Calculating spatiotemporally modulated surfaces: a dynamical differential formalism

TL;DR

This paper introduces a novel dynamical differential formalism for analyzing electromagnetic waves interacting with spatiotemporally modulated surfaces, avoiding traditional eigenmode or Green's function methods.

Contribution

The authors develop a new dynamical differential approach that simplifies the analysis of space and time dependent electromagnetic systems without relying on eigenmodes or Green's functions.

Findings

Diffraction symmetry is broken by traveling-wave spatiotemporal modulation.

The method effectively captures frequency conversion and diffraction effects.

It offers a simplified alternative to conventional analytical techniques.

Abstract

Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the dyadic Green's function in space and time dependent media. Here, we propose a dynamical differential method which does not require either of them. Our method utilises a dynamical coordinate transformation in order to simplify the calculation of the optical response of the space and time dependent system. We reveal that the diffraction symmetry is broken in the presence of traveling-wave type spatiotemporal modulation.