1PL
Metamaterial and Topological Physics Approaches for
Designing Efficient Acoustic/Elastic Devices
効率的な音響/弾性デバイス設計のためのメタマテリアルおよびトポロジカル物理的アプローチ
Kenji Tsuruta1† (1Faculty of Nat. Sci. & Technol., Okayama Univ.)
鶴田健二（岡山大院自然）1. Introduction
Among metamaterials, which are artificial
materials showing unique wave response
characteristics, “Acoustic metamaterials" [1,2] haveprovided novel insights in the development ofacoustic devices. Also, "topological phononics/mechanics" [3,4] based on the analogy of theclassical vibration to the electron wave function in
the topological insulator has initiated a new trend of
the ultrasonic technology. These approaches havebeen examined and verified in the wide frequency
band from audible range (kHz) to extreme ultrasonicwave (GHz) [5] until now. Especially, time inversion
asymmetry (nonreciprocity) and propagation
efficiency improvement in the extreme ultrasonicfrequency regime are expected to contribute to therealization of the next generation (Beyond 5G/6G)
information device through the combination withelectronic and/or optical devices. In this presentation,
I try to survey recent research trends on acoustic
metamaterial design, specifically metasurfaces, andon topological physics approach for acoustic
waveguide design utilizing the phase invariant ofphonon band of PnC.
2. Acoustic Metasurfaces
Recent attention on the metasurface has begun in
the context of the generalization of Snell’s law [6]applied to controlling light reflection/refraction on asurface by introducing phase discontinuities induced
resonantly by plasmonic nanostructures fabricatedartificially on the surface. As acoustic waves also
follow the generalized Snell’s law, the concept canbe allied to tailor wavefront on sound-wave
refraction, as schematically illustrated in Fig.1.
Modulation of the sound with longer wavelengththan the thickness of the metamaterial is realized, forexample, by tuning of the material’s impedance
through resonators built in the structure and its
nonuniform distribution [7]. Among the various
attempts to realize such exotic acoustic properties,
nearly perfect sound absorbers based on acoustic
metasurfaces have been attracting much attention asa simple yet powerful concept to design new acoustic
devices for practical applications such as noise
shielding. Different from conventional soundabsorbers, which rely on materials loss and/or theinterference with transmitting and reflecting waves,the metasurface utilizes strong wave-matterinteraction of resonators to produce perfect
impedance matching at the interface as well as strongloss in the thin structure.

Fig. 1. Schematic of an acoustic metasurface with awavefront controllability for an incident wave.

Fig. 2 Absorption spectrum of dual circular DMR
model and their resonance mode at peaks 698Hz,922Hz, and1254Hz.

As an example, the Decorated Membrane
Resonators (DMR) have demonstrated such uniqueproperties [8]. The high sound absorption occurs
when the membrane and air layer vibrate to dissipate
sound energy as heat. The high efficiency for soundabsorption of the DMR is achieved by thehybridization of vibration modes in the membrane
and the backing air layer in the DMR, whose
effective impedance can be expressed as 𝑍
𝑍 , where 𝑍𝑀 and 𝑍 are the impedance of𝑍
the membrane and that of the air layer in the DMR,
respectively.
In spite of the nearly 100% sound absorption at theresonance frequency of the DMR, the very narrowspectrum hampers to apply the design concept topractical sound insulations. We have recently
proposed a novel metasurface structure which canexhibit broader absorption spectra [9]. Our approachis based on the multiplication of membrane modes
by simply introducing an asymmetry in themembrane shape. Figure 2 shows designed
structures with dual circular shape of the membrane
along with its absorption spectrum obtained by anumerical simulation. The results show multiplexing
and broadening of the absorption peak with a single
DMR structure.
3. Topological Phononics
The discoveries of the quantum Hall effect andtopological insulators have stimulated the search foranalogous topological states in classical systems
such as light, sound, and mechanical waves.
Topological invariance in dispersion curves drawn in
the reciprocal space is hold also in the classicalsystems.

Fig. 3 Schematics of topological phase transition inphononic band and an edge mode generated at theinterface between bands with different phases (C).
The acoustic topological insulator has two
different topologies near the band gap in its
dispersion characteristics, and there exists a band
which shows the phase transition of the band
topology via the continuous change of the structure.
Figure 3 illustrates a schematic of topological phasetransition in phononic bands and localized
propagation modes (edge modes) generated at theinterface between bands with different phases.
Transmission characteristic with very small loss isobtained due to the propagation through this
topologically protected state. We have applied thisconcept to the topological acoustic waveguidedesign by the phononic structure in water and havedemonstrated numerically and experimentally thatrobust wave transmission, i.e., immune tobackscattering by defects and/or corners in thewaveguide, is possible even in the waveguides withcomplex propagation paths as long as the edge modeis properly excited in the paths [10].
Recently, further attempts have been made tocontrol elastic waves at ultra-high frequency regime(GHz) in thin films with phononic crystals [5,11,12].
In the presentation, I will discuss an extension of the
topological physics approach to elastic waves in thinfilms, such as those depicted in Fig.4 [13].

Fig. 4 Out-of-plane displacement in a membrane
topological phononic waveguide for the elasticwave propagation (a) at 1.926 GHz and (b) at 2.69
GHz via a finite-element simulation.
Acknowledgment
I am grateful for helpful discussions, guidance,and collaborative works related to this study
provided by collaborators (mainly in USE
participants), namely, Profs. Osamu Matsuda,
Masaaki Misawa, Keiji Sakai, Motonobu Tomoda,
Oliver B. Wright, Ken Yamamoto, and Drs. DaikiHatanaka, Atsushi Ishikawa, Hiroshi Yamaguchi, as
well as present/former graduate students in Okayama
Univ. This work was supported in part by the JSPS
KAKENHI Grant Numbers JP21H05020 andJP21K18877.
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