Jackiw-Rebbi states in interfaced binary waveguide arrays with Kerr nonlinearity

We systematically investigate the optical analogs of quantum relativistic Jackiw-Rebbi states in binary waveguide arrays in the presence of the Kerr nonlinearity with both self-focusing and self-defocusing cases. The localized profiles of these nonlinear Jackiw-Rebbi states can be calculated exactly by using the shooting method. We show that these nonlinear Jackiw-Rebbi states have a very interesting feature which is totally different from all other well-known nonlinear localized structures, including optical solitons. Namely, the profiles of nonlinear Jackiw-Rebbi states with higher peak amplitudes can totally envelope those with lower peak amplitudes. We demonstrate that media with the positive nonlinear coefficient can support stable Jackiw-Rebbi states for a wide range of peak amplitudes, whereas media with the negative nonlinear coefficient are only able to support Jackiw-Rebbi states with low peak amplitudes. A general rule for the detuning of nonlinear Jackiw-Rebbi states in binary waveguide arrays is found.