  Third order parametric down-conversion describes a class of nonlinear
processes in which a pump photon can be down-converted into triplets of
photons. It has been identified as a source of non-classical light, with
capabilities beyond those offered by better-established processes such as
spontaneous four-wave mixing. Here we discuss the implementation of TOPDC in
integrated photonic systems. We derive equations for the rates of TOPDC in a
non-resonant (waveguide) and resonant (microring) platform, such that the
scaling with experimental parameters can be plainly seen. We find that
generally non-resonant platforms should be pursued for spontaneous TOPDC
(SpTOPDC), whereas resonant platforms are more suitable for stimulated TOPDC
(StTOPDC). We present a sample calculation for TOPDC rates in sample systems
with conservative and accessible parameters. We find that StTOPDC should be
observable with the current fabrication technology, and that with some progress
in the design of TOPDC platforms, integrated SpTOPDC too could be demonstrated
in the near term.
