  We theoretically investigate and optimize four-wave mixing (FWM) in silicon
nitride (SiN) waveguides integrated with two-dimensional (2D) layered graphene
oxide (GO) films. Based on extensive previous measurements of the material
parameters of the GO films, we perform detailed analysis for the influence of
device parameters including waveguide geometry, GO film thickness, length, and
coating position on the FWM conversion efficiency (CE) and conversion bandwidth
(CB). The influence of dispersion and photo-thermal changes in the GO films is
also discussed. Owing to the strong mode overlap between the SiN waveguides and
the highly nonlinear GO films, FWM in the hybrid waveguides can be
significantly enhanced. We obtain good agreement with previous experimental
results and show that by optimizing the device parameters to balance the
trade-off between Kerr nonlinearity and loss, the FWM CE can be improved by as
much as ~20.7 dB and the FWM CB can be increased by ~4.4 folds, relative to the
uncoated waveguides. These results highlight the significantly enhanced FWM
performance that can be achieved in SiN waveguides by integrating 2D layered GO
films.
