The Limiting Absorption Principle and Features of Electromagnetic Field Excitation in Weakly Dissipative and Non-Dissipative Media

Physically consistent solutions of Maxwell’s equations for excitation of electromagnetic fields in weakly dissipative and absolutely non-dissipative media are analyzed. The expansion over vector spherical harmonics demonstrates that there is no continuous transition postulated by the limiting absorption principle between physically realizable solutions for dissipative and non-dissipative media. Instead, two solutions change stepwise under switching on/off the medium dissipation. Such solutions’ behaviour explains how the classical theories of radiation in vacuum with electromagnetic fields propagating outward to infinity find agreement with numerous experiments, despite the physical inconsistency of their spatial distributions for the field momentum density. The analysis performed shows that the classical radiation solutions correspond to excitation of electromagnetic fields not in vacuum, as it is commonly thought, but in a weakly absorbing medium. Concerning the nonzero radiant power given by those theories, it appears a consequence of the wrongly defined applicability limits for the obtained solutions and should be corrected by considering the medium dissipation. According to this correction, the true power radiated outward and carried away by the fields from the electrodynamic system appears to be zero.