# An Introduction to Metamaterials and Waves in Composites by Biswajit Banerjee

By Biswajit Banerjee

Requiring no complex wisdom of wave propagation, **An creation to Metamaterials and Waves in Composites** makes a speciality of theoretical elements of metamaterials, periodic composites, and layered composites. The e-book supplies newbies a platform from which they could begin exploring the topic in additional detail.

After introducing innovations regarding elasticity, acoustics, and electrodynamics in media, the textual content offers airplane wave recommendations to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the aircraft wave growth of assets in addition to scattering from curved interfaces, particularly spheres and cylinders. the writer then covers electrodynamic, acoustic, and elastodynamic metamaterials. He additionally describes examples of modifications, features of acoustic cloaking, and purposes of pentamode fabrics to acoustic cloaking. With a spotlight on periodic composites, the textual content makes use of the Bloch-Floquet theorem to discover the powerful habit of composites within the quasistatic restrict, offers the quasistatic equations of elastodynamic and electromagnetic waves, and investigates Brillouin zones and band gaps in periodic buildings. the ultimate bankruptcy discusses wave propagation in easily various layered media, anisotropic density of a periodic layered medium, and quasistatic homogenization of laminates.

This booklet offers a release pad for study into elastic and acoustic metamaterials. a few of the rules awarded have not begun to be discovered experimentally―the ebook encourages readers to discover those principles and produce them to technological maturity.

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**Extra resources for An Introduction to Metamaterials and Waves in Composites**

**Sample text**

64) The quantity ε is called the electrical permittivity of the medium and the ratio ε /ε0 is called the dielectric constant. For a medium that does not have a time-dependent response D(x) = ε (x) · E(x) . ∗ Linearity applies as long as the fields do not become too large. This can be an issue for some metamaterials where large fields are predicted close to resonance. ∗ Note that the assumption that the material is local in space is reasonable for poor conductors but may fail for good conductors or small-scale structures due to Debye screening.

Let us now consider the magnetic flux density produced by a current. A current is a motion of charges and is described by a current density (J). Consider an element of length dl carrying a current J. The Biot-Savart law relates the elemental magnetic flux density (dB) produced at a point x due to the current in the element located at point y and can be expressed as dB = k J dl × (x − y) x−y 3 where k is a constant. In SI units k = µ0 /(4π) where µ0 is the magnetic permeability of free space and has units of henry/m (H/m).

Our approach is based on Jackson (1999) and a detailed exposition of the subject can be found in that text. 1 Governing equations Coulomb’s law of electrostatics is an equation for the force between point charges at rest. If qx and qy are two charges located at the points x and y, the force between the two charges is given by x−y fxy = k qx qy x−y 3 where k is a constant. The electric field is defined at the force per unit charge. Therefore the electric field at a point x due to a charge qy at point y can be expressed as x−y E(x) = k qy .