Background in Maxwell’s Electromagnetism and Maxwell’s Equations
This book being devoted to an up-to-date version of electromagnetic scattering theory, Maxwell’s equations constitute the unescapable starting block. An usual attitude in textbooks dealing with scattering theory is to straightaway introduce special Maxwell’s equations which are sufficient to develop the theory when only local, linear, homogeneous, isotropic and stationary media are considered. The reader wanting to adhere to such a point of view could immediately jump to section I.2. To build the house on firmer foundations, section I.1 is nevertheless devoted to a very general setting in order to emphasize assumptions underlying special Maxwell’s equations that we shall have to cope with. It might appear strange to many people that writing Maxwell’s equations in material arbitrary media is still an open problem, but such is the case indeed. Our account of this problem relies on Petit  and Dettwiller .
KeywordsConstitutive Relationship Poynting Vector Gaussian Laser Beam Algebraic Operator Complex Representative
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