Asymptotic fields for a Hamiltonian treatment of nonlinear electromagnetic phenomena

We discuss the use of asymptotic-in and -out fields in a Hamiltonian treatment of nonlinear electromagnetic problems. Our approach allows a description of nonlinear phenomena in a number of geometries and is suitable to treat integrated photonic structures, particularly cavities. We present examples in which the nonlinear phenomena are weak enough for pump depletion to be neglected, and we report some results related to the description of second-order nonlinear processes in ring resonators and layered structures.