  Using the approach of coupled wave equations, we consider spontaneous
parametric down-conversion (SPDC) in the narrow-band regime and its
relationship to classical nonlinear processes such as sum-frequency generation.
We find simple expressions in terms of mode overlap integrals for the absolute
pair production rate into single spatial modes, and simple relationships
between the efficiencies of the classical and quantum processes. The results,
obtained with Green function techniques, are not specific to any geometry or
nonlinear crystal. The theory is applied to both degenerate and non-degenerate
SPDC. We also find a time-domain expression for the correlation function
between filtered signal and idler fields.
