Preface -- Contents -- 1 Introduction -- Part I: Acoustic waves in sonic crystals -- 2 Scalar waves in periodic media -- 2.1 Scalar waves in homogeneous media -- 2.1.1 One-dimensional wave propagation -- 2.1.2 Three-dimensional wave propagation -- 2.2 Bloch's theorem -- 2.3 Physical origin of band gaps -- 2.3.1 1D periodic media -- 2.3.2 Two- and three-dimensional cases -- 2.3.3 Local resonance -- 2.4 Lattices, Brillouin zones and the band structure -- 2.4.1 Bravais lattice -- 2.4.2 Primitive cell -- 2.4.3 Reciprocal lattice -- 3 Acoustic waves -- 3.1 Dynamical equations of acoustic waves -- 3.1.1 1D acoustic equations -- 3.1.2 3D acoustic equations -- 3.1.3 Poynting's theorem for acoustic waves -- 3.1.4 Constants of fluids, loss -- 3.2 Reflection and refraction -- 3.3 Finite element modeling of scattering acoustic problems -- 3.3.1 Mesh, finite element space, weak form, problem solving -- 3.3.2 Weak form of the acoustic wave equation -- 3.3.3 Radiation boundary condition -- 3.3.4 Representation of an internal source of waves -- 3.3.5 Perfectly matched layer for monochromatic waves -- 3.3.6 Scattering of an incident plane wave -- 4 Sonic crystals -- 4.1 Modeling of sonic crystals -- 4.1.1 Dynamical equations -- 4.1.2 Plane wave expansion (PWE) method -- 4.1.3 Multiple scattering theory (MST and LMS) -- 4.1.4 Finite-difference time-domain (FDTD) -- 4.1.5 Finite element modeling (FEM) -- 4.1.6 Other methods -- 4.2 2D sonic crystal -- 4.2.1 Rigid cylinders in air -- 4.2.2 Steel cylinders in water -- 4.2.3 Deaf bands and unit cell symmetry -- 4.2.4 Sonic crystal design -- 4.3 3D sonic crystals -- 4.3.1 Air bubbles in water -- 4.3.2 Tungsten carbide beads in water -- 4.A Derivation of PWE equations -- 4.B Some properties of eigenvalue problems -- Part II: Elastic waves in phononic crystals -- 5 Elastic waves.

5.1 Elastodynamic equations -- 5.2 Bulk waves in elastic solids -- 5.3 Piezoelectric media -- 5.4 Bulk waves in piezoelectric media -- 5.5 Reflection and refraction -- 5.6 Plate waves -- 5.7 Surface waves -- 5.A Tensors -- 5.B Modeling bulk, plate, and surface waves with FEM -- 5.B.1 Variational formulation for elastic waves -- 5.B.2 Finite element implementation -- 6 Phononic crystals for bulk elastic waves -- 6.1 Modeling of phononic crystals -- 6.1.1 Dynamical equations -- 6.1.2 Plane wave expansion (PWE) method -- 6.1.3 Finite-difference time-domain method (FDTD) -- 6.1.4 Finite element modeling (FEM) -- 6.2 2D phononic crystals -- 6.2.1 Stiff-in-soft composition -- 6.2.2 Soft-in-stiff composition -- 6.2.3 Solid-void composition -- 6.2.4 Crystals containing anisotropic elastic solids -- 6.2.5 Crystals containing piezoelectric solids -- 6.3 3D phononic crystals -- 7 Phononic crystals for surface and plate waves -- 7.1 Bloch waves of phononic crystal slabs -- 7.1.1 Analysis with FEM -- 7.1.2 Analysis with PWE -- 7.2 Experiments with phononic crystal slabs -- 7.2.1 Holey phononic crystal slab -- 7.2.2 Solid-solid phononic crystal slab -- 7.3 Surface Bloch waves -- 7.3.1 Expansion in partial waves -- 7.3.2 Surface boundary conditions -- 7.3.3 Semi-infinite surface phononic crystals -- 7.3.4 Finite-depth surface phononic crystals -- 7.4 Surface phononic crystals -- Part III: Wave phenomena in phononic crystals -- 8 Coupling of acoustic and elastic waves in phononic crystals -- 8.1 Coupling of acoustic and elastic waves -- 8.2 Sonic crystal of solid inclusions in a fluid -- 8.2.1 Solid rods in water -- 8.2.2 Nylon rods in water -- 8.3 Fluid-filled inclusions in 2D phononic crystals -- 8.3.1 Air holes in 2D phononic crystals -- 8.3.2 Liquid-filled inclusions as sensors -- 8.4 Corrugated surfaces and plates.

9 Evanescent Bloch waves -- 9.1 Evanescent waves and Bloch's theorem -- 9.2 Evanescent Bloch waves of sonic crystals -- 9.2.1 Analysis via the plane wave expansion -- 9.2.2 Finite element modeling -- 9.2.3 Complex band structure -- 9.3 Evanescent Bloch waves of phononic crystals -- 9.3.1 Analysis via the plane wave expansion -- 9.3.2 Analysis via the finite element method -- 9.3.3 Complex band structure -- 9.3.4 Viscoelastic losses -- 9.4 Supercells and defect modes -- 10 Locally-resonant crystals -- 10.1 Local resonance and Fano resonance -- 10.2 1D arrays of resonators grafted on waveguides -- 10.3 Locally-resonant sonic crystals -- 10.4 Locally-resonant phononic crystals -- 10.5 Phononic crystal slab with pillars -- 10.6 Surface phononic crystal of pillars -- 11 Mirrors, waveguides, and cavities -- 11.1 Phononic crystal functions -- 11.2 Mirrors -- 11.3 Defect cavities -- 11.4 Defect waveguides -- 11.4.1 Waveguides in 2D sonic crystals -- 11.4.2 Waveguides in phononic crystal slabs -- 11.4.3 Waveguides in surface phononic crystals -- 11.4.4 Coupled-resonator acoustic waveguides (CRAW) -- 11.4.5 The phononic crystal fiber -- 12 Spatial and temporal dispersion -- 12.1 Dispersion relations -- 12.2 Refractive sonic crystal lenses -- 12.3 Negative refraction in sonic crystals -- 12.4 Collimation -- 12.5 Gradient-index phononic crystals -- 12.6 Negative refraction in phononic crystals -- 12.7 Reflection and refraction at a crystal boundary -- 12.8 Sonic crystal as a diffraction grating -- 12.9 Temporal dispersion and tunneling -- 13 Conclusion -- Bibliography -- Index.