# Shift vector as the geometric origin of beam shifts

## TL;DR

This paper presents a geometric and gauge-invariant framework for understanding beam shifts like Goos-Hanchen and Imbert-Fedorov, introducing a shift vector concept that clarifies their intrinsic and extrinsic origins.

## Contribution

It introduces a general geometric description of beam shifts using a shift vector and Wilson loops, providing a model-independent link to symmetry properties.

## Key findings

- GH/IF shifts can be described by a gauge-invariant shift vector.
- Intrinsic shifts depend solely on the system's bulk properties.
- Symmetry determines the presence or absence of intrinsic and extrinsic shifts.

## Abstract

Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts are lateral and transverse displacements of a wavepacket reflecting off a surface. A dramatic real-space manifestation of wavepacket phases, they have traditionally been analyzed in a model dependent fashion. Here we argue that GH and IF shifts admit a general geometrical description and arise from a gauge invariant geometric phase. In particular, we show GH/IF shifts can be naturally captured by a shift vector, analogous to the shift vector from shift currents in the bulk photovoltaic effect. Employing Wilson loops to visualize the scattering processes contributing to the shift vector, we separate the shift into an intrinsic (depends solely on the system bulk) and an extrinsic part. This enables to establish a clear model-independent link between symmetry and the presence/absence of intrinsic and extrinsic GH/IF shifts.