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The sound of
silence
Physical Review Letters 88,
104301 (22 February 2002)
Much like electrons in a semiconductor,
photons in a photonic crystal are restricted to
energy bands that are characteristic of the
material's periodic structure. At energies
falling between these bands, photon transmission
is forbidden the material has a photonic
bandgap. This is a seemingly quantum-mechanical
effect, but because its origin is in the wave
nature of quantum particles, similar phenomena
should occur with classical waves. This was
demonstrated for sound waves seven years ago1
using a two-dimensional array of parallel
metallic bars (actually part of a sculpture in
Madrid created by Eusebio Sempere). A 'phononic'
bandgap was found, with acoustic propagation
being largely forbidden for a certain frequency
range.
Writing in Physical Review Letters,
Suxia Yang and colleagues now probe the analogy
further using a three-dimensional array of
scatterers. They reveal a close connection
between classical wave propagation and the
quantum physics of tunnelling in crystalline
environments.
To create their phononic crystal, Yang et
al. used tungsten carbide beads 0.8 mm in
diameter, which they assembled by hand into a
face-centred cubic pattern supported on an
acrylite template. Immersing the entire structure
in water, the team probed how ultrasonic pulses
were transmitted between transducers located on
either side of the crystal. The results show
striking bandgap behaviour (see figure).
Comparison of the Fourier spectra for input and
output pulses for a six-layer sample shows that
the input is gaussian with centre frequency of 1
MHz, but the output has a significant dip around
this frequency, suggesting a gap centred around 1
MHz.
|
Figure
Fourier spectra for an ultrasound
pulse propagating through a six-layer
crystal (input on left, output on right).
The depression in transmitted amplitude
near 1 MHz reflects the acoustic band
gap.|
high-resolution version |
|
The propagation of acoustic waves through a
crystalline environment is an excellent
illustration of classical scattering theory.
Indeed, Yang et al. find their results to
be in good agreement with numerical calculations,
which predict a gap of between 0.8 and 1.2 MHz
caused by destructive interference. Pursuing the
analogy further, Yang et al. also show
that for thinner samples, sound waves at the
forbidden frequencies can traverse the crystal
through a process resembling quantum-mechanical
tunnelling although the underlying physics
is certainly different.
But phononic crystals are not just playthings
for acoustic physicists. As Yang et al. note
in their paper, structures of this kind might be
useful for the design of noise-proof devices or
sound filters.
- Martínez-Sala, R. et
al. Nature 378, 241
(1995).
Ultrasound Tunneling through 3D Phononic Crystals
SUXIA YANG, J. H. PAGE, ZHENGYOU LIU, M. L.
COWAN, C. T. CHAN, AND PING SHENG
We report the study of ultrasound tunneling in 3D
phononic crystals, consisting of fcc arrays of
close-packed tungsten carbide beads in water. The
transmission coefficient, phase velocity, and
group velocity were measured along the [111]
direction, allowing us to systematically
investigate the tunneling of ultrasound at
frequencies in the lowest band gap. Our
experimental data are interpreted using multiple
scattering theory, which provides a good
explanation of our results. The effect of
absorption and the difference between the
tunneling of classical waves and quantum waves
are discussed.
Physical Review Letters 88, 104301
(22 February 2002)
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©2002 The American Physical Society
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