New Acoustics Based on Metamaterials

WS Gan introduced symmetry properties of the acoustic field in 2007. This has been confirmed by the successful fabrication of the acoustical metamaterials, diverse applications of time reversal acoustics and that phonon is a Goldstone mode. The form invariance of the linear acoustic field equation demonstrates the symmetry properties of acoustic fields. Likewise, form invariance is also applicable to nonlinear acoustic field equations such as Burgers equation, Westervelt equation and Shapiro–Thurstone equation. The symmetry between the acoustic velocity field and stress field is a further demonstration of the symmetry properties of acoustic fields. Symmetry is the theoretical framework of acoustical metamaterials. The propagation of sound waves in fluids obeys both translational and rotational symmetry, whereas propagation of sound waves in solids obeys rotational symmetry but broken translational symmetry due to the discrete and periodic nature of the crystal gives rise to phonons. The scale invariance or symmetry property of the turbulence field also supports the symmetry properties of acoustic fields as turbulence field is intrinsically acoustic field considering that turbulence is the source of the aerodynamic noise.

Negative refraction is not only the consequence of the negative mass density and negative bulk modulus of the acoustical metamaterial but also can produce phononic crystal’s band gap. Acoustical cloaking is an application of the form invariance of the acoustic field equation. It is the first application of sound propagation in curvilinear space-time. It enables the bending and the manipulation of the direction of the sound wave to our requirement. Both negative refraction and acoustical cloaking can be derived from coordinates transformation of the acoustic field equation. In fact, negative refraction is a special case of acoustical cloaking when the value of the determinant of the coordinates transformation equals -1. Negative refraction enables the production of super-resolution lens and acoustical cloaking can be used for shielding objects.

The three basic forms of sound propagation in solids are diffraction, refraction and scattering. Acoustical metamaterials will enable the control and manipulation of these three mechanisms and hence the manipulation of the direction of sound propagation in solids. A detailed description of this three mechanisms for the case of negative mass density and negative bulk modulus enabling negative acoustical metamaterial are given.

Acoustical metamaterials with negative mass density and negative bulk modulus enable negative elasticity and in turn artificial elasticity. This demonstrates the form invariance or symmetry of the acoustic field equation and in turn the symmetry properties of the acoustic fields. An example of an acoustical metamaterial demonstrating artificial elasticity is given.

First, piezoelectricity is explained as an example of second-order phase transition with the spontaneous symmetry electrical polarization and spontaneous symmetry breaking. Artificial piezoelectricity with negative permittivity, negative piezoelectric strain constant and negative piezoelectric stress constant is described. The stiffened Christoffel equation for artificial piezoelectricity is given. Artificial piezoelectricity opens the way for artificial second-order phase transition and control and manipulation of artificial second-order phase transition.

The acoustic diode is an application of metamaterial in the nonlinear acoustics regime. Here, the broken time reversal symmetry is achieved by introducing a nonlinear medium made of nonlinear phononic crystal. The acoustic diode has potential application in acoustical imaging such as medical imaging with the elimination of acoustic disturbances caused by sound waves going in two directions at the same time and interfering with each other. The propagation direction of output wave can be controlled freely and precisely. This enables clearer images.

Energy can be harvested from the heat energy produced by phonon–phonon interaction. Acoustical metamaterial in the form of phononic crystal will be used in the structure of the system for energy harvesting. Here, one needs to design the phononic crystal structure. To enable this, one needs to design the phononic crystal system’s dispersion relation and phonon–phonon interaction in the structure. A classical treatment using continuum medium is used. The thermoelectric efficiency is defined and its relation to the phononic crystal structure is described.

The local resonance in the material was discovered in 2000. Since then, it has been developed as an acoustical metamaterial. The local resonance enables negative mass density and negative bulk modulus. A detailed description of the physics of local resonance is given. This is followed by several applications and even a list of potential areas under the early stage of development is given.

Time reversal acoustics is based on the time reversal symmetry of the acoustic fields. A detailed description of the acoustic field equation showing the time reversal symmetry property of S the solution is given. A geometric structure of a metamaterial for both an electromagnetic wave and acoustic wave is given. Then, the geometric structure of the metamaterial to implement time reversal acoustics is given. Time reversal acoustics has been successfully applied to non-destructive testing, medical ultrasound imaging, and underwater acoustics. The advantage of using metamaterial in time reversal acoustics is that it supports modes which radiate spatial information of the near field of a source efficiently in the far field.

Acoustical cloaking is the first example of sound propagation in curvilinear spacetime. Previous works are concerned only with the application of curvilinear coordinates to describe a stationary object’s geometrical structure. The cloaking of underwater objects is an extension of the cloaking of objects in the air. This is more complex than cloaking in the air. The theory of sound propagation underwater is given. The form invariance of the Westervelt equation is shown. This enables the bending of sound around the object and the shielding of the object underwater. The application to anti-sonar work is described.

The seismic metamaterial is an application of the cloaking of objects to shielding of buildings and large objects from seismic waves. This enables the bending of seismic waves away from the structures. The detailed theory and adaptation to the required situation are given. This is an example of the scaling up the capability of the acoustical metamaterials from nanometre size to building scale.

First, the application of finite amplitude wave to acoustical cloaking is given. This is an extension of coordinate transformations from the linear acoustic field equation to nonlinear acoustic field equation which also shows form invariance. Then, metamaterial is applied to two examples of nonlinear acoustics. First to acoustic radiation force. Metamaterial enables a negative radiation force. Previous work on negative acoustic radiation force has the limitation only to Bessel beam. The second example is to apply to force of levitation. Metamaterial enables the control and manipulation of the force of levitation and allows for the levitation and suspension of larger objects.

First is the introduction to the subject. Then, there are the usual applications to the theory of general relativity. Two examples of applications to acoustical imaging are given: vibrography and elasticity imaging.

An introduction to transport theory and transport properties followed by the discovery that metamaterial is in fact artificial phase transition. Singularity behaviour of the transport properties at the critical point of phase transition is given. Then, there is the use of the transport properties to explore new forms of metamaterials. Metamaterials as artificial phase transition is a breakthrough to a new world of artificial materials.