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

Band gap engineering in simultaneous phononic and photonic crystal slabs

We discuss the simultaneous existence of phononic and photonic band gaps in two types of phononic crystals slabs, namely periodic arrays of nanoholes in a Si membrane and of Si nanodots on a SiO2 membrane. In the former geometry, we investigate in detail both the boron nitride lattice and the square lattice with two atoms per unit cell (these include the square, triangular and honeycomb lattices as particular cases). In the latter geometry, some preliminary results are reported for a square lattice

Phonon-Plasmon Interaction in Metal-Insulator-Metal Localized Surface Plasmon Systems

We investigate theoretically and numerically the coupling between elastic and localized surface plasmon modes in a system of gold nanocylinders separated from a thin gold film by a dielectric spacer of few nanometers thickness. That system supports plasmon modes confined in between the bottom of the nanocylinder and the top of the gold film, which arise from the formation of interference patterns by short-wavelength metal-insulator-metal propagating plasmon. First we present the plasmonic properties of the system though computer-simulated extinction spectra and field maps associated to the different optical modes. Next a simple analytical model is introduced, which allows to correctly reproduce the shape and wavelengths of the plasmon modes. This model is used to investigate the efficiency of the coupling between an elastic deformation and the plasmonic modes. In the last part of the paper, we present the full numerical simulations of the phononic properties of the system, and then compute the acousto-plasmonic coupling between the different plasmon modes and five acoustic modes of very different shape. The efficiency of the coupling is assessed first by evaluating the modulation of the resonance wavelength, which allows comparison with the analytical model, and finally in term of time-modulation of the transmission spectra on the full visible range, computed for realistic values of the deformation of the nanoparticle.Comment: 12 pages, 9 figure