  We present a method to simultaneously engineer the energy-momentum dispersion
and the local density of optical states. Using vertical symmetry-breaking in
high-contrast gratings, we enable the mixing of modes with different parities,
thus producing hybridized modes with controlled dispersion. By tuning geometric
parameters, we control the coupling between Bloch modes, leading to flatband,
M- and W-shaped dispersion as well as Dirac dispersion. Such a platform opens
up a new way to control the direction of emitted photons, and to enhance the
spontaneous emission into desired modes. We then experimentally demonstrate
that this method can be used to redirect light emission from weak emitters --
defects in Silicon -- to optical modes with adjustable density of states and
angle of emission.
