Effect of scattering loss on connections between classical and quantum processes in second-order nonlinear waveguides

We show that a useful connection exists between spontaneous parametric down conversion (SPDC) and sum frequency generation in nonlinear optical waveguides with arbitrary scattering loss, while the same does not hold true for SPDC and difference frequency generation. This result refines the relationship between these quantum and classical second-order nonlinear optical processes in waveguides, and identifies the most accurate characterization of a waveguide's quantum performance in the presence of loss based solely on classical measurements.