Modeling nonlinear optics in lossy integrated photonic structures: two strategies

We present two complementary strategies for modeling nonlinear quantum optics in realistic integrated optical devices, where scattering loss is present. In the first strategy, we model scattering loss as an attenuation; in the second, we employ a Hamiltonian treatment that includes a mechanism for scattering loss, such as a ‘phantom waveguide.’ These strategies can be applied to a broad range of structures and processes. As an example, we use these two approaches to model spontaneous four-wave mixing in (i) a ring-channel system and (ii) an add-drop system. We present the rates of photon pairs, broken pairs, and lost pairs for both systems, the latter two only accessible via the second stategy. We identify a full biphoton wavefunction (BWF) including the effects of scattering, and find that for a high-finesse resonator coupled to an arbitrary number of channels, the full BWF can be extracted from the BWF associated with photon pairs in an experimentally accessible output channel.

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