Contents -- 1 Basic concepts and basic equations -- 1.1 Introduction -- 1.2 Newton's equation and electrical conductivity -- 1.3 Maxwell's equations, fields and potentials -- 1.4 The wave equation and boundary conditions -- 1.5 Hollow metal waveguides -- 1.6 Refraction at a boundary: Snell's law and the Ewald circle construction -- 1.7 Fermat's principle -- 1.8 The optical path and lens design -- 1.9 The effective ε in the presence of a current -- 1.10 Surface waves -- 1.11 Plane wave incident upon a slab -- 1.12 Dipoles -- 1.13 Poynting vector -- 1.14 Radiation resistance -- 1.15 Permittivity and permeability tensors -- 1.16 Polarizability -- 1.17 Working with tensors -- 1.18 Dispersion: forward and backward waves -- 1.19 Mutual impedance and mutual inductance -- 1.20 Kinetic inductance -- 1.21 Four-poles: impedance and chain matrices -- 1.22 Transmission line equations -- 1.23 Waves on four-poles -- 1.24 Scattering coefficients -- 1.25 Fourier transform and the transfer function -- 2 A bird's-eye view of metamaterials -- 2.1 Introduction -- 2.2 Natural and artificial materials -- 2.3 Determination of the effective permittivity/dielectric constant in a natural material -- 2.4 Effective plasma frequency of a wire medium -- 2.5 Resonant elements for metamaterials -- 2.6 Loading the transmission line -- 2.6.1 By resonant magnetic elements in the form of LC circuits -- 2.6.2 By metallic rods -- 2.6.3 By a combination of resonant magnetic elements and metallic rods -- 2.7 Polarizability of a current-carrying resonant loop: radiation damping -- 2.8 Effective permeability -- 2.9 Dispersion equation of magnetoinductive waves derived in terms of dipole interactions -- 2.10 Backward waves and negative refraction -- 2.11 Negative-index materials -- 2.11.1 Do they exist? -- 2.11.2 Terminology -- 2.11.3 Negative-index lenses -- 2.11.4 The flat-lens family.

2.11.5 Experimental results and numerical simulations -- 2.11.6 Derivation of material parameters from reflection and transmission coefficients -- 2.12 The perfect lens -- 2.12.1 Does it exist? -- 2.12.2 The ideal situation, ε[sub(r)] = -1 and μ[sub(r)] = -1 -- 2.12.3 The periodic solution -- 2.12.4 The electrostatic limit: does it exist? -- 2.12.5 Far field versus near field: Veselago's lens versus Pendry's lens -- 2.13 Circuits revisited -- 3 Plasmon-polaritons -- 3.1 Introduction -- 3.2 Bulk polaritons. The Drude model -- 3.3 Surface plasmon-polaritons. Semi-infinite case, TM polarization -- 3.3.1 Dispersion. Surface plasmon wavelength -- 3.3.2 Effect of losses. Propagation length -- 3.3.3 Penetration depth -- 3.3.4 Field distributions in the lossless case -- 3.3.5 Poynting vector: lossless and lossy -- 3.4 Surface plasmon-polaritons on a slab: TM polarization -- 3.4.1 The dispersion equation -- 3.4.2 Field distributions -- 3.4.3 Asymmetric structures -- 3.5 Metal-dielectric-metal and periodic structures -- 3.6 One-dimensional confinement: shells and stripes -- 3.7 SPP for arbitrary ε and μ -- 3.7.1 SPP dispersion equation for a single interface -- 3.7.2 Domains of existence of SPPs for a single interface -- 3.7.3 SPP at a single interface to a metamaterial: various scenarios -- 3.7.4 SPP modes for a slab of a metamaterial -- 4 Small resonators -- 4.1 Introduction -- 4.2 Early designs: a historical review -- 4.3 A roll-call of resonators -- 4.4 A mathematical model and further experimental results -- 4.4.1 Distributed circuits -- 4.4.2 Results -- 4.4.3 A note on higher resonances -- 5 Subwavelength imaging -- 5.1 Introduction -- 5.2 The perfect lens: controversy around the concept -- 5.2.1 Battle of wits -- 5.2.2 Non-integrable fields -- 5.2.3 High spatial frequency cutoff -- 5.3 Near-perfect lens -- 5.3.1 Introduction.

