1Pa1-3
Reconfigurable Waveguide Design in Valley-TopologicalPhononic Crystal
Md. Shuzon Ali‡, Motoki Kataoka, Masaaki Misawa, and Kenji Tsuruta*(Grad. School Nat. Sci. Eng., Okayama Univ., Japan)
1. Introduction
The reconfigurability of valley phononic
waveguide, as well as its robustness against defects
and bends, is one of the keys to controlling energy
transmittance in highly integrated switchable
acoustic devices. In 2018, Z. Zhang et al. [1]proposed a reconfigurable structure for topologicallyprotected sound propagation by rotating three-legged
unit cells without altering the lattice structure. In thelater year, A. Darabi et al. [2] proposed another typeof reconfigurability in topological elastic-wave
insulator and demonstrated it experimentally. In thepresent study, we focus on continuous translation of
circular rod arrays for local symmetry inversion in aphononic crystal to propose a reconfigurable
waveguide interface, as graphically illustrated in
Fig.1(a) and 1(b). The two-dimensional valley
phononic waveguide based on the two differently
oriented C3v symmetric geometries has exhibited
highly robust immunity as well as high energy
transmittance of acoustic wave via the topologicallyprotected valley edge state [3]. The proposed
structural change leaves a dimer array at the interface
region, which may induce localized mode leading toless energy transfer in the reconfigurable waveguide.
We show, however, that despite the presence of thelocalized mode the reconfigurable straightwaveguide interface can accommodate wave
transmission with the robustness as high as that in
the valley topological phononic waveguide without
the dimers. In addition, the continuous translation ofrod to break the local symmetry can also be applied
for switching on and off the band-gap opening. These
analyses are performed based on finite-element
calculations and simulations by using a general
purpose software package (COMSOL Multiphysics).
2.

Continuous Translation
Symmetry Inversion

forLocal

C3v

We arrange a supercell in which each hexagonalunit cell is composed of three circular rods made ofstainless-steel based on differently oriented C3v
symmetric structures. We have set the lattice
constant a = 2.2 [mm] and the diameter of eachcircular rod d = 0.7 [mm], respectively. The speed of*Corresponding author:tsuruta@okayama-u.ac.jp

sound and mass density of water and stainless-steelrods are 1490[m/s], 1000[kg/m3]; 5780[m/s],7800[kg/m3], respectively. Here, the width andheight of the rectangular super cell are defined as 𝑎and30𝑎√3, respectively. The two pseudo-spin modes

appear near the K point in the supercell’s Brillouin
Zone [Fig. 1(c)]. Both the upper and lower bulk
bands are identical, and the edge states appear
around 310-430 kHz. On the other- hand, when weconstruct a uniform C3v symmetric structure ofrectangular array of the unit cell with the orientation
𝛼 = 30° , no edge mode appears in the frequency
range. By using continuous translation, i.e. shifting
one rod from all layers below an interface, one canconstruct 𝛼 = −30° oriented rod array in the lower
layer.
(a)

(b)

(c)

(d)

Fig.1 (a)Schematic of uniform structure of a rod array ina valley-topological phononic crystal, (b) reconfigurable
structure constructed by continuous translation of a rod
array in the structure illustrated in (a), (c) band diagram
for supercell structures of valley phononic crystal, and (d)that of reconfigurable phononic crystal.

The reconfigured supercell band diagram depicted
in Fig. 1(d) shows that the upper band is regarded asa bulk band, whereas the lower band corresponds toan independent (localized) mode attributed to thepresence of dimer array at the interface. This canimpact not only on the wave transmission due to thelocalization of the mode but also on the band
topology.

3. Reconfigurable Valley-Topological Waveguide
Based on the band-structure design describedabove, we first constructed a valley topologicalwaveguide with rectangular arrays of differently
oriented (𝛼 = 30° and 𝛼 = −30° ) C3v symmetricunit cells made of stainless-steel rods immersed inwater. Fig. 2(a) depicts the waveguide structure
along with the pressure field distribution in the casethat an incident acoustic wave at 400 kHz was input
from the left port region (designated as “input”) andthe transmittance was measured at the region“output”. The figure clearly shows that highly
efficient wave transmission was realized at thefrequency that was aimed from the band-structure
design in the previous section.

with band gap topology via protected edge state
appear around the gap frequency range 350-430 kHz,as shown in Fig. 1(c). Fig. 2(a) shows that theincident wave can transmit efficiently via the edge
state at 400 kHz. Fig. 2(b) shows, on the other hand,slightly degraded pressure field in the waveguidepath. Nevertheless, transmittance for incident wave
around the same frequency range is nearly the sameas in the case of Fig. 2(a). It reveals that even thereis the localized mode present in the path ofreconfigured waveguide interface, the acoustic wave
can still propagate robustly as comparable with an
ideal valley phononic waveguide. This indicates that
acoustic energy transport can be controlled bydesigning the robust reconfigurable waveguideinterface with continuous translation of rods via thetopologically protected edge state. This approachdemonstrates a new practical way to controllingenergy transmission toward robust switchable aswell as reconfigurable device based on continuoustranslation of the unit cell structure for local C3v
symmetry inversion in the valley-topologicalphononic crystals.
Acknowledgement

Fig. 2 (a) Pressure field in valley phononic waveguide at
400 kHz and (b) in the reconfigurable phononic
waveguide.

To show that a topological waveguide can beconstructed by the continuous translation of rod
arrays proposed in the previous section, we firstprepared a rectangular array of unit cells with auniform C3v symmetric structure with single
orientation 𝛼 = 30°. We shifted one rod from each
unit cell in all the layers below an interface by using⃗ = (− 𝑎 , − √3 𝑎 + √3𝑑) .
the translation vector 𝑇22The rod array with orientation 𝛼 = −30° wasthereby created in the lower half layer. The uniform
phononic structure was shown to be reconfigured toa waveguide with an interface between upward anddownward convex with C3v symmetric structure(𝛼 = 30° in upper layer and 𝛼 = −30° in lowerlayer, respectively) as depicted in Fig. 2(b). It should
be noted here that the continuous translation of rod
leaves a dimer array with C2v local symmetry in thewaveguide.
4. Results and Discussion
The wave-transmission phenomena in a
topological phononic structure are closely connected

This work was supported in part by the JSPS
KAKENHI Grant
Numbers 21H05020 and21K18877.
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