We propose an adiabatic all-optical switch that is composed of an asym
metric Y-branch ion-exchanged glass waveguide with a strip of nonlinea
r polymer loaded on top of one branch. The properties of nonlinear wav
e propagation in the device are investigated in detail. By extending t
he effective-index method to the analysis of nonlinear waveguides, we
calculate the nonlinear dispersion curves in successive sections to ex
plain the evolution of normal modes in the device. As the multivalued
propagation constants exist in the tapered directional coupler region,
the device possess an abrupt switching behavior and nonreciprocal pro
perties. To demonstrate nonlinear switching behaviors in the Y-branch
waveguide further, we employ a beam propagation method to simulate opt
ical-field propagation. The inputs by three different ports are invest
igated, and the results agree well with the dispersion-curve analysis.