  The propagation of several spatial modes has a significant impact on the
structure of the emission from parametric down-conversion in a nonlinear
waveguide. This manifests itself not only in the spatial correlations of the
photon pairs but also, due to new phase-matching conditions, in the output
spectrum, radically altering the degree of entanglement within each pair. Here
we investigate both theoretically and experimentally the results of
higher-order spatial-mode propagation in nonlinear waveguides. We derive
conditions for the creation of pairs in these modes and present observations of
higher-order mode propagation in both the spatial and spectral domains.
Furthermore, we observe correlations between the different degrees of freedom
and finally we discuss strategies for mitigating any detrimental effects and
optimizing pair production in the fundamental mode.
