Symmetry Breaking in Photonic Crystals: On-Demand Dispersion from Flatband to Dirac Cones

Abstract

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...

Completely Subradiant Multi‐Atom Architectures Through 2D Photonic Crystals

“…This phenomenon resembles flatbands in 1D, where the flatness of a band implies zero group velocity and thus localized (non‐propagating) waves. In the 2D case we have zero velocity in a given direction (say ), and thus localization in that direction, and normal propagation in the orthogonal one (say ).…”

Dimerized high contrast gratings

“…Symmetry breaking in planar photonic crystals results in a well-known phenomenon of introducing sharp Fano resonances excitable by free-space illumination [31,[40][41][42][43][44][45][46]. There are two requirements for such a feature to be observed at normal incidence: (1) a mode must exist in the band diagram at the center ("Gamma point") of the First Brillouin Zone (FBZ) and (2) the mode must not be excluded by symmetry considerations.…”

Artificial flat band systems: from lattice models to experiments

“…Perfectly flat bands are not stable against generic perturbations, which typically induce nonzero dispersion. For this reason, some authors broaden the definition of flat bands to include partially-flat bands that have vanishing dispersion only along particular directions or in the vicinity of special Brillouin zone points [4][5][6]. In this review our focus is on bands that are perfectly flat, which require either fine-tuning of system parameters, or protection by a lattice symmetry.…”