  We consider continuous-wave (CW) states and dark solitons (DSs) in a system
of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a
planar waveguide with the quadratic nonlinearity, the FF components being
linearly coupled by resonant reflections on the Bragg grating. We demonstrate
that, in contrast with the usual situation in quadratic spatial-domain models,
CW states with the phase shift between the FF and SH components are
modulationally stable in a broad parameter region in this system, provided that
the CW wavenumber does not belong to the system's spectral gap. Stationary
fundamental DSs are found numerically, and are also constructed by means of a
specially devised analytical approximation. Bound states of two and three DSs
are found too. The fundamental DSs and two-solitons bound states are stable in
all the cases when the CW background is stable, which is shown by dint of
calculation of the corresponding eigenvalues, and verified in direct
simulations. Tilted DSs are found too. They attain a maximum contrast at a
finite value of the tilt, that does not depend on the phase mismatch. At a
maximum value of the tilt, which grows with the mismatch, the DS merges into
the CW background. Interactions between the tilted solitons are shown to be
completely elastic.
