Phononic crystals and acoustic metamaterials

The optical characteristics and applications of the quasicrystal, a special form of aperiodic engineered structure, are explored in this Review article.

Optics of photonic quasicrystals

In this Letter we propose the use of hypersonic phononic crystals to control the emission and propagation of high frequency phonons. We report the fabrication of high quality, single crystalline hypersonic crystals using interference lithography and show that direct measurement of their phononic band structure is possible with Brillouin light scattering. Numerical calculations are employed to explain the nature of the observed propagation modes. This work lays the foundation for experimental studies of hypersonic crystals and, more generally, phonon-dependent processes in nanostructures.

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Hypersonic phononic crystals.

We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.

https://iopscience.iop.org/article/10.1088/1367-2630/10/2/023004/pdf

Anisotropic mass density by two-dimensional acoustic metamaterials

In this work we consider the role of aperiodic order-order without periodicity-in the design of different optical devices in one, two and three dimensions. To this end, we will first study devices based on aperiodic multilayered structures. In many instances the recourse to Fibonacci, Thue-Morse or fractal arrangements of layers results in improved optical properties compared with their periodic counterparts. On this basis, the possibility of constructing optical devices based on a modular design of the multilayered structure, where periodic and quasiperiodic subunits are properly mixed, is analyzed, illustrating how this additional degree of freedom enhances the optical performance in some specific applications. This line of thought can be naturally extended to aperiodic arrangements of optical elements, such as nanospheres or dielectric rods in the plane, as well as to three-dimensional photonic quasicrystals based on polymer materials. In this way, plentiful possibilities for new tailored materials naturally appear, generally following suitable optimization algorithms. Then, we present a detailed discussion on the physical properties supporting the preferential use of aperiodic devices in a number of optical applications, opening new avenues for technological innovation. Finally we suggest some related emerging topics that deserve some attention in the years to come.

https://iopscience.iop.org/article/10.1088/0034-4885/75/3/036502/pdf

Exploiting aperiodic designs in nanophotonic devices

We study the transmission properties of light through the Fibonacci-class quasiperiodic multilayers. The trace map of the propagation matrices, its invariant of motion, and the expression for the transmission coefficient are obtained. For the normal incidence of light, the transmission coefficient exhibits a switchlike property in a family of the Fibonacci-class multilayers, while a six-cycle feature in another family is found.

Transmission properties of light through the Fibonacci-class multilayers

An efficient numerical method is developed to calculate the transmission coefficient of the phononic crystals. By this method, the transmission properties of a two-dimensional phononic crystals constructed by the rectangle elastic isotropic lead rods embedded in uniform epoxy is investigated as an example. The transmission spectrum of the system is in excellent agreement with the band structure for the incident waves including both longitudinal and transverse polarized waves, The transmission spectra of the in-plane oblique incident waves are also calculated and discussed.

Calculational method to study the transmission properties of phononic crystals

The physical origin that the plane wave expansion method fails to deal with the fluid/solid phononic crystals is presented. We find that the Bloch theorem is singular in some areas of this kind of system. The unphysical flat bands which appear in the band structure of the fluid/solid systems resulted from the plane wave expansion method can be gotten rid of only when the singularity is removed. As an example, an effective method is presented to calculate the band structure and transmission spectrum of the air/rigid system, in which how to correctly use the Bloch theorem in such kind of systems is shown.

Singularity of the Bloch theorem in the fluid/solid phononic crystal

The effective acoustic velocity along two highly symmetric directions of the first Brillouin zone is studied in a two-dimensional squarely arranged solid-solid phononic crystal. The relationship between the effective elastic velocity and the wave frequency of the two lowest bands is presented, which gives the same results as those obtained directly from the band structure. Numerical calculations show that the effective acoustic velocity of the phononic crystal decreases with frequency increasing from zero to the band edge.

Xiujun Fu

Papers

Transmission properties of light through the Fibonacci-class multilayers

Calculational method to study the transmission properties of phononic crystals

Singularity of the Bloch theorem in the fluid/solid phononic crystal

Effective elastic parameters of the two-dimensional phononic crystal.

Spectral structure of two-dimensional Fibonacci quasilattices.