Potential Formalisms in Electromagnetic-Field Analysis

The theory of electromagnetic (EM) potentials is as old as the Maxwell equations, which treat the field vectors ${\bf{E}}$ and ${\bf{H}}$ directly. Yet the vector and scalar potentials are often regarded as nothing more than an auxiliary mathematical concept, which does not necessarily reflect a physically existing phenomenon. This widely accepted opinion does not have sound theoretical or experimental validation. The EM potentials are as “real” as the field vectors—they describe observable phenomena and play a crucial role in the explanation of light-matter interactions, radiation, and propagation. We discuss the methodological value of the potential formalism in electromagnetism and the advantages of the potential-based computational approaches in EM analysis. The key points of the discussion are supported by examples of the analysis of classical problems such as the radiation from a small dipole and the field propagation in waveguide structures: a waveguide bend and an $H$-plane filter. These examples include animations of the propagation of the EM-field potentials and the respective field vectors.