  We propose and analyse a cascaded optical parametric system which involves
three interacting modes across two octaves of frequency difference. Our system,
combining degenerate optical parametric oscillation (OPO) with second harmonic
generation (SHG), promises to be a useful source of squeezed and entangled
light at three differing frequencies. We show how changes in damping rates and
the ratio of the two concurrent nonlinearities affect the quantum correlations
in the output fields. We analyse the threshold behaviour, showing how the
normal OPO threshold is changed by the addition of the SHG interactions. We
also find that the inclusion of the OPO interaction removes the self-pulsing
behaviour found in normal SHG. Finally, we show how the Einstein-Podolsky-Rosen
correlations can be controlled by the injection of a coherent seed field at the
lower frequency.
