  A comprehensive physical model of adiabatic three wave mixing is developed
for the fully nonlinear regime, i.e. without making the undepleted pump
approximation. The conditions for adiabatic evolution are rigorously derived,
together with an estimate of the bandwidth of the process. Furthermore, these
processes are shown to be robust and efficient. Finally, numerical simulations
demonstrate adiabatic frequency conversion in a wide variety of physically
attainable configurations.
