Optical analogue of relativistic Dirac solitons in binary waveguide arrays

•An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested.•Analytical solutions to pseudo-relativistic solitons are presented.•A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory.