  We demonstrate supermode-based second harmonic generation in an integrated
nonlinear interferometer made of linear and nonlinear directional couplers. We
use a fully-fibered pump shaper to demonstrate second harmonic generation
pumped by the symmetric or anti-symmetric fundamental spatial modes. The
selection of the pumping mode and thus of a specific SHG spectral profile is
achieved through the selection of the fundamental wavelength and via a robust
phase setting scheme. We use two methods: either post-selecting or actively
setting the pumping mode. Such a modal phase matching paves the way for
classical and quantum applications of coupled nonlinear photonic circuits,
where multimode excitation, encoding and detection are a route for multiplexing
and scaling up light-processing.
