Adiabatic geometric phase in the nonlinear coherent coupler

We introduce the concept of geometric phase to the nonlinear coherent coupler. With considering the adiabatic change of the distance-dependent phase mismatch, we calculate the adiabatic geometric phase related to the supermode of the coupler analytically. We find that the phase depends on the input light intensity explicitly. In particular, in the low and high intensity limits, the phase equals half of the area on the Poincare sphere enclosed by the evolution loop of the system. At the critical intensity where different supermodes merge, the phase diverges, which can be considered as the signal of a continuous phase transition.