Electromagnetic vector potentials in isotropic non-homogeneous materials: mode equivalence and scalarisation

Electromagnetic mode equivalence and mode coupling are considered in the context of a time-domain vector potential formalism valid in a non-homogeneous isotropic lossy medium that may contain sources. General expressions for equivalent mode transformations are derived. The necessary conditions for the field scalarisation (known also as TE/TM decomposition) are outlined. A scalarisation technique based on mode equivalence is proposed and the analysis of transient problems in terms of two scalar functions (a vector potential pair of given orientation) is discussed. The scalar wave potential model and the theory of mode equivalence are illustrated through numerical examples. It is shown that the numerical approaches based on the scalar wave potential analysis offer better accuracy and reduced computational load in comparison with approaches based on direct field analysis.