We report solutions for stable compound solitons supported by a
three-dimensional (3D) quasi-phase-matched (QPM) photonic crystal in a medium
with the quadratic (χ(2)) nonlinearity. The photonic crystals are
introduced with a checkerboard structure, which can be realized by means of the
available technology. The solitons are built as four-peak vortex modes of two
types, rhombuses and squares. Their stability areas are identified in the
system's parametric space, while all bright vortex solitons are subject to
strong azimuthal instability in uniform χ(2) media. Possibilities for
experimental realization of the solitons are outlined too.Comment: 6 pages, 6 figures, 39 reference