Related Experiment Video
Updated: Jun 17, 2026
11:08
Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
Published on: November 30, 2012
Effective velocity of 2D phononic crystals with rectangular lattice
Xiao-Wei Zhou1, Xin-Ye Zou, Tie-Hai Wang
1Key Laboratory of Modern Acoustics, MOE, and Institute of Acoustics, Nanjing University, Nanjing 210093, China.
Ultrasonics
|January 5, 2010
Summary
This study shows that elastic wave velocities in 2D phononic crystals are anisotropic for all modes. Rectangular lattices offer higher anisotropy than square ones, controllable for engineering applications.
Area of Science:
- Materials Science
- Acoustics
- Solid Mechanics
Background:
- Phononic crystals offer tunable wave propagation properties.
- Anisotropy in wave velocity is crucial for advanced material design.
- Understanding elastic wave behavior in different lattice structures is essential.
Purpose of the Study:
- To investigate the effective velocity of elastic waves in 2D phononic crystals with a rectangular lattice.
- To analyze the anisotropy and symmetry of slowness curves for all three elastic wave modes (L, SV, SH).
- To explore the influence of filling fraction, lattice geometry, and material contrast on wave velocity anisotropy.
Main Methods:
- Numerical simulations were employed to study elastic wave propagation.
- The long-wavelength limit was considered for effective velocity calculations.
- Systematic variation of parameters like filling fraction and lattice dimensions was performed.
Main Results:
- Effective velocities for in-plane (L, SV) and out-of-plane (SH) modes exhibit distinct anisotropy.
- Slowness curves for all modes display twofold symmetry.
- Anisotropy increases with filling fraction and decreasing width-to-length ratio.
- Rectangular lattices demonstrate significantly higher anisotropy compared to square lattices for identical materials.
Conclusions:
- The effective elastic wave velocity in 2D phononic crystals is highly anisotropic.
- Rectangular lattices provide a pathway to achieve high anisotropy, exceeding that of square lattices.
- The observed anisotropy is controllable through lattice design and material selection, offering engineering potential.
More Related Videos
10:35Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
13:02Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation
Published on: February 25, 2017
Related Concept Videos
01:28Standing Waves in a Cavity
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
01:27Lattice Energies of Ionic Crystals
Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
01:29Determination of Crystal Structures
In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
02:33Lattice Centering and Coordination Number
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Types of Unit Cells
Imagine taking a large number of identical...
01:18Unit Cells
A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...
00:51Speed of Sound in Solids and Liquids
Most solids and liquids are incompressible—their densities remain constant throughout. In the presence of an external force, the molecules tend to restore to their original positions, which is only possible because the constituents interact. The interactions help the constituents pass on information about external disturbances, like sound waves. Therefore, sound waves travel faster through these media. Compared to solids, the constituents in a liquid are less tightly bound. Thus, sound waves...