  We systematically investigate two types of localized states - one is the
optical analogue of the quantum relativistic Jackiw-Rebbi states, and the other
is the trivial localized state - in interfaced binary waveguide arrays in the
presence of cubic-quintic nonlinearity. By using the shooting method we can
exactly calculate the profiles of these nonlinear localized states. Like in the
case with Kerr nonlinearity, we demonstrate that these nonlinear localized
states in the case with cubic-quintic nonlinearity also have a distinguishing
feature which is completely different from all other well-known nonlinear
localized structures in other media. Namely, the profiles of nonlinear
localized states with higher peak amplitudes in interfaced binary waveguide
arrays can totally envelope those with lower peak amplitudes. We show that high
values of the saturation nonlinearity parameter can help to generate and
stabilize these intense localized states during propagation, especially in the
case with negative coefficient for the cubic nonlinearity term.
