New face-centered photonic square lattices with flat bands

Abstract

We report two new classes of face-centered photonic square lattices with flat bands which we call the Lieb-I and the Lieb-II lattices. There are 5 and 7 sites in the corresponding unit cells of the simplest Lieb-I and Lieb-II lattices, respectively. The number of flat bands $m$ in the new Lieb lattices is related to the number of sites $N$ in the unit cell by $m=(N-1)/2$. Physical properties of the lattices with even and odd number of flat bands are different. We also consider localization of light in such Lieb lattices. If the input beam excites the flat-band mode, it will not diffract during propagation, owing to the strong localization in the flat-band mode. For the Lieb-II lattice, we also find that the beam will oscillate and still not diffract during propagation, because of the intrinsic oscillating properties of certain flat-band modes. The period of oscillation is determined by the energy difference between the two flat bands. This study provides a new platform for the investigation of flat-band modes.

9 pages, 4 figures, comments and criticisms are welcome

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Cited by in corpus (14)

• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Transport properties in the photonic super-honeycomb lattice - a hybrid fermionic and bosonic system
• Disorder effects in the two-dimensional Lieb lattice and its extensions
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Compact localised states in magnonic Lieb lattices
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions
• Two-dimensional flat-band solitons in superhoneycomb lattices
• Quantum engineering for compactly localized states in disordered Lieb lattices
• Altermagnetism in an interacting model of Kagome materials
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Localization and Flat Bands in Bond-Inflated Lattices
• RKKY couplings in the Lieb lattice: flat-band induced frustration