PHOTONIC CRYSTAL

Photonic Crystal



Photonic Crystal

Introduction

Phononic crystals are periodic composite materials made from constituents with different densities and acoustic wave velocities. These synthetic materials, which are analogous to photonic crystals for electromagnetic waves, are of growing interest because they can change the way in which sound or ultrasound travels through matter, leading to a number of novel applications. Phononic crystals may be constructed by arranging identical objects [for example, rods in two dimensions (2D) or spheres in three dimensions (3D)] in a regular periodic array or crystal lattice, and embedding these elementary units in a host material or matrix.

Band Gaps

One of the main features of phononic crystals that distinguishes them from uniform materials is the existence of the frequency ranges, known as band gaps, in which acoustic waves cannot propagate. When the gap exists in all directions, it is called a complete band gap, while if there are no modes only in certain directions, the term stop band is used. The effects of periodic structure on wave propagation are most conveniently represented by a band structure plot, where the frequency is plotted as a function of wave vector along different crystal directions (Fig. 1a ). The example shown depicts the band structure, calculated using multiple scattering theory, for a three-dimensional phononic crystal of 0.8-mm-diameter tungsten carbide beads immersed in water. The band structure can be investigated experimentally by measuring the ultrasonic phase velocity as a function of frequency; representative data are shown in Fig. 1a . This phononic crystal has a complete band gap near 1 MHz, at which frequency the spacing between adjacent planes of beads is approximately half the ultrasonic wavelength in water. For the frequencies in the band gap, the transmission coefficient or fraction of the incident wave amplitude that is transmitted through the crystal exhibits a deep minimum (Fig. 1b).

However, in a band gap the transmitted signal is not zero, although there are no propagating modes. The origin of this signal is explained by the tunneling of ultrasound, an effect that is completely analogous to the tunneling of a quantum-mechanical particle through a potential barrier. As a result, the transmission coefficient decreases exponentially with crystal thickness in a band gap, and is thus very small even for thin crystals.

Application to Noise Suppression

The factors that control the width of the band gap are the shapes of the scattering elements, the symmetry of the crystal lattice, and the filling fraction, which is the ratio of the volume occupied by the scatterers to the total volume. One practical example that has been proposed for blocking traffic noise along the edges of a highway is a 2D phononic crystal fence made from an array of solid cylinders in air. Another is the use of locally resonant microstructures to construct compact crystals with band gaps in the audible range.

Applications of Defects

Another promising field with numerous potential applications takes advantage of defects to modify wave transport in phononic crystals. Defects may be any objects breaking the symmetry in the otherwise ...