Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

The phonon is the physical particle representing mechanical vibration and is responsible for the transmission of everyday sound and heat. Understanding and controlling the phononic properties of materials provides opportunities to thermally insulate buildings, reduce environmental noise, transform waste heat into electricity and develop earthquake protection. Here I review recent progress and the development of new ideas and devices that make use of phononic properties to control both sound and heat. Advances in sonic and thermal diodes, optomechanical crystals, acoustic and thermal cloaking, hypersonic phononic crystals, thermoelectrics, and thermocrystals herald the next technological revolution in phononics.

Sound and heat revolutions in phononics

Structured, periodic optical materials can be used to form photonic crystals capable of dispersing, routing, and trapping light A similar phenomena in periodic elastic structures can be used to manipulate mechanical vibrations Here we present the design and experimental realization of strongly coupled optical and mechanical modes in a planar, periodic nanostructure on a silicon chip 200-Terahertz photons are co-localized with mechanical modes of Gigahertz frequency and 100-femtogram mass The effective coupling length, which describes the strength of the photon-phonon interaction, is as small as 29 microns, which, together with minute oscillator mass, allows all-optical actuation and transduction of nanomechanical motion with near quantum-limited sensitivity Optomechanical crystals have many potential applications, from RF-over-optical communication to the study of quantum effects in mesoscopic mechanical systems

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Optomechanical Crystals

We have fabricated a new type of composite which displays localized sonic resonances at ∼350– 2000 Hz with a microstructure size in the millimeter to centimeter range. Around the resonance frequencies the composite behaves as a material with effective negative elastic constants and as a total wave reflector—a 2 cm slab of this material is shown to break the conventional mass-law of sound transmission by order(s) of magnitude. When the microstructure is periodic, our composites exhibit large elastic wave band gaps at the sonic frequency range, with a lattice constant order(s) of magnitude smaller than the corresponding sonic wavelength in air. Good agreement is obtained between theory and experiment.

Locally resonant sonic materials

Surface waves in topological states of quantum matter exhibit unique protection from backscattering induced by disorders, making them ideal carriers for both classical and quantum information. Topological matters for electrons and photons are largely limited by the range of bulk properties, and the associated performance trade-offs. In contrast, phononic metamaterials provide access to a much wider range of material properties. Here we demonstrate numerically a phononic topological metamaterial in an elastic-wave analogue of the quantum spin Hall effect. A dual-scale phononic crystal slab is used to support two effective spins for phonons over a broad bandwidth, and strong spin-orbit coupling is realized by breaking spatial mirror symmetry. By preserving the spin polarization with an external load or spatial symmetry, phononic edge states are shown to be robust against scattering from discrete defects as well as disorders in the continuum, demonstrating topological protection for phonons in both static and time-dependent regimes.

https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=1016&context=qc_pubs

Topologically protected elastic waves in phononic metamaterials

In this Letter we present an experimental analysis of the acoustic transmission of a two-dimensional periodic array of rigid cylinders in air with two different geometrical configurations: square and triangular. In both configurations, and above a certain filling fraction, we observe an overlap, in the range of the audible frequencies, between the attenuation peaks measured along the two high-symmetry directions of the Brillouin zone. This effect is considered as the fingerprint of the existence of a full acoustic gap. Nevertheless, the comparison with our calculation of band structures shows that the triangular lattice has band states in that frequency range. We call them deaf bands. This contradictory result is explained by looking at the symmetry of the deaf bands; they cannot be excited by experiments of sound transmission. [S0031-9007(98)06295-4]

