Dirac equation in one dimensional transformation optics

TL;DR

This paper demonstrates how the propagation of TE polarized waves in one-dimensional inhomogeneous media can be modeled as a Dirac equation, enabling optical simulations of relativistic quantum phenomena like the Jackiw-Rebbi zero mode.

Contribution

It establishes a novel analogy between photonic wave propagation and the Dirac equation, allowing experimental simulation of relativistic quantum effects in optical structures.

Findings

TE wave propagation can be described by the Dirac equation in 1D.

Optical implementation of the Jackiw-Rebbi zero mode is feasible.

Refractive index landscapes can control soliton-like states.

Abstract

We show that the propagation of transverse electric (TE) polarized waves in one dimensional inhomogeneous settings can be written in the form of the Dirac equation in one space dimension with a Lorentz scalar potential, and consequently perform photonic simulations of the Dirac equation in optical structures. In particular, we propose how the zero energy state of the Jackiw-Rebbi model can be implemented in a optical set up by controlling the refractive index landscape, where TE polarized waves mimic the Dirac particles and the soliton field can be implemented and tuned by adjusting the refractive index.