Download An Introduction to Metamaterials and Waves in Composites by Biswajit Banerjee PDF

By Biswajit Banerjee

Requiring no complex wisdom of wave propagation, An advent to Metamaterials and Waves in Composites makes a speciality of theoretical features of metamaterials, periodic composites, and layered composites. The booklet supplies beginners a platform from which they could commence exploring the topic in additional detail.

After introducing innovations on the topic of 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 enlargement of resources 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 changes, features of acoustic cloaking, and functions 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 potent 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 publication offers a release pad for study into elastic and acoustic metamaterials. the various rules offered haven't begun to be discovered experimentally―the e-book encourages readers to discover those rules and produce them to technological maturity.

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E(x,t) = Re{E(x) e−iωt } ; B(x,t) = Re{B(x) e−iωt } D(x,t) = Re{D(x) e−iωt } ; H(x,t) = Re{H(x) e−iωt } where ω has an infinitesimally small imaginary part. Show that Maxwell’s equations under these conditions can be written as ∇ × E = iω µ (x, ω) · H(x) ; ∇ ·B = 0 ; ∇ × H = −iω ε (x, ω) · E(x) ∇ ·D = 0 . Why does ω need a small imaginary part? Compare these equations with the Fourier transformed form of Maxwell’s equations. 12 Show that the transverse electric (TE) wave equation for a material with anisotropic permeability and permittivity     ε11 0 0 µ11 0 0 µ = µ (x2 , x3 ) ≡  0 µ22 µ23  and ε = ε (x2 , x3 ) ≡  0 ε22 ε23  0 ε23 ε33 0 µ23 µ33 is given by ∇· R ⊥ · M −1 · R T⊥ · ∇ E1 + ω2 ε11 E1 = 0 where ∇ indicates the two-dimensional gradient, and M≡ µ22 µ23 0 1 ; R⊥ ≡ .

Therefore, D(x) = ε 0 · E(x) + i i σ · E(x) = ε · E(x) with ε := ε 0 + σ . ω ω When we discuss electromagnetic metamaterials in Chapter 4 we will see that we get a different relation for the permittivity at high frequencies. 6 TE and TM modes in electromagnetism Let us now consider two important modes of electromagnetic wave propagation: the transverse electric field and transverse magnetic field. These modes are closely analogous to antiplane shear in elastodynamics and to acoustic waves. A transverse electric (TE) field (also called an ‘s’-polarized wave) is a special twodimensional solution of Maxwell’s equations that has the form E1 ≡ E1 (x2 , x3 ) and E2 = E3 = 0 in rectangular Cartesian coordinates.

3 Πe ∂Π + µ ∇ × Πm . ∂t Cartesian and curvilinear coordinates Recall that the curl of a vector expressed in components with respect to a Cartesian basis is given by ∂v j ∇ × v = ei jk ek = eki j v j,i ek ∂xi where ei jk = eki j = e jki = −ek ji = −e jik = −eik j = 1(i = j = k) is the permutation symbol. 69) for media can be expressed as ∂Bk ; ∂t Bi,i = 0 ; eki j E j,i = − ∂Dk + Jk ∂t Di,i = ρ . 77) Di = εi j E j . 70) are Hi = µ−1 ij Bj ; The expression for the curl of the curl of a vector in Cartesian coordinates is ∇ × ∇ × v = empq eqi j v j,ip em .

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