# Geometrical phase and Hall effect associated with the transverse spin of light

## TL;DR

This paper reveals a new geometrical phase and a Hall effect in light propagation caused by transverse spin and curvature, expanding understanding of light's geometric and spin-related phenomena.

## Contribution

It introduces a novel geometrical phase and Hall effect linked to transverse spin and curvature, and unifies gauge fields in a comprehensive framework.

## Key findings

- Light acquires a new geometrical phase during propagation along curved paths.
- A novel Hall effect of light is induced by torsion and transverse spin.
- Different gauge fields describe the usual and novel geometrical phases.

## Abstract

By analyzing the vectorial Helmholtz equation within the thin-layer approach, we find that light acquires a novel geometrical phase, in addition to the usual one (the optical Berry phase), during the propagation along a curved path. Unlike the optical Berry phase, the novel geometrical phase is induced by the transverse spin along the binormal direction and associated with the curvature of the curve. Furthermore, we show a novel Hall effect of light induced by the torsion of the curve and associated with the transverse spin along the binormal direction, which is different from the usual spin Hall effect of light. Finally, we demonstrate that the usual and novel geometrical phase phenomena are described by different geometry-induced U(1) gauge fields in different adiabatic approximations. In the nonadiabatic case, these gauge fields are united in one effective equation by SO(3) group.