results motivate further investigation into light-matter and light-field interactions in the axion electrodynamics regime, accessible with current and near-future experimental optics platforms.