Spin-Orbit Coupling in Helical Waveguides: A Local Duality Perspective and Emergent Gauge Fields

TL;DR

The paper investigates light propagation in spin-degenerate media through localization of the electromagnetic duality symmetry, revealing an emergent dual gauge field that governs spin–orbit interactions. By recasting Maxwell's equations in an optical-Dirac framework in a helicity basis, it shows that the local dual transformation induces a Berry connection along the propagation path, with a covariant derivative and Berry curvature that produce spin-dependent transport effects. The authors derive explicit Lagrangian terms for gauge-field interactions ($\mathcal{L}_A$) and medium-derivative contributions ($\mathcal{L}_Q$), and demonstrate their equivalence in helical fiber geometries, linking EOAM to spin–orbit coupling via torsion $\tau$. They also extend the formalism to vortex (IOAM) beams, giving a momentum-space gauge structure with a Berry curvature $\boldsymbol{F} = \lambda_\sigma \mathbf{k}/k^3$ and a Wilson-loop description of geometric phases, thereby unifying spin Hall physics of light within a gauge-theoretic framework. The work offers a fundamental perspective on light–matter interactions and suggests avenues for non-Abelian generalizations and symmetry-breaking terms such as a $\gamma^5$ contribution.

Abstract

Dual symmetry is an intrinsic property of Maxwell's equations, corresponding to a global U(1) symmetry in vacuum, with helicity as the associated conserved quantity. In this paper, we investigate light propagation in a spin-degenerate medium using a field-theoretical approach and introduce an effective gauge field A_s that emerges from the localization of dual symmetry. Within the geometric optics approximation, we show that the helical trajectory of light rays reveals this gauge field as a manifestation of spin-orbit coupling. Although orbital-orbit coupling also arises in such systems, the spin-orbit interaction possesses deeper physical significance, as it originates from the intrinsic dual symmetry embedded in Maxwell's equations.