  We experimentally investigate unusual light propagation inside a
three-dimensional (3D) superlattice of resonant cavities that are confined
within a 3D photonic band gap. Therefore, we fabricated 3D diamond-like
photonic crystals from silicon with a broad 3D band gap in the near-infrared
and doped them with a periodic array of point defects. In position-resolved
reflectivity and scattering microscopy, we observe narrow spectral features
that match well with superlattice bands in band structures computed with the
plane wave expansion. The cavities are coupled in all three dimensions when
they are closely spaced and uncoupled when they are further apart. The
superlattice bands correspond to light that hops in high symmetry directions in
3D - so-called Cartesian Light - that opens applications in 3D photonic
networks, 3D Anderson localization of light, and future 3D quantum photonic
networks.
