Two-dimensional Phononic Crystals Research Articles

Absolute band gaps and waveguiding in free standing and supported phononic crystal slabs

Using the finite element method (FEM), we investigate the existence of absolute band gaps and localized modes associated with a guide in thin films of phononic crystals. Two different structures based on two-dimensional (2D) phononic crystals are considered, namely a free standing plate and a plate deposited on a silicon substrate. The 2D phononic crystal is constituted by a square array of cylindrical holes drilled in an active piezoelectric PZT5A matrix. We demonstrate the existence of absolute band gap in the band structure of the phononic crystal plate and, then, the possibility of guided modes inside a linear defect created by removing one row of air holes. In the case of the supported plate, we show the existence of an absolute forbidden band in the plate modes when the thickness of the substrate significantly exceeds the plate thickness.

Frequency degeneracy of acoustic waves in two-dimensional phononic crystals

Degeneracies of acoustic wave spectra in 2D phononic crystals (PC) and PC slabs are studied. A PC structure is constituted of parallel steel rods immersed into water and forming the quadratic lattice. Given the projection kz of the wave vector on the direction of rods, the bulk wave spectrum of the infinite PC is a set of frequency surfaces fi(kx, ky), i = 1,2,..., where kx,y are the components of the wave vector in the plane perpendicular to the rods. An investigation is performed of the shape of frequency surfaces in the vicinity of points (kdx, kdy), where these surfaces fall into contact. In addition, the evolution of the degeneracy with changing rod radius and cross-section shape is examined. Degeneracy in the spectrum of leaky modes propagating along a single waveguide in a PC slab is also investigated.

Waveguiding in supported phononic crystal plates

We investigate, with the help of the finite element method, the existence of absolute band gaps in the band structure of a free-standing phononic crystal plate and of a phononic crystal slab deposited on a substrate. The two-dimensional phononic crystal is constituted by a square array of holes drilled in an active piezoelectric (PZT5A or AlN) matrix. For both matrix materials, an absolute band gap occurs in the band structure of the free-standing plate provided the thickness of the plate is on the order of magnitude of the lattice parameter. When the plate is deposited on a Si substrate, the absolute band gap still remains when the matrix of the phononic crystal is made of PZT5A. The AlN phononic crystal plate losses its gap when supported by the Si substrate. In the case of the PZT5A matrix, we also study the possibility of localized modes associated with a linear defect created by removing one row of air holes in the deposited phononic crystal plate.

Locally resonant phononic crystals with multilayers cylindrical inclusions

Using a Finite Difference Time Domain (FDTD) method, we investigate the formation of band gaps in the audible frequency range with the help of locally resonant two-dimensional (2D) phononic crystals. It is shown that in a phononic crystal in which the cylindrical inclusions are consisting of a hard steel core coated with a soft rubber and the matrix is a solid such as epoxy, the gap associated with the local resonance may become large by increasing the filling factor. We also consider the case of inclusions consisting of a coaxial cylindrical multi-layers consisting of several alternate shells of soft polymer and steel. Then, the former gap is divided into several smaller gaps separated by narrow transmission bands.

The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectricelastomer cylindrical actuator

By calculating the transmission coefficients by finite-element software, the study of thetunable acoustic band gap for two-dimensional (2D) phononic crystals composedof a square array of hollow cylinders in an air background is considered. Theinclusions are a dielectric elastomer cylindrical actuator, which is made of a hollowcylinder sandwiched between two compliant electrodes. By applying a voltagebetween the compliant electrodes, the radial strain of the silicone-made actuator isinvestigated. The acoustic band gaps are changed due to the radial strain of thedielectric elastomer. The frequency range of the dielectric elastomer composite canbe extended by increasing the applied voltage. A tunable acoustic band gap ofthe phononic crystal is realized via the unique character of dielectric elastomer.The calculations also demonstrate that there exists a local stop band within the pass band.With a local stop band gap, 2D phononic crystals may thus serve as an acoustic filter orswitch.

Acoustic Bloch oscillations in a two-dimensional phononic crystal

We report the observation of acoustic Bloch oscillations at megahertz frequency in a two-dimensional phononic crystal. By creating periodically arrayed cavities with a decreasing gradient in width along one direction in the phononic crystal, acoustic Wannier-Stark ladders are created in the frequency domain. The oscillatory motion of an incident Gaussian pulse inside the sample is demonstrated by both simulation and experiment.

