  The intensity buildup of light inside a lossy microring resonator can be used
to enhance the generation of squeezed states via spontaneous parametric
downconversion (SPDC). In this work, we model the generation of squeezed light
in a microring resonator that is pumped with a Gaussian pulse via a
side-coupled channel waveguide. We theoretically determine the optimum pump
pulse duration and ring-to-channel coupling constant to minimize the quadrature
noise (maximize the squeezing) in the ring for a fixed input pump energy. We
derive approximate analytic expressions for the optimal coupling and pump pulse
duration as a function of scattering loss in the ring. These results will
enable researchers to easily determine the optimal design of microring
resonator systems for the generation of quadrature-squeezed states.
