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An introduction to phononic crystals (5)


Sound behind bars

A perfect mirror

A perfect mirror

Wave traps

Wave traps

A phononic crystal exhibiting a complete band gap is in theory a perfect trap for any wave generated within it. Consequently, if an acoustic source is positioned in the center of a phononic cavity, the emitted energy is trapped forever since it is unable to escape. In practice, however, there will always exist imperfections leading to losses; in addition, since an infinite phononic crystal cannot be handcrafted, the trap cannot be perfect. If the wave source is instead positioned outside the phononic crystal, it will be possible to transfer some acoustic energy to the phononic cavity, via tunneling. This transfer, however, can only occur efficiently for precisely defined frequencies, the resonance frequencies of the phononic cavity. Such an object enabling the selection of a highly pure frequency is a resonator. Acoustic resonators fabricated in quartz crystals are nowadays vastly employed for the fabrication of ultra stable clocks. Time will tell whether phononic crystals can bring a decisive improvement to such clocks through an improvement in the confinement of waves.

The cavity we have just described is in fact a defect of the phononic crystal. By properly choosing the organization of a sequence of defects, it becomes possible to constrain waves to follow a determined path, which is termed a wave guide. Indeed, the waves incident at the entrance of the wave guide have no choice but to follow the direction of the defects, since any other direction is forbidden in the phononic crystal. It thus becomes possible to define relatively arbitrary paths, provided different the waveguide branches always remain separated by a sufficient phononic crystal thickness. Strongly bent wave guides can thus be achieved, together with multiplexing and channel-distribution systems. This possibility opens the path towards phononic circuitry, i.e. the distribution of acoustic energy to multiple points in space. Potential applications are to signal processing for communications but also to the routing of acoustic waves in ultrasound imaging or therapy systems.

Linear phononic wave guide

Linear phononic wave guide

Couped cavity phononic wave guide

Couped cavity phononic wave guide

Bent phononic waveguide

Bent phononic waveguide

Very efficient wave guides can be managed in a phononic crystal. For instance, picture (a) shows the result of the numerical simulation of the propagation of acoustic waves along a rectilinear wave guide created by removing a full line of inclusions. For all frequencies inside a complete band gap, the waves incident at the entrance of the wave guide have no choice but to follow the direction of defects, since all other directions are forbidden within the phononic crystal.
In the example of picture (b), a wave guide has been created by removing only one inclusion every two along a line. In this case, the progression of waves occur by successive coupling from one defect to the next and involves evanescent waves, i.e. waves that exist only in the immediate vicinity of the source that created them and remain attached to it.
It is possible to define a relatively arbitrary path, provided that the different branches are always separated by large enough thickness of phononic crystal. It is for instance possible to achieve strongly bent wave guides, as illustrated by the numerical simulation in picture (c).

Complete band gaps are not the only assets of phononic crystals. As already discussed above, propagation through a phononic crystal is strongly dispersive, and the wave properties depend acutely on both the frequency and the propagation direction. A phononic crystal is thus an artificial material, or a meta material, exhibiting properties that its initial constituents do not possess. By properly choosing the elementary period, it is possible to tune the meta material properties within a large range. Zhang and Liu at the University of Wuhan in Chine, and Yang et al. at the University of Manitoba in Canada have shown in 2004 that artificial acoustic lenses could be designed from this principle. These novel lenses can even involve what is called negative refraction. This unusual refraction property is not displayed by any conventional material; it amounts to the possibility of focusing initially diverging acoustic beams incident on a plane interface.