Electromagnetic Heterostructures

Part 1. Elementary concepts and definitions Chapter 1.1 Maxwell equations and basic electromagnetic theory Chapter 1.2 Polarization in a static electric field Chapter 1.3 Polarization and permittivity in an alternating electric field Part 2. Analytical approaches Chapter 2.1 Prelude: A historical examination Chapter 2.2 Some preliminary considerations Chapter 2.3 Mixing laws Chapter 2.4 Effective-medium approximation: its basis and formulation Chapter 2.5 Bounds for the homogenization of dielectric composite materials Chapter 2.6 Percolation: Crossing the great divide of bulk heterogeneous matter Chapter 2.7 Reciprocity relations and extensions Part 3. Computational approaches Chapter 3.1 Some preliminary considerations: the problem in context Chapter 3.2 Finite differences method Chapter 3.3 Finite-difference time-domain propagation Chapter 3.4 Finite element method Chapter 3.5 Integral equation approaches Chapter 3.6 Monte Carlo method Chapter 3.7 Other selected methods Appendices: Section 1: Appendix 1A: Analogy between magnetism, thermal conduction, diffusion, flow in a porous medium, and electrostatics Appendix 1B: Maxwell stress tensor and electrostatic force acting on an isolated body in an electric field Appendix 1C: Electric dipole and polarizability Appendix 1D: Solving Laplace’s equation for the CS spherical model Appendix 1E: Electric modulus Appendix 1F: Mie theory, quasistatic approximation, and discrete dipole approximation for calculating the optical properties of particles Section 2: Appendix 2A: Microstructure characterization and statistical descriptors Appendix 2B: Percus-Yevick integral equation Appendix 2C: Selected mixing laws Appendix 2D: Herglotz function, sum rules, and bounds on the effective permittivity Appendix 2E: Incremental MG formalism for homogenizing particulate composite media