5.3.2 Field quantities in the three regions -- 5.3.3 Effect of losses: Transfer function, cutoff, electrostatic limit -- 5.3.4 Lossless near-perfect lens with ε[sub(r)] ≃ -1, μ[sub(r)] ≃ -1 -- 5.3.5 Near-perfect? Near-sighted! -- 5.3.6 General cutoff frequency relationships -- 5.3.7 Effect of discretization in numerical simulations -- 5.4 Negative-permittivity lens -- 5.4.1 Introduction -- 5.4.2 Dependence on thickness -- 5.4.3 Field variation in the lens -- 5.4.4 Other configurations: compression -- 5.4.5 The electrostatic approximation revisited -- 5.4.6 Experimental results -- 5.5 Multilayer superlens -- 5.6 Magnifying multilayer superlens -- 5.7 Misconceptions -- 6 Phenomena in waveguides -- 6.1 Introduction -- 6.2 Propagation in cutoff waveguides -- 6.3 Filters in coplanar and microstrip waveguides -- 6.4 Tunnelling -- 6.5 Phase shifters -- 6.6 Waveguide couplers -- 6.7 Imaging in two dimensions: transmission-line approach -- 7 Magnetoinductive waves I -- 7.1 Introduction -- 7.2 Dispersion relations -- 7.3 Matching the transmission line -- 7.4 Excitation -- 7.5 Eigenvectors and eigenvalues -- 7.6 Current distributions -- 7.7 Poynting vector -- 7.8 Power in a MI wave -- 7.9 Boundary reflection and transmission -- 7.10 Tailoring the dispersion characteristics: biperiodic lines -- 7.11 Experimental results -- 7.12 Higher-order interactions -- 7.13 Coupled one-dimensional lines -- 7.14 Rotational resonance -- 7.15 Applications -- 7.15.1 Introduction -- 7.15.2 Waveguide components -- 7.15.3 Imaging -- 7.15.4 Detection of nuclear magnetic resonance -- 8 Magnetoinductive waves II -- 8.1 MI waves in two dimensions -- 8.1.1 Introduction -- 8.1.2 Dispersion equation, group velocity, power density -- 8.1.3 Reflection and refraction -- 8.1.4 Excitation by a point source: reflection and diffraction -- 8.1.5 Spatial resonances in hexagonal lattices.

8.1.6 Imaging -- 8.2 MI waves retarded -- 8.2.1 Introduction -- 8.2.2 Dispersion equation -- 8.2.3 The nature of the dispersion equation -- 8.2.4 A 500-element line -- 8.2.5 Conclusions -- 8.3 Non-linear effects in magnetoinductive waves -- 8.3.1 Introduction -- 8.3.2 Phase matching -- 8.3.3 Theoretical formulation of amplification for the single array -- 8.3.4 Theoretical formulation for the coupled arrays -- 8.3.5 MRI detector -- 9 Seven topics in search of a chapter -- 9.1 Introduction -- 9.2 Further imaging mechanisms -- 9.2.1 Parallel sheets consisting of resonant elements -- 9.2.2 Channelling by wire structures -- 9.2.3 Imaging by photonic crystals -- 9.3 Combinations of negative-permittivity and negative-permeability layers -- 9.4 Indefinite media -- 9.5 Gaussian beams and the Goos-Hanchen shift -- 9.6 Waves on nanoparticles -- 9.7 Refractive index close to zero -- 9.7.1 Introduction -- 9.7.2 Wavefront conversion -- 9.7.3 Effect of low phase variation -- 9.8 Invisibility and cloaking -- 10 A historical review -- 10.1 Introduction -- 10.2 Forerunners -- 10.2.1 Effective-medium theory -- 10.2.2 Negative permittivity -- 10.2.3 Negative permeability -- 10.2.4 Plasmon-polaritons -- 10.2.5 Backward waves -- 10.2.6 Theory of periodic structures -- 10.2.7 Resonant elements small relative to the wavelength -- 10.2.8 Chiral materials -- 10.2.9 Faster than light -- 10.2.10 Frequency filters made of periodically arranged resonant elements -- 10.2.11 Slow-wave structures -- 10.2.12 Waves arising from nearest-neighbour interactions -- 10.2.13 Superdirectivity, superresolution, subwavelength focusing and imaging -- 10.2.14 Inverse scattering -- 10.2.15 Bianisotropy -- 10.2.16 Photonic bandgap materials -- 10.2.17 Waves on nanoparticles -- 10.3 ... and the subject went on and flourished... -- A: Acronyms.

B: Field at the centre of a cubical lattice of identical dipoles -- C: Derivation of material parameters from reflection and transmission coefficients -- D: How does surface charge appear in the boundary conditions? -- E: The Brewster wave -- F: The electrostatic limit -- F.1 Single interface -- F.2 Symmetric slab -- G: Alternative derivation of the dispersion equation for SPPs for a dielectric-metal-dielectric structure: presence of a surface charge -- H: Electric dipole moment induced by a magnetic field perpendicular to the plane of the SRR -- I: Average dielectric constants of a multilayer structure -- J: Derivation of mutual inductance between two magnetic dipoles in the presence of retardation -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Z.