Localized electromagnetic fields in nondispersive media. I

Summary form only given. The authors presented a direct scattering theory for localized electromagnetic fields in three dimensions. Many localized solutions to the 3-D time-dependent wave equation can be derived from group-theoretical considerations. These solutions can be generalized to the vector wave equation to obtain solutions to the classical electromagnetic field equations. The authors related such solutions to Maxwell´s equations to the long-standing problem of finding an adequate linear wave formalism to describe relativistic particles. In particular, vector fields satisfying E=h omega and phk simultaneously were derived and related to the directive model of atomic radiation, without recourse to nonlinearities to explain the localization phenomenon. Engineering applications derived from this approach include the synthesis of miniaturized superdirective antennas, and the launching of electromagnetic waves that can approximate with arbitrary precision the localization properties of particles in free space and in linear dispersive media.<>