By Richard V. Craster, Sébastien Guenneau
About the ebook: This e-book is the 1st complete assessment on acoustic metamaterials; novel fabrics that may manage sound waves in excellent methods, which come with collimation, focusing, cloaking, sonic screening and amazing transmission. It covers either experimental and theoretical elements of acoustic and elastic waves propagating in based composites, with a spotlight on powerful homes linked to detrimental refraction, lensing and cloaking. such a lot comparable books within the box tackle electromagnetic metamaterials and concentrate on numerical tools, and little (or no) experimental part. every one bankruptcy may be authored via an said specialist, among the subjects coated may be experimental effects on non-destructive imaging, cloaking via floor water waves, flexural waves in skinny plates. functions in clinical ultrasound imaging and modeling of metamaterials may be emphasised too. The ebook can function a reference for researchers who desire to construct a superior origin of wave propagation during this category of novel materials.
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Extra resources for Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking
30, 1204–1206 (2005) 19. : Acoustic meta-materials for sound focussing and confinement. New J. Phys. 9, 399 (2007) 20. : Oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres. Proc. R. Soc. Lond. A 459, 2215–2263 (2003) 21. : Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces. C. R. Phys. 10, 352–378 (2009) 22. : Negative refraction in 2d checkerboards related by mirror anti-symmetry and 3d corner lenses.
E. not holey, cross-section as shown in Fig. 13). The rods have a permittivity of εr and they are embedded in a host medium of permittivity εη . 35) where k = 2π/λ = ω/c is the wavenumber in vacuum, with λ the (fixed) wavelength, ω the radian frequency and c the speed of light in vacuum. Here, ε is a piecewise constant function equal to εr inside the rods, to εe in the host medium and to 1 (air) outside the overall structure. In order to derive the effective parameters of the photonic crystal, we assume that the wavelength λ is large with respect to the period d of the crystal and we denote by the small positive parameter η = d/λ.
4. Let us now consider the case of circular inclusions of radius r = R. The eigenfunctions are Bessel functions. e. 69) are Λnm = (χnm /R)2 . These eigenvalues are twice degener± (y) = ate except for n = 0 and the associated normalized eigenfunctions are φnm −1 ± (y) dy = 0 for n = 0, the |πR 2 Jn (χnm )| Jn (rχnm /R) exp(±inθ ). 405. 4 Correspondences Between Zhikov’s Function and Floquet-Bloch Diagrams The aforementioned Zhikov’s functions can be computed numerically for instance with Matlab and depending upon the value of μr , we can see that the effective density takes some negative values near the resonance for the case of circular cylinders, or square inclusions, as shown in Figs.