  Frequency conversion (FC) and type-II parametric down-conversion (PDC)
processes serve as basic building blocks for the implementation of quantum
optical experiments: type-II PDC enables the efficient creation of quantum
states such as photon-number states and Einstein-Podolsky-Rosen-states
(EPR-states). FC gives rise to technologies enabling efficient atom-photon
coupling, ultrafast pulse gates and enhanced detection schemes. However,
despite their widespread deployment, their theoretical treatment remains
challenging. Especially the multi-photon components in the high-gain regime as
well as the explicit time-dependence of the involved Hamiltonians hamper an
efficient theoretical description of these nonlinear optical processes.
  In this paper, we investigate these effects and put forward two models that
enable a full description of FC and type-II PDC in the high-gain regime. We
present a rigorous numerical model relying on the solution of coupled
integro-differential equations that covers the complete dynamics of the
process. As an alternative, we develop a simplified model that, at the expense
of neglecting time-ordering effects, enables an analytical solution.
  While the simplified model approximates the correct solution with high
fidelity in a broad parameter range, sufficient for many experimental
situations, such as FC with low efficiency, entangled photon-pair generation
and the heralding of single photons from type-II PDC, our investigations reveal
that the rigorous model predicts a decreased performance for FC processes in
quantum pulse gate applications and an enhanced EPR-state generation rate
during type-II PDC, when EPR squeezing values above 12 dB are considered.
