Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model

Polarization of Acoustic Waves in Two-Dimensional Phononic Crystals Based on Fused Silica

The two-dimensional square-lattice phononic crystal is one of the recently proposed acoustic metamaterials. Strong anisotropic propagation of elastic waves makes the material promising for various potential applications in acoustics and acousto-optics. This paper presents a study of the propagation of elastic waves in two-dimensional phononic crystals based on fused silica. The band structures of a phononic crystal are obtained by solving the wave equation in its variational form by the finite element method. The main phononic crystal acoustic characteristics that are of practical interest in acousto-optics are calculated based on the analysis of the dispersion relations. It is shown that the choice of the phononic crystal geometry makes it possible to control the distributions of both the inverse phase velocities and the energy walk-off angles of acoustic modes. The calculations of the acoustic modes' polarization are in a particular focus. It is demonstrated that under certain conditions, there are exactly three acoustic modes propagating in a phononic crystal, the averaged polarization vectors of which are mutually orthogonal for any directions of the acoustic wave's propagation. It is argued that the acoustic properties of phononic crystals meet the requirements of acousto-optics.

Gradient stretching to produce variable aspect ratio colloidal ellipsoids

Developing reliable synthetic methods for producing shape-anisotropic polymer colloids is essential for their use in novel functional materials. In designing such materials from ellipsoidal particles, it is often necessary to screen a wide range of particle sizes and aspect ratios to appropriately understand how microscopic particle characteristics dictate macroscopic material response. Here, we describe a technique to simultaneously produce a broad range of aspect ratio polymer ellipsoid samples from a single synthetic step. The technique extends the traditional film-stretching approach to create ellipsoids by introducing a gradient in strain and film cooling, which results in varying degrees of particle stretching. We empirically calibrate the device such that the final particle elongation may be predicted from the film characteristics, enabling the selective harvesting of ellipsoids with desired dimensions and which can be isolated by aspect ratio. The method is applied successfully to a wide range of seed particle diameters (500 nm - 10 μm) and enables the rapid synthesis of variable aspect ratio particles for systematic studies of anisotropic particles.

Topological Optimization of Phononic Crystal Thin Plate by a Genetic Algorithm

Genetic algorithm (GA) is used for the topological optimization of phononic crystal thin plate composed of aluminum and epoxy resin. Plane wave expansion (PWE) method is used for calculations of band gaps. Fourier displacement property is used to calculate the structure function in PWE. The crossover rate and the mutation rate are calculated according to the adaptive GA method. Results indicate that filling rates, symmetry, polymerization degree and material parameters are key factors for design of topological configurations. The relations between the key factors and different topologies are studied in detail.