Dirac solitons in square binary waveguide lattices

We study optical analogs of two-dimensional (2D) Dirac solitons in square binary waveguide lattices with two different topologies in the presence of Kerr nonlinearity. These 2D solitons turn out to be quite robust. We demonstrate that with the found 2D solitons, the coupled mode equations governing light dynamics in square binary waveguide lattices can be converted into the nonlinear relativistic 2D Dirac equation with the four-component bispinor. This paves the way for using binary waveguide lattices as a classical simulator of quantum nonlinear effects arising from the 2D Dirac equation, something that is thought to be impossible to achieve in conventional (i.e., linear) quantum field theory.