Uniform-Velocity Spacetime Crystals

TL;DR

This paper provides a comprehensive analysis of uniform-velocity bilayer spacetime crystals, extending classical concepts with new results in interface analysis, interference phenomenology, dispersion approximation, and truncation effects, laying groundwork for future spacetime metamaterials.

Contribution

It introduces new theoretical extensions and analytical methods for understanding uniform-velocity spacetime crystals, including an extension of the Stokes principle and interference analysis.

Findings

Extended Stokes principle to spacetime interfaces

Developed interference phenomenology for spacetime crystals

Provided linear approximation of dispersion diagrams

Abstract

We perform a comprehensive analysis of uniform-velocity bilayer spacetime crystals, combining concepts of conventional photonic crystallography and special relativity. Given that a spacetime crystal consists of a sequence of spacetime discontinuities, we do this by solving the following sequence of problems: 1) the spacetime interface, 2) the double spacetime interface, or spacetime slab, 3) the unbounded crystal, and 4) the truncated crystal. For these problems, we present the following respective new results: 1) an extension of the Stokes principle to spacetime interfaces, 2) an interference-based analysis of the interference phenomenology, 3) a quick linear approximation of the dispersion diagrams, a description of simultaneous wavenumber and frequency bandgaps, and 4) the explanation of the effects of different types of spacetime crystal truncations, and the corresponding scattering coefficients. This work may constitute the foundation for a virtually unlimited number of novel canonical spacetime media and metamaterial problems.