Sagittal acoustic waves in phononic crystals:k-dependent polarization

We have studied the polarization states of the sagittal acoustic waves in one- and two-dimensional phononic crystals. Our theoretical results show the continuous variation of the field displacement components when the Bloch wave vector sweeps the Brillouin zone; thus, the vibrational modes of the same dispersion curve $\ensuremath{\omega}(\mathbf{k})$ can have different polarizations. We first present the polarization map of sagittal waves in an epoxy/Sn superlattice. The band polarization---the transverse and longitudinal contributions---is discussed and related to the characteristics of the transmission spectra of a multilayer sample. In addition, we discuss the polarization of the sagittal bands in two-dimensional phononic crystals. We calculated the band polarization for two arrays of cylindrical holes in epoxy which recently were constructed for experimental tests in the hypersonic regime [T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, Phys. Rev. Lett. 94, 115501 (2005)]. As we shall see, the mixed modes can be either predominantly transverse or predominantly longitudinal. For calculations, we have used an energy balance criterion.

Surface acoustic waves in two-dimensional phononic crystals: Dispersion relation and the eigenfield distribution of surface modes

In this paper, we have demonstrated the existence of surface acoustic waves in two-dimensional phononic crystals with fluid matrix, which is composed of a square array of steel cylinders put in air background. By using the supercell method, we investigate the dispersion relation and the eigenfield distribution of surface modes. Surface waves can be easily excited at the surface of a finite size phononic crystal by line source or Gaussian beam placed in or launched from the background medium, and they propagate along the surface with the form of ``beat.'' Taking advantage of these surface modes, we can obtain a highly directional emission wave beam by introducing an appropriate corrugation layer on the surface of a waveguide exit.

SYMMETRY AND COUPLING EFFICIENCY OF THE DEFECT MODES IN TWO-DIMENSIONAL PHONONIC CRYSTALS

We study theoretically the symmetric property and coupling efficiency of the defect modes in a two-dimensional phononic crystal by calculating band structures, field distributions and transmission coefficients of the defect modes. The results show that the point defect could act as a microcavity surrounded by the phononic crystal, and the confining ability of the phononic crystal to the resonant modes strongly depends on the thickness of the phononic crystal. By investigating the transmission spectra, we also find that the defect modes cannot be absolutely excited by the normally incident plane waves. The transmission coefficients are calculated by using the eigen-mode match theory method under the supercell technique, which is applied to the phononic crystals with the defects for the first time.

Dynamics of elastic waves in two-dimensional phononic crystals with chaotic defect

The authors study dynamics of wave function in two-dimensional phononic crystals with different billiard defects. It is found that the elastic wave is localized in the defect region with soft material. The spatial statistical properties of wave function are studied. More strikingly, they find that given the same area, the chaotic billiard contains more energy than the integrable billiards such as rectangular and circular billiards. The dependence of this “chaotic effect” on wave number k is also studied.

Direct observation of a hypersonic band gap in two-dimensional single crystalline phononic structures

Brillouin light scattering is employed to record the phonon dispersion relation of two-dimensional (2D) hypersonic phononic crystals with square lattice plane group p4mm symmetry. The samples are single crystalline arrays of cylindrical holes with a lattice constant of 750nm and 35% porosity patterned in epoxy using interference lithography. The dispersion relation reveals the presence of a phononic band gap between 1.21 and 1.57GHz at the edge of the first Brillouin zone for elastic waves propagating along the [10] direction and conclusively demonstrates a band gap in a single crystalline 2D polymer based phononic structure at hypersonic frequencies.

Time-resolved vibrations of two-dimensional hypersonic phononic crystals

We fabricate e-beam lithographied two-dimensional lattices of nanometric metal cubes of various sizes and lattice parameters. Using ultrafast laser acoustics, we time resolve two kinds of vibrations in such crystals: individual cube vibrations and lower frequencies strongly dependent on the lattice parameter. From complementary experiments and an analytical model, we assign these modes to acoustic collective vibrations (i.e., acoustic phonons) of the artificial crystal. Their unprecedented detection takes advantage of another periodicity effect acting on the optical field.

Larger acoustic band gaps obtained by configurations of rods in two-dimensional phononic crystals

A method is introduced to optimize the acoustic band structures of two-dimensional phononic crystals (PCs). The acoustic band gap (ABG) between any two bands could be maximized by introducing an additional rod at a suitable position in a unit cell. The results also show that the symmetry reduction of the system is more efficient in creating the ABGs except for the first one. This additional rod method will be useful in designing the ABGs of PCs.

Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates

It is shown that it is possible to obtain complete planar phononic bandgaps in square and hexagonal (honeycomb) lattice phononic crystals formed by etching a periodic array of circular holes in a thin silicon plate (or membrane). Also, better bandgap properties are obtained using the hexagonal lattice structure; and, with practical structure sizes, it is possible-to-obtain a gap-to-midgap ratio of 18–35%.

Surface Resonant-States-Enhanced Acoustic Wave Tunneling in Two-Dimensional Phononic Crystals

We show that by placing a metal plate next to a two-dimensional phononic crystal, acoustic waves can tunnel through the combined structure at a specific frequency that lies inside the band gap of the phononic crystal. The enhanced transmission is attributed to the coupling of the input waves with the acoustically resonant states created between the metal plate and the phononic crystal. Experiments are in excellent agreement with the theoretical predictions.

Control analysis of the tunable phononic crystal with electrorheological material

The elastic band structure of a two-dimensional phononic crystal (PC) with electrorheological (ER) material is investigated and the plane-wave-expansion (PWE) method is adopted to solve the problem in this paper. The ER material is used to act as a tunable elastic composite inserts and its material parameter can be changed by the applied electric fields. Variations of the band gaps for the phononic composite system are also calculated with various electric fields and it is found to have a significant effect on the band gaps of the phononic system with ER material inserts. The band gaps of the smart system can be controlled and the acoustic characteristics of the system are also changed by applied different electric fields.

Waveguiding in two-dimensional piezoelectric phononic crystal plates

We investigate the possibility of designing phononic crystal-based devices for telecommunication applications using materials commonly employed in microfabrication. We focus our attention on a phononic crystal made of a square array of cylindrical holes drilled in an active piezoelectric PZT5A matrix. Two different structures are considered, namely, a freestanding phononic crystal plate and a plate deposited on a silicon substrate. The geometrical characteristics of the phononic crystal plates (lattice parameter and thickness) were chosen to ensure the existence of an absolute band gap around 1.5GHz; a common frequency in radio frequency telecommunications. Computations of the dispersion curves of these active structures were conducted with the help of the finite element method. We demonstrate the existence of absolute band gaps in the band structure of the phononic crystal plates and, then, the possibility of guided modes inside a linear defect created by removing one row of air holes in the phononic crystal. In the case of the supported phononic crystal plates, we show the existence of an absolute forbidden band in the plate modes when the thickness of the substrate significantly exceeds the plate thickness. We discuss the conditions to realize waveguiding through a linear defect inside the supported plate. The present work provides evidences that phononic crystal properties can be integrated with existing silicon based microdevice technology.

Surface guided waves in two-dimensional phononic crystals

With FDTD (finite-difference time-domain) calculations we study the acoustic waves propagating in a semi-infinite, two-dimensional (2D) periodic elastic structure, i.e., a 2D phononic crystal, with a flat surface together with a line defect. Specifically we search for the acoustic modes localized near the surface and at the same time confined inside the straight line defect, i.e., the surface guided waves. The surface assumed is perpendicular to the axis of circular cylinders (steel) embedded periodically in a background material (polymer). These surface guided waves found are unstable in general due to the interaction with bulk acoustic waves but can propagate the distances over several hundreds of lattice constants for a certain range of frequencies.

Experimental demonstration of directional acoustic radiation based on two-dimensional phononic crystal band edge states

The authors have experimentally studied the radiation of a point acoustic source placed inside a two-dimensional phononic crystal of square lattice. They show that a highly directional radiation with a half-power angular width of 6° can be achieved when operating at the band edge frequency for the phononic crystal. Such combination of a point source and a phononic crystal may serve as highly directional acoustic source in applications.

Flat superlens by using negative refraction in two-dimensional phononic crystals

We experimentally and theoretically demonstrated a flat superlens by negative refraction imaging for acoustic waves in a two-dimensional phononic crystal. The sample consists of a square array of steel cylinders immersed in water. The dispersion surfaces at the first band for this sample are nearly circular around point M in the first Brillouin zone, which makes the index of the negative refraction for the phononic crystal sample be well defined for all angles of incidence. Both the observed negative refraction behavior and imaging effect are in excellent agreement with numerical simulations by the Multiple Scattering Theory method.