Resonant and Non-Local Properties of Phononic Metasolids

We derive a general theory of effective properties in metasolids based on phononic crystals with low frequency resonances. We demonstrate that in general these structures need to be described by means of a frequency-dependent and non-local anisotropic mass density, stiffness tensor and a third- rank coupling tensor, which shows that they behave like a non-local Willis medium. The effect of non-locality and coupling tensor manifest themselves for some particular resonances whereas they become negligible for other resonances. Considering the example of a two-dimensional phononic crystal, consisting of triangular arrangements of cylindrical shells in an elastic matrix, we show that its mass density tensor is strongly resonant and anisotropic presenting both positive and negative divergent values, while becoming scalar in the quasi-static limit. Moreover, it is found that the negative value of transverse component of the mass density is induced by a dipolar resonance, while that of the vertical component is induced by a monopolar one. Finally, the dispersion relation obtained by the effective parameters of the crystal is compared with the band structure, showing a good agreement for the low-wave number region, although the non-local effects are important given the existence of some resonant values of the wave number

Valley and pseudospin-valley topologically protected edge states in symmetric pillared phononic crystals

We present a symmetric double-sided pillared phononic crystals (PPnCs) that can emulate both quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE) by solely imposing different geometric perturbations. Indeed, the Dirac cones can occur in the low (deep subwavelength) and high frequency regime by judiciously turning the parameters of the attached pillars and even a double Dirac cone can be achieved. We realize the valley-protected, the pseudospin-protected or the pseudospin-valley coupled edge states with the proposed platform. Besides, we show a variety of refraction phenomena (positive, negative and evanescent) of the valley-polarized edge state at the zigzag termination when emulating QVHE. Further, we illustrate the valley-dependent feature of the pseudospin-valley coupled edge state and demonstrate the valley based splitting of the pseudospin-protected edge states in a Y-junction wave guide.Comment: 4 figure

Gradient index phononic crystals and metamaterials

Phononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals

Bound states in the continuum in circular clusters of scatterers

In this work, we study the localization of flexural waves in highly symmetric clusters of scatterers. It is shown that when the scatterers are placed regularly in the perimeter of a circumference the quality factor of the resonances strongly increases with the number of scatterers in the cluster. It is also found that in the continuous limit, that is to say, when the number of scatterers tends to infinite, the quality factor is infinite so that the modes belong to the class of the so called bound states in the continuum or BICs, and an analytical expression for the resonant frequency is found. These modes have different multipolar symmetries, and we show that for high multipolar orders the modes tend to localize at the border of the circumference, forming therefore a whishpering gallery mode with an extraordinarily high quality factor. Numerical experiments are performed to check the robustness of these modes under different types of disorder and also to study their excitation from the far field. Although we have focused our study to flexural waves, the methodology presented in this work can be applied to other classical waves, like electromagnetic or acoustic waves, being therefore a promissing approach for the design of high quality resonators based on finite clusters of scatterers

Light modulation in phoxonic nanocavities

We report on the occurrence of strong nonlinear acousto-optic interactions in phoxonic structures, that support, simultaneously, acoustic and optical localized resonant modes, under the influence of acoustic losses. Deploying a detailed theoretical investigation of the acousto-optic coupling in the specific case of a one-dimensional phoxonic cavity, realized by homogeneous SiO2 and Si layers, we demonstrate the possibility for an enhanced modulation of light with sound through multi-phonon exchange mechanisms. A full electrodynamic and elastodynamic multiple scattering approach is employed to describe the optical and acoustic modes, and to account for their mutual interaction and the underlying effects both in time and frequency domains. In particular, we discuss the influence of hypersonic attenuation on the acousto-optic interaction by considering typical acoustic losses in the GHz regime