Subwavelength sound screening by coupling space-coiled Fabry-Perot resonators

We explore broadband and omnidirectional low frequency sound screening based on locally resonant acoustic metamaterials. We show that the coupling of different resonant modes supported by Fabry-Perot cavities can efficiently generate asymmetric lineshapes in the transmission spectrum, leading to a broadband sound opacity. The Fabry-Perot cavities are space-coiled in order to shift the resonant modes under the diffraction edge, which guaranty the opacity band for all incident angles. Indeed, the deep subwavelength feature of the cavities leads to avoid diffraction that have been proved to be the main limitation of omnidirectional capabilities of locally resonant perforated plates. We experimentally reach an attenuation of few tens of dB at low frequency, with a metamaterial thickness fifteen times smaller than the wavelength (lambda / 15). The proposed design can be considered as a new building block for acoustic metasurfaces having a high level of manipulation of acoustic waves.Comment: 7 pages, 8 figure

Steering in-plane shear waves with inertial resonators in platonic crystals

Numerical simulations shed light on control of shear elastic wave propagation in plates structured with inertial resonators. The structural element is composed of a heavy core connected to the main freestanding plate through tiny ligaments. It is shown that such a configuration exhibits a complete band gap in the low frequency regime. As a byproduct, we further describe the asymmetric twisting vibration of a single scatterer via modal analysis, dispersion and transmission loss. This might pave the way to new functionalities such as focusing and self-collimation in elastic plates

Electrostriction and guidance of sound by light in optical fibers

We investigate the generation of phonon wavepackets in optical fibers via electrostriction from coherent optical waves. Solving the elastodynamic equation subject to the electrostrictive force, we are able to reproduce experimental spectra found in standard and photonic crystal fibers. We discuss the two important practical cases of forward interaction, dominated by elastic resonances of the fiber, and backward interaction, for which an efficient mechanism of phonon guidance by light is found. The latter result describes the formation of the coherent phonon wavepacket involved in stimulated Brillouin scattering

Strongly bounded groups and infinite powers of finite groups

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman. Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded.Comment: 10 pages, no figure. Versions 1-3 were entitled "Uncountable groups with Property (FH)". To appear in Comm. Algebr

On strongly just infinite profinite branch groups

For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the condition that every non-trivial normal subgroup is open; compact groups enjoying the last condition are called strongly just infinite. For strongly just infinite profinite branch groups with mild additional assumptions, we verify the invariant automatic continuity property and the locally compact automatic continuity property. Examples are then presented, including the profinite completion of the first Grigorchuk group. As an application, we show that many Burger-Mozes universal simple groups enjoy several automatic continuity properties.Comment: Typos and a minor error correcte

Design of Optomechanical Cavities and Waveguides on a Simultaneous Bandgap Phononic-Photonic Crystal Slab

In this paper we study and design quasi-2D optomechanical crystals, waveguides, and resonant cavities formed from patterned slabs. Two-dimensional periodicity allows for in-plane pseudo-bandgaps in frequency where resonant optical and mechanical excitations localized to the slab are forbidden. By tailoring the unit cell geometry, we show that it is possible to have a slab crystal with simultaneous optical and mechanical pseudo-bandgaps, and for which optical waveguiding is not compromised. We then use these crystals to design optomechanical cavities in which strongly interacting, co-localized photonic-phononic resonances occur. A resonant cavity structure formed by perturbing a "linear defect" waveguide of optical and acoustic waves in a silicon optomechanical crystal slab is shown to support an optical resonance at wavelength 1.5 micron and a mechanical resonance of frequency 9.5 GHz. These resonances, due to the simultaneous pseudo-bandgap of the waveguide structure, are simulated to have optical and mechanical radiation-limited Q-factors greater than 10^7. The optomechanical coupling of the optical and acoustic resonances in this cavity due to radiation pressure is also studied, with a quantum conversion rate, corresponding to the scattering rate of a single cavity photon via a single cavity phonon, calculated to be 292 kHz.Comment: 18 pages, 10 figures. minor revisions; version accepted for publicatio