Electromagnetic wave propagating along a space curve

TL;DR

This paper derives an effective equation for electromagnetic waves along a space curve, revealing geometric effects like spin-orbit coupling, helicity inversion, and gauge invariance protection due to torsion and curvature.

Contribution

It introduces a novel thin-layer approach to analyze electromagnetic wave propagation along space curves, uncovering new geometric phase and polarization effects.

Findings

Identification of intrinsic and extrinsic spin-orbit couplings induced by torsion.

Demonstration of helicity inversion caused by curvature.

Protection of gauge invariance by geometrically induced gauge potential.

Abstract

Using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit and extrinsic orbital angular momentum and intrinsic orbital angular momentum couplings induced by torsion, which can lead to geometric phase, spin and orbital Hall effects. And we show the helicity inversion induced by curvature that can convert the right-handed circularly polarized electromagnetic wave into left-handed polarized one, vice verse. Finally, we demonstrate that the gauge invariance of the effective dynamics is protected by the geometrically induced gauge potential.