We demonstrate that symmetry breaking opens a new degree of freedom to tailor the energymomentum 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.Engineering the energy-momentum dispersion of photonic structures is at the heart of contemporary optics research. This fundamental feature molds the light propagation [1], dictates the coupling with free space [2], and tailors light-matter interactions [3]. Such a dispersion engineering is generally achieved through a designed periodic arrangement of materials with different permittivities in photonic crystals, metamaterials and metasurfaces. Recently, two particular types of dispersions have been intensively studied: flatband dispersion [4][5][6][7][8][9][10][11][12][13] and Dirac dispersion [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The first one provides slow light of zero group velocity with high density of states for a broad range of the Brillouin zone, thus greatly enhances light-matter interaction and nonlinear behaviors for low-threshold micro-lasers and information processing applications [30,31]. Moreover, flatband gives rise to localized stationary eigenstates which are extremely sensitive to disorder effects due to an infinite effective mass [7,14]. This suggests new regime of light localization [8,9] other than conventional concepts such as Anderson localization [32,33] and optical bound states in continuum [34,35]. Being an opposite extreme to flat dispersion, Dirac dispersion (double Dirac cones with no bandgap) corresponds to massless photonic states. By analogy with the propagation of electrons in graphene, Dirac photons propagation could lead to phenomena such as Klein tunneling [19] and Zitterbewegung [20] for photons. Moreover, photonic Dirac dispersion opens the way to realize large-area single mode lasers [21,22]; and enables many exotic physical features such as zero-refractive index materials for transformation optics applications [15,17,18] and photonic topological insulator [23][24][25][26][27][28]. Due to their completely opposite characteristics, flatband and Dirac dispersion are usually attributed to different bands of the photonic structures (2D tight-binding lattices [5,6,8,9], accidental degeneracy in 2D photonic crystal [15][16][17][18]). Other configurations exhibit the sole presence of flatband states (1D tight-binding lattices [7,10], dispersio...

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.