Flat band degeneracy and near-zero refractive index materials in acoustic crystals

Abstract

A Dirac-like cone is formed by utilizing the flat bands associated with localized modes in an acoustic crystal (AC) composed of a square array of core-shell-structure cylinders in a water host. Although the triply-degeneracy seems to arise from two almost-overlapping flat bands touching another curved band, the enlarged view of the band structure around the degenerate point reveals that there are actually two linear bands intersecting each other at the Brillouin zone center, with another flat band passing through the same crossing point. The linearity of dispersion relations is achieved by tuning the geometrical parameters of the cylindrical scatterers. A perturbation method is used to not only accurately predict the linear slopes of the dispersions, but also confirm the linearity of the bands from first principles. An effective medium theory based on coherent potential approximation is developed, and it shows that a slab made of the AC carries a near-zero refractive index around the Dirac-like point. Full-wave simulations are performed to unambiguously demonstrate the wave manipulating properties of the AC structures such as perfect transmission, unidirectional transmission and wave front shaping.

Hermitian and Non-Hermitian Dirac-Like Cones in Photonic and Phononic Structures

“…The concept of Dirac-like cones has also been developed in other kinds of classical wave structures including acoustic and elastic structures [23,28,148,[159][160][161][162][163][164][165][166][167][168][169][170][171][172][173][174].…”

“…The EP is a singularity in a non-Hermitian system where two or more eigenvalues and their associated eigenfunctions collapse into one eigenvalue or eigenfunction [156][157][158]. Besides photonic structures, the concept of Dirac-like cones has also been applied to other kinds of classical wave structures, including acoustic and elastic structures [23,28,148,[159][160][161][162][163][164][165][166][167][168][169][170][171][172][173][174].…”

Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial

“…Phononic metamaterials with flat or nearly-flat bands have been investigated previously [30][31][32][33], mainly in the context of modifying refraction properties. More broadly, flat bands provide a setting for exotic strongly-correlated phenomena in electron systems [34] and a means to control signal speed and diffraction in photonics [35].…”

Dual Dirac cones in elastic Lieb-like lattice metamaterials

“…Acoustic Dirac-like cones can be categorized into three ways: (1) A single Dirac cone composed of two linearly touching bands at the corner of the Brillouin zone (BZ); 23,24 (2) A Dirac cone derived from an accidental threefold degeneracy of two linearly dispersing bands and an additional flat-band, where the Dirac point appears at the center of BZ (C point); [25][26][27][28][29][30] (3) An emerging double-Dirac cone with a fourfold degeneracy, where a pair of identical Dirac cones overlap at a single Dirac point at the BZ center. [31][32][33][34][35] Recent demonstration of Dirac/ Dirac-like cones at the center of BZ possesses enormous potential to realize the double-zero-index properties of electromagnetic (epsilon-and-mu-near-zero) 25,36,37 and acoustic (concurrent zero effective density and infinite bulk modulus [26][27][28][29][30] ) waveguides, for exciting applications like perfect tunneling, wave-front shaping, acoustic beam collimation, and asymmetric transmission. [26][27][28]30 Compared to electromagnetic and acoustic waves, the extension of zero-index structural systems to elastic waveguides remains an open challenge since elastic waves in solid structures have more polarization degrees of freedom, various deformation modes, and scattering complexity.…”

“…[31][32][33][34][35] Recent demonstration of Dirac/ Dirac-like cones at the center of BZ possesses enormous potential to realize the double-zero-index properties of electromagnetic (epsilon-and-mu-near-zero) 25,36,37 and acoustic (concurrent zero effective density and infinite bulk modulus [26][27][28][29][30] ) waveguides, for exciting applications like perfect tunneling, wave-front shaping, acoustic beam collimation, and asymmetric transmission. [26][27][28]30 Compared to electromagnetic and acoustic waves, the extension of zero-index structural systems to elastic waveguides remains an open challenge since elastic waves in solid structures have more polarization degrees of freedom, various deformation modes, and scattering complexity. 38,39 Recently, Zhu and Semperlotti 40 have reported the experimental realization of a double-zero-index elastic phononic waveguide to achieve the corresponding cloaking and supercoupling effects.…”