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We systematically investigate the optical analogs of quantum relativisticJackiw-Rebbi states in binary waveguide arrays in the presence of Kerrnonlinearity with both self-focusing and self-defocusing cases. The localizedprofiles of these nonlinear Jackiw-Rebbi states can be calculated exactly byusing the shooting method. We show that these nonlinear Jackiw-Rebbi stateshave a very interesting feature which is totally different from all otherwell-known nonlinear localized structures, including optical solitons. Namely,the profiles of nonlinear JR states with higher peak amplitudes can totallyenvelope the ones with lower peak amplitudes. We demonstrate that media withthe positive nonlinear coefficient can support stable Jackiw-Rebbi states for awide range of peak amplitudes, whereas media with the negative nonlinearcoefficient are only able to support Jackiw-Rebbi states with low peakamplitudes. A general rule for the detuning of nonlinear Jackiw-Rebbi states inbinary waveguide arrays is found.

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