  We demonstrate that symmetry breaking opens a new degree of freedom to tailor
the energy-momentum dispersion in photonic crystals. Using a general
theoretical framework in two illustrative practical structures, we show that
breaking symmetry enables an on-demand tuning of the local density of states of
a same photonic band from zero (Dirac cone dispersion) to infinity (flatband
dispersion), as well as any constant density over an adjustable spectral range.
As a proof-of-concept, we experimentally demonstrate the transformation of a
very same photonic band from conventional quadratic shape to Dirac dispersion,
flatband dispersion and multivaley one, by finely tuning the vertical symmetry
breaking. Our results provide an unprecedented degree of freedom for optical
dispersion engineering in planar integrated photonic devices.
