Zooming into the Near-fields: Embedding Generalized- and Pseudo-functions in the Solution Space of Maxwell's Equations

摘要

In solving Maxwell's equations subject to boundary conditions, simulation of near-field phenomena generally manifests itself as a prohibitively difficult undertaking; in particular, when anisotropic and inhomogeneous material coefficients are involved. Near-fields, being associated with various singularities, have so far defied a unified regularization procedure. In this paper a universal method has been proposed, which offers deep insight into the nature of near-fields. The proposed formal machinery embeds generalized- and pseudo functions in the solution space of Maxwell's equations. Conceptually, the introduced scheme provides a framework for interpreting "sources" in terms of "fields," redefining traditionally perceived roles of "cause" and "effect." Thereby, self-regularization of divergent terms takes place "naturally" without any ad hoc interventions, as it has been customarily the case.