  We present a detailed analysis of strongly driven spontaneous four-wave
mixing in a lossy integrated microring resonator side-coupled to a channel
waveguide. A nonperturbative, analytic solution within the undepleted pump
approximation is developed for a cw pump input of arbitrary intensity. In the
strongly driven regime self- and cross-phase modulation, as well as multi-pair
generation, lead to a rich variety of power-dependent effects; the results are
markedly different than in the low power limit. The photon pair generation
rate, single photon spectrum, and joint spectral intensity (JSI) distribution
are calculated. Splitting of the generated single photon spectrum into a
doublet structure associated with both pump detuning and cross-phase modulation
is predicted, as well as substantial narrowing of the generated signal and
idler bandwidths associated with the onset of optical parametric oscillation at
intermediate powers. Both the correlated and uncorrelated contributions to the
JSI are calculated, and for sufficient powers the uncorrelated part of the JSI
is found to form a quadruplet structure. The pump detuning is found to play a
crucial role in all of these phenomena, and a critical detuning is identified
which divides the system behaviour into distinct regimes, as well as an optimal
detuning strategy which preserves many of the low-power characteristics of the
generated photons for arbitrary input power.
