Dirac equation in one dimensional transformation optics

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.