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Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Electromagnetism --- Stochastic control theory. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Control theory --- Stochastic processes --- Mathematics. --- AtkinsonЗilcox expansion theorem. --- Beltrami fields. --- Faedo-Galerkin approach. --- Herglotz wave functions. --- Hilbert Uniqueness method. --- Maxwell equations. --- Maxwell operator. --- PDEs. --- applied mathematics. --- auxiliary elliptic problems. --- boundary controllability. --- boundary integral equation. --- boundary value problem. --- chiral material. --- chiral media. --- chirality. --- compact embeddings. --- complex electromagnetic media. --- complex media. --- constitutive relations. --- controllability problem. --- controllability. --- decompositions. --- differential equations. --- dispersive media. --- dyadics. --- eigenvalue problems. --- electric flux density. --- electrical engineering. --- electromagnetic complex media. --- electromagnetic fields. --- electromagnetic media. --- electromagnetic wave scattering. --- electromagnetic waves. --- electromagnetics. --- evolution family approach. --- evolution operators. --- evolution problems. --- exterior problems. --- finite-dimensional space. --- fixed point approach. --- frequency. --- function spaces. --- general scattering theorem. --- generalised integral transforms. --- geometry. --- handedness. --- homogenisation problem. --- homogenisation. --- homogenised media. --- homogenised system. --- infinite Frchet differentiability. --- integrodifferential equations. --- integrodifferential evolution equation. --- interior domain problem. --- magnetic flux density. --- mathematical modelling. --- mathematical theory. --- nonlinear PDEs. --- nonlinear model. --- nonlinear phenomena. --- nonlinear problems. --- nonlinearity. --- operators. --- optical theorem. --- penetrable obstacle. --- perfectly conducting obstacle. --- periodic media. --- physics. --- plane electromagnetic waves. --- reciprocity principle. --- scattering problems. --- scattering process. --- scattering theories. --- scattering theory. --- semigroup approach. --- semigroup arguments. --- semigroup-based approach. --- solvability. --- spaces. --- spectral theory. --- standard differential. --- stochastic integrodifferential equations. --- time domain. --- time-harmonic electromagnetic wave. --- time-harmonic problems. --- time. --- trace operators. --- two-scale expansion. --- variational formulation. --- vector analysis. --- wave motions. --- wave operators. --- well posedness.