2P1-4
Valley vortex edge modes in a phononic crystal at
ultrahigh frequencies
Paul Otsuka1†, Katsuya Nishimata1, Motonobu Tomoda1, Daiki Hatanaka2, Hiroshi
Yamaguchi2, Kenji Tsuruta3, Osamu Matsuda1*, (1Grad. School Eng., Hokkaido Univ.;
2
NTT Basic Laboratories; 3Dept. Electr. Electron. Eng., Okayama Univ.)
1. Introduction
Waveguide modes formed by defects inphononic crystals have been well studied
experimentally and numerically. While they havebeen shown to be effective in guiding acoustic waves,transmission efficiency is limited by scattering at
corners and discontinuities.1,2)
By appropriate choice of unit cell, phononic
crystals can form topological insulators, which
support robust one-way propagation along interfacesthat are highly resistant to imperfections and bendingof the interface.3,4,5) Such materials undergo a
topological transition in their wavefunction uponsome continuous change in their structure, resulting
in protected edge states at interfaces between
different topological phases, while being insulatorsin their bulk.
A topological phase transition can be producedby the breaking of some symmetry, such as timereversal symmetry or inversion symmetry, in orderto open a band gap at the Dirac points. In analogy
with the Quantum Valley Hall effect, a phasetransition in acoustic materials can be produced bybreaking mirror symmetry, leading to chiral valley
vortex states in the unit cell.3,6) Here we investigate
the mode patterns in a topological phononic crystal
at frequencies up to 500 MHz by performing
numerical simulations and optical measurements ofphonon propagation, particularly the guiding ofbounded edge states. We analyze the mode patterns
and investigate the k-space behavior by Fourier
analysis.
2. Sample
We investigate a sample consisting of ahexagonal array of voids in a GaAs slab of 1μm
thickness and unit cell spacing of 3.65 μm. The unit
cell, shown in Fig 1, is a 3-fold symmetric structurewith a central hole of radius 0.90 μm andsurrounding lobes each with a radius of 0.72 μm.
Mirror symmetry is broken by either a +5°(anitclockwise) or −5° (clockwise) rotation of thelobes in each unit cell. An interface between different
topological phases is formed by rotating theE-mail: †paul@eng.hokudai.ac.jp,*omatsuda@eng.hokudai.ac.jp

Fig. 1 Topological phononic crystal structure
consisting of a hexagonal array of lobed holes
with 3-fold symmetry.

Fig. 2
Snapshot of the experimental field
pattern of propagation along an interface(represented by the dashed line) at a frequency of493 MHz. The top (+5°) and bottom (−5°)
regions differ by an in-plane rotation of the unit
cell. The arrow shows the direction ofpropagation.

individual unit cell orientations in different regions
by ±5° with respect to each other. We investigatedvarious arrangements with different boundary
geometries.
3. Experiment
Surface acoustic waves of fixed frequency aregenerated in the samples via one of a set ofelectrically excited interdigital transducers (IDTs) on
different sides of the PC. The accessible frequency
range of the transducers is between 465 MHz and505 MHz. The excited plane waves propagate fromthe IDT to the PC, where, depending on theconditions at the PC boundary, guided modes may beexcited at an internal interface.
The resulting surface motion is probed withperiodic pulses from a mode-locked laser focusedthrough a microscope objective to a spot of ~1 μm
diameter.7) The surface displacements are detectedfrom the reflected beam by an interferometer
together with a lock-in amplifier, which issynchronized with the laser and electrical excitation
by a heterodyne set-up. From the lock-in output wecan extract the amplitude and phase of the surface
motion. A tilting mirror system in the probe beam
path before the objective lens allows twodimensional images to be obtained by scanning theprobe spot over the surface. The imaging results
show the mode patterns at the interface boundaries.
Fig 2 shows an example of a field pattern of a
propagating mode in the structure at 493 MHz, withexcitation from the right-hand side. This frequency
lies in the phononic crystal band gap. The image
shows a complex field pattern confined to thevicinity of the interface.
4. Simulation
We performed numerical time-domain
simulations to investigate the patterns of the
propagating modes at the interface boundaries. A
three-dimensional model of an array of unit cells wasarranged with an interface bounded by regions ofunit cells of +5° on one side and −5° on the other.
Excitation was by a short implosive pulse, producing
a broadband frequency distribution centered on~490 MHz. The results are found to be consistent
with the experimental result.
5. Conclusion
We performed numerical and experimental
imaging measurements of valley vortex edge modes
in a micron-scale topological phononic crystal at
ultrahigh frequencies. The results demonstraterobust propagation in different waveguideconfigurations and help to elucidate the dynamics ofthe propagating modes. The results should help guidethe development of topological phononic crystal
designs for high frequency applications.
Acknowledgment
We acknowledge Grants-in-Aid for Scientific
Research from the Ministry of Education, Culture,Sports, Science and Technology (MEXT). This work
was supported by JSPS KAKENHI Grant Number
JP21H05020.
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