Cover; Half Title; Title; Copyrights; Contents; Preface; Chapter 1 General Introduction toWeak Spatial Dispersion; 1.1 Natural and Composite Media withWeak Spatial Dispersion; 1.1.1 Chirality; 1.1.2 Artificial Magnetism; 1.1.3 About Non-Local Description of Media with Chirality and Artificial Magnetism; 1.2 Homogenization; 1.2.1 Homogenization in General; 1.2.2 About Bulk Homogenization; 1.2.3 About Homogenization of Interfaces; 1.2.4 How to Apply the Homogenization Model; 1.2.5 About Homogenization of Media withWeak Spatial Dispersion
1.3 Weak Spatial Dispersion versus Strong Spatial Dispersion1.4 Continuity and Locality; 1.4.1 Relations by Kramers and Kronig and Their Violation; 1.4.2 Lorentzian Dispersion of Material Parameters; 1.5 About this Book; 1.5.1 How Our Theory Is Presented; 1.5.2 Peculiarities of Notations in this Book; Chapter 2 Quasi-Static Averaging of Microscopic Fields and the Concept of Bianisotropy; 2.1 View onWeak Spatial Dispersion in the Available Literature; 2.2 Introduction to Quasi-Static Homogenization; 2.3 Classical Derivation of the Clausius-Mossotti-Lorenz-Lorentz Formulas
2.4 CMLL Formulas in Optical Theories2.4.1 Homogenization of Semi-Infinite Crystals; 2.4.2 On the Effect of Surface Polaritons; 2.4.3 On the Impact of Randomness; 2.4.4 A Bit More about the Anisotropy; 2.5 Maxwell Garnett Model for Dielectric and Magneto-Dielectric Composites; 2.5.1 Maxwell Garnett and His Studies of Metal Glasses; 2.5.2 Maxwell Garnett Model for Magneto-Dielectric Composites; 2.6 Bianisotropic Media; 2.6.1 Introduction to Bianisotropy; 2.6.2 Chiral Media, Omega-Media and Their Microwave Realizations; 2.6.3 Magnetoelectric Coupling in Metal Bianisotropic Particles
2.6.4 Maxwell Garnett Model for a Medium with Both Chirality and Artificial Magnetism2.7 Some Restrictions of Our Study Subject; 2.7.1 WhyWe Do Not Consider the Condensed Composites of Complex-Shape Metal Particles; 2.7.2 On Composites of Dielectric Particles; Chapter 3 Multipolar Theory ofWeak Spatial Dispersion; 3.1 Preliminary Speculations; 3.2 Main and Auxiliary Vectors of the Macroscopic Electromagnetic Field; 3.3 Multipole Expansion of the Macroscopic Polarization Current; 3.3.1 Microscopic and Macroscopic Multipole Densities
3.3.2 Attempts to Avoid Multipoles in the Model of Weak Spatial Dispersion3.3.3 On the Advantages of Multipoles; 3.3.4 Multipole Moments; 3.3.5 Polarization Current in Media withWeak Spatial Dispersion; 3.3.6 Electric and Magnetic Polarization Currents; 3.4 Material Equations for Media withWeak Spatial Dispersion; 3.4.1 Non-Covariant Constitutive Equations; 3.4.2 Why Non-Covariant Equations Cannot Be Used in Boundary Problems; 3.4.3 Material Equations Covariant in the First Order of WSD; 3.4.4 Material Equations Covariant in the Second Order ofWSD
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This book presents a modern theory of so-called weak spatial dispersion (WSD) in composite media of optically small inclusions without natural magnetism and optical nonlinearity. WSD manifests in two important phenomena called bianisotropy and artificial magnetism, whose microscopic origin is thoroughly studied in this book. The theory of this book is applicable to the natural media with WSD, such as chiral materials. However, emphasis is given to artificial media, too, with the idea to engineer needed electromagnetic properties. The text describes a homogenization model of effectively continuous media with multipole electromagnetic response, taking into account the interface effects. Another model is developed for so-called metamaterials in which artificial magnetism can be a resonant phenomenon and may result in the violation of Maxwell's boundary conditions and other challenges. The book will hopefully improve the understanding of WSD and help readers to correctly describe and characterize metamaterials.