  We systematically investigate the optical analogs of quantum relativistic
Jackiw-Rebbi states in binary waveguide arrays in the presence of 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 JR states with higher peak amplitudes can totally
envelope the ones 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.
