An Introduction to Metamaterials and Waves in Composites: 1st Edition (Hardback) book cover

An Introduction to Metamaterials and Waves in Composites

1st Edition

By Biswajit Banerjee

CRC Press

376 pages | 109 B/W Illus.

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pub: 2011-06-07
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Requiring no advanced knowledge of wave propagation, An Introduction to Metamaterials and Waves in Composites focuses on theoretical aspects of metamaterials, periodic composites, and layered composites. The book gives novices a platform from which they can start exploring the subject in more detail.

After introducing concepts related to elasticity, acoustics, and electrodynamics in media, the text presents plane wave solutions to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the plane wave expansion of sources as well as scattering from curved interfaces, specifically spheres and cylinders. The author then covers electrodynamic, acoustic, and elastodynamic metamaterials. He also describes examples of transformations, aspects of acoustic cloaking, and applications of pentamode materials to acoustic cloaking. With a focus on periodic composites, the text uses the Bloch-Floquet theorem to find the effective behavior of composites in the quasistatic limit, presents the quasistatic equations of elastodynamic and electromagnetic waves, and investigates Brillouin zones and band gaps in periodic structures. The final chapter discusses wave propagation in smoothly varying layered media, anisotropic density of a periodic layered medium, and quasistatic homogenization of laminates.

This book provides a launch pad for research into elastic and acoustic metamaterials. Many of the ideas presented have yet to be realized experimentally—the book encourages readers to explore these ideas and bring them to technological maturity.


… this book provides a thorough and modern introduction to a rapidly developing field of research with enormous potential for application.

—Chris Linton, Contemporary Physics, March 2012

Table of Contents

Elastodynamics, Acoustics, and Electrodynamics

A note about notation




Plane Waves and Interfaces

Plane wave solutions

Plane wave solutions in elastodynamics

Plane wave solutions in acoustics

Plane wave solutions in electrodynamics

Wave propagation through a slab

Sources and Scattering

Plane wave expansion of sources

Single scattering from spheres

Multiple scattering

Electrodynamic Metamaterials

A model for the permittivity of a medium

Negative permittivity materials

Artificial magnetic metamaterials

Negative refraction and perfect lenses

Acoustic and Elastodynamic Metamaterials

Dynamic mass density

Frequency-dependent moment of inertia

Negative elastic moduli

Band gaps, negative index and lenses

Anisotropic density

Willis materials in elastodynamics

A Milton-Willis model material

Extremal materials

Transformation-Based Methods and Cloaking


Cloaking of electrical conductivity

Cloaking for electromagnetism

Inertial acoustic cloaking

Transformation-based cloaking in elastodynamics

Acoustic metafluids and pentamode materials

Waves in Periodic Media

Periodic media and the Bloch condition

Elastodynamics in the quasistatic limit

Electromagnetic waves in the quasistatic limit

Band gap phenomena in periodic composites

Waves in Layered Media

Wave equations in layered media

Piecewise-constant multilayered media

Smoothly varying layered media

Propagator matrix approach

Periodic layered media

Quasistatic homogenization of layered media




About the Author

Biswajit Banerjee works at Industrial Research Limited in Auckland, New Zealand, where he researches and develops elastic wave control and deformation sensing technologies. He was previously a research professor of mechanical engineering and mathematics at the University of Utah.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics
SCIENCE / Solid State Physics