Quadrature and number fluctuations produced by parametric devices driven by pulsed pumps

Two sets of formulas are derived for the field-quadrature and photon-number fluctu- ations (variances and correlations) produced by parametric amplifiers and frequency convertors that are driven by pulsed pumps and act on pulsed signals. The first set is based on the Green functions for the underlying parametric processes, whereas the second is based on the associated Schmidt coefficients and modes. These formulas facilitate the modeling and performance optimization of parametric devices used in a wide variety of applications.