# Fresnel reflection coefficients in the Fourier domain for a planar surface in uniform motion parallel to its interface

## TL;DR

This paper calculates how light reflects from a moving surface, showing that motion causes cross-polarization and changes surface plasmon behavior.

## Contribution

The paper introduces a new method to calculate reflection coefficients in the Fourier domain for a moving surface.

## Key findings

- Cross-polarization occurs due to surface motion, except when motion is along the plane of incidence.
- Surface plasmon dispersion tilts with motion, causing unidirectionality and non-reciprocity.
- The Drude model is used to demonstrate movement-induced changes in surface modes.

## Abstract

The optical reflection coefficient of a medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a function of the incident frequency and wavevector, valid in both the far- and near-field regimes. It is found that cross-polarisation appears as a consequence of the motion, except when it is directed along the plane of incidence. As an example, using a Drude model for the permittivity of the surface at rest, the dispersion relation of its surface modes is calculated. A tilting of the dispersion relation is observed, leading to movement-induced surface plasmon unidirectionality and non-reciprocity.