Mode analysis of a class of spatiotemporal photonic crystals

TL;DR

This paper provides an analytical study of the modes in a class of spatiotemporal photonic crystals with periodic dielectric variations in space and time, including dispersion diagrams and solutions for separable permittivity functions.

Contribution

It introduces analytic solutions and dispersion diagrams for a specific class of spatiotemporal photonic crystals with separable dielectric functions.

Findings

Analytic solutions for permittivity separated in space and time.

Dispersion diagrams for the studied photonic crystal.

Characterization of mode behavior in spatiotemporal structures.

Abstract

A detailed analysis is presented of the modes of a class of spatiotemporal photonic crystal. The structure analyzed is a perfect dielectric with periodic variation of {\epsilon} in a single spatial direction, as well as periodic variation in time. Analytic solutions are presented for {\epsilon} being separated in both variables, that is {\epsilon}(z,t)={\epsilon}0{\epsilon}r(z){\epsilon}t(t), and dispersion diagrams are presented.