http://personales.upv.es/jsanched/JVSanchez_PRL80_5325_98.pdf

Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders

We show that absolute sonic band gaps produced by two-dimensional square and triangular lattices of rigid cylinders in air can be increased by reducing the structure symmetry. In the case of square lattices, symmetry reduction is achieved by a smaller diameter cylinder placed at the center of each unit cell. For triangular lattices the reduction is achieved by decreasing the diameter of the cylinder at the center of the hexagons in the lattice. Theoretical predictions are also demonstrated experimentally: starting from a honeycomb lattice ~using cylinders of 4 cm of diameter size and 6.35 cm nearest-neighbor distance! we have studied the transition to a triangular symmetry by putting rods with increasing diameter ~in the range 0.6‐4 cm! at the center. The greatest enhancement of the attenuation strength observed in transmission experiments has been obtained in the high frequency region for diameter ratios in the range 0.1‐0.3. @S1063-651X~99!51212-9# PACS number~s!: 43.20.1g, 42.25.Bs, 52.35.Dm Since the seminal work of Yablonovitch @1# and John @2#, who open the research in photonic crystals ~PC!, we have witnessed the appearance of new devices based on the existence of photonic band gaps ~PBG! in these dielectric periodic structures. Also, because the underlying theory is applicable to other kind of waves, acoustic and elastic, a search for periodic structures having properties of sonic band gap ~SBG! or elastic band gap ~EBG!, respectively, is currently being performed. Therefore, the design, construction, and technological applications of a completely new type of crystals that could be called classical wave crystals is becoming a very promising project at the beginning of the new century. In the field of acoustics much theoretical work has been done proposing structures having SBG’s properties @3‐6#. The existence of SBG is due to a complex interplay between the sound velocity and density ratios of the composite materials, and their spatial arrangement. Experimentally, a few works have claimed to observe absolute band gaps @7,8#. Therefore, the actual possibility of building up composite material having SBG open a new technological research on environmental protection. One of the goals of PBG and SBG theory is the search of materials and/or topologies producing large gaps at the desired range of frequencies. In PC it has been shown that full PBG can be enlarged by decreasing the crystal symmetry through the introduction of a two-point basis set. Thus, for example, 3D PC based on a face-centered-cubic structure do not possess a full PBG between the first and second bands, but the ones having a diamond structure do because the additional point basis lifts the degeneracy of some bands @9# .I n the same manner, in two-dimensional ~2D! structures, Anderson and Giapis @10# obtained larger gaps when they add a different size rod at the center of each unit cell of square and honeycomb lattices. The latest conclusion awakened our interest about whether this sort of mechanism is effective in creating large SBG and/or enhancing the attenuation measured in some 2D sonic crystals ~SC! previously studied by us @8#. In this Rapid Communication we show that this mechanism is also effective in SC, being the cause for such SBG enlargement a combination of two mechanism: ~i! the achievement of higher filling fractions, and ~ii! the symmetry reduction. Also, here we demonstrate that mechanism ~ii! is much more effective than mechanism ~i!. The wave equation for the propagation of pressure waves p(r), with harmonic frequency, v, in a 2D-space r5(x, y) defined by a composite system having a sound velocity, v(r), and density, r(r), can be written as

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Large two-dimensional sonic band gaps.

In this paper, we report experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes. The experiments were performed in a marble quarry by drilling cylindrical holes in two different configurations: honeycomb and triangular lattices. The attenuation spectra of the surface waves show the existence of absolute band gaps for elastic waves in these semi-infinite two-dimensional crystals. Results are compared with theoretical calculations based on a scalar-wave approach. The scaling property of the underlying theory has led us to explore the possible application of the results obtained to the attenuation of surface waves in seismic movements. @S0163-1829~99!07419-6#

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Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal

Control of noise by trees arranged like sonic crystals

It is well known that sonic crystals are periodic structures that present acoustic band gaps attenuation centered at frequencies related with the lattice constant of the structure. We present an approach based on genetic algorithms to create band gaps in a predetermined range of frequencies. The mechanism used by genetic algorithms to achieve this objective is the creation of vacancies in a starting sonic crystal, built with air-embedded rigid scatterers. As a result of the optimization process, we obtain quasiordered structures on which acoustic properties are based in the multiple scattering theory.

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Jaime Llinares

Papers

Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders

Large two-dimensional sonic band gaps.

Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal

Control of noise by trees arranged like sonic crystals

Band gap creation using quasiordered structures based on sonic crystals