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An introduction to phononic crystals

Phononic Crystals

While trying to propagate in a periodically structured media, acoustic waves may experience situations in which their way forward is totally forbidden, but they can also be confined or constrained to follow the most complicated routes, on a wavelength scale. These artificial media mimicking the periodical organization of natural crystals could lead to the design of surprising phononic circuits.

Vincent Laude, Abdelkrim Khelif and Sarah Benchabane
MN2S Department, MINANO group

Just try and imagine a little kid playing marbles. He gets tired of his game and starts trying to pile the marbles up. He only selects those which are identical in size and color. Without even being aware of it, our little player has just built a three dimensional periodical structure. This perfect arrangement of identical elements equally distributed in space is actually similar to the perfect arrangement of atoms in a crystal, but for the difference in scale. Now, let us leave our little character to his game and try to imagine a forest inside which all trees are planted following a perfectly periodical arrangement, a forest where the distance between each tree is almost the same. With a little more imagination, assume the diameter of the tree trunks to be almost the same for every tree. You have just figured out a two-dimensional periodical structure. Try now and picture a path in this perfect forest. Someone walking along this path would be surprised to discover that the sounds he hears are distorted by the time they reach him. More precisely, listening to the music played by a nearby orchestra, he would distinctly hear the low tones of cellos or the high tones of violins, but would realize that a full range of the audible spectrum between these two extrema is missing! This apparent attenuation of a certain range of the spectrum is a signature of a band gap for sound, a consequence of the periodical arrangement of trees. Such a forest is an example of what physicists call a phononic crystal.

A sonic sculpture by Eusebio Sempere

A sonic sculpture by Eusebio Sempere

This reproduction of a minimalist sculpture by Eusebio Sempere sits in a park in Madrid, Spain. Though it is older than the phononic crystal concept, it displays some of its characteristic properties. The steel cylinders have a diameter of 2.9 cm and are

An example of a perfectly real but fortuitous phononic crystal is the minimalist sculpture by Eusebio Sempere (1923-1985) sitting in a park in the Spanish capital, Madrid. This sculpture basically is a two-dimensional periodical arrangement of steel tubes. In 1995, Francisco Meseguer and colleagues determined experimentally its aural filtering properties, by disposing microphones around the sculpture. Their measurements showed that attenuation occurs at certain frequencies, a phenomenon that can not be explained by absorption, since the steels tubes are extremely stiff and behave as very efficient scatterers for sound waves. The explanation can be found in the multiple interference of sound waves scattered by the steel tubes. Because of the periodic distribution of the tubes, these interferences can be either constructive or destructive depending on the frequency of the waves. In the case of destructive interferences, physicists speak of forbidden bands, or band gaps, as acoustic waves are strongly attenuated when they travel through the phononic crystal. Moreover, the larger the number of periods, the thicker the phononic crystal, the stronger the attenuation.

The idea that a two- or three-dimensional periodical structuration of a material can act quite strongly on acoustic wave propagation is not that old. Indeed, its birth can arguably be traced back to the beginning of the 1990's, with the publication of papers by Sigalas and Economou at the University of Heraklion in Crete (Greece), and by Kushwaha, Halevi, Dobrzynski and Djafari-Rouhani at the University of Lille in France. The concept of phononic crystal for acoustic waves followed by a few years the analogous concept for photonic crystals (1987) for optical and electromagnetic waves. Photonic and phononic crystals share many analogies, among which the fact that they are both periodical structures acting on the propagation of waves, from a classical physics point of view. In a particle or quantum mechanical description, the phonon is the elementary elastic vibration of matter, as the photon is the elementary particle of light.

In what follows, we will be trying to explain what phononic crystals are and which applications physicists have in mind for them. By describing a hot and permanently evolving research field, we face the risk that our vision will not completely resist the course of time and that some perspectives may remain pure science-fiction. However, the temptation to hold sound behind bars is the strongest!