How does it scale? Comparing quantum and classical nonlinear optical processes in integrated devices

We present equations for the power generated via spontaneous (quantum) and stimulated (classical) nonlinear optical processes in integrated devices. Equations for the same structure and same order process are derived from the same Hamiltonian, allowing for direct and easy comparison including the ability to estimate the efficiency of a quantum process based solely on experimental data from a classical process in the same device. We show that, in the CW limit and under the undepleted pump approximation, the average energy of a generated photon divided by a characteristic time plays the role of the classical "seed" signal in a quantum process, and that extending the length of a structure or taking advantage of a resonant cavity does not enhance spontaneous processes the same way as stimulated processes.