3Pa1-3
Higher-order Band Control and Topological Elastic Waveguide
Design using Resonant-type Phononic Crystals
Yuito Ohashi† , Motoki Kataoka, Hiroaki Takeshita, Masaaki Misawa,and Kenji Tsuruta* (Grad. School Nat Sci. & Technol., Okayama Univ)
1. Introduction
Recently, phononic crystals have attracted attention
as a method for controlling sound waves. Phononic
crystal [1-5] is a periodic structure of different
elastic materials, and its phonon dispersion has thebandgap that prohibits sound propagation in thecrystal. Phononic crystal has been applied fordesigning acoustic lenses, waveguides, andmodulators in wide frequency ranges. However, theconventional phononic crystal waveguides sufferfrom large transmission loss at curved portions in
the waveguide paths. In this study, we focused on
topological acoustic waveguides, which exhibit
highly robust wave propagation against defects andcorners. A topological acoustic waveguide [6] has
the characteristics of a conductor at the boundary
and an insulator in the interior, similar to a
topological electrical insulator. This is due to theband topology invariance, a common feature in thewave mechanics. The unidirectional transmission ofsound waves and high robustness against
disturbance can be realized through chirality of theedge state which emerges at the boundary between
bands with different band topologies. Althoughmany phononic structures have been proposed inrecent years, not many investigations on the controlof the higher-order band gap have been reported.
The boundary surface state can be changed bymodulating the edge state through resonancestructures [6]. As a result, it is possible to realize
robust topological valley transport along apredetermined path with high controllability overthe desired frequency band. In this study, we
numerically designed a topological phononicstructure with an internal resonance structure tocontrol the higher-order band gap and to achieve
efficient sound wave propagation.

that maximizes the second-order bandgap wassearched by changing structural parameters, i.e., a, b,c, and d in the inset of Fig. 1.

Fig. 1 Dispersion diagram of phononic structure with Yshaped grooved ellipses.

Figure 2 shows the dependence of the bandgap on
the groove width (d) of the hollow elliptical column.
The optimum structure, which has larger band gap
with different band topologies at the upper and lower
edges of the band gap, was searched by changing d as
well as other structural parameters. By constructing a
supercell having interfaces between two oppositelyoriented crystals of the optimized structure, weconfirmed that a band topology transition occurs inthe second-order bandgap and that edge modes appear
within the gap.
Numerical simulations using the finite element
method confirmed that in the Z-shaped waveguide
formed with the topological interface, as illustrated inFig. 3 an incident acoustic wave propagated with very
little loss (transmittance of approximately 90%) at thecorners of the waveguide.

2. Band Gap Control and Topological Acoustic
Waveguides Design
Figure 1 shows that a crystal structure ofhexagonal lattice of grooved elliptical columns ofstainless steel in water with a period of 2.2 cm
arranged with C3v symmetry forms second-orderbandgap in its dispersion within the ultrasonic range
between 600 and 700 kHz. The optimum structure*Corresponding author:tsuruta@okayama-u.ac.jp

Fig. 2 Dependence of width of the second-order bandgap
on a structural parameter, d.

[5] K. Okuno and K. Tsuruta, Jpn. J. Appl. Phys. 59,SKKA05 (2020).
[6] Y.-F. Tang, B. Liang, J. Yang, J. Yang, and J.-C.
Cheng, Appl. Phys. Express 12, 094002 (2019).

Fig. 3 Numerical simulation of edge mode propagation inZ-shaped waveguide with the interface between two
oppositely oriented phononic structures.

3. Conclusion．
The present study showed that it is possible tocontrol effectively the band gap using the resonant
structure with Y-shaped grooved hollow ellipses
built into a unit cell. The phononic structure wasoptimized by adjusting structural parameters in theresonant structure so that topological edge mode
emerges within the second-order band gap. The
waveguide formed with a topological interface canmake acoustic wave propagate with little
backscattering along the waveguide at a higher-orderedge mode frequency. Currently we are designing athree-dimensional phononic structure toward anexperimental demonstration. In the presentation, wewill report details on the design of a phononicstructure with elastic plates loaded with a pillar
structure as a component resonating at desired
frequencies.
Acknowledgement
This work was supported in part by the JSPS
KAKENHI Grant Numbers 21H05020 and21K18877.
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