On Poynting's Theorem and Reciprocity Relations for Discontinuous Fields

Poynting's theorem and reciprocity relations are investigated, based on the postulate that Maxwell's equations are always valid in the sense of distributions. Three special cases of practical importance in which the fields possess bounded discontinuities on simple (nonmaterial) and material interfaces between two different media are rigorously examined, incorporating the basic properties of the Heaviside unit step function and the Dirac delta distribution for multiple variables.