Decomposition of Electromagnetic Potentials in Partial Functions of Dispersive Electrodynamic Lines

The utilization of partial functions, or oscillets, as the basis functions localized in all spatial coordinates, is proposed for the expansion of non-stationary, non-harmonic electromagnetic potentials within lengthy three-dimensional dispersive electrodynamic systems, such as electrodynamic lines (ELs). These functions are derived as linear transformations of the manifold of EL eigenfunctions, aiming to minimize the spatial extension of each oscillet. Emphasis is placed on the adoption of these new functions in electrodynamic and electronic computations, particularly in the optimization of irregular ELs found in various microwave and optical sources, including those with open-ended configurations featuring a continuous spectrum of eigenfunctions. An illustrative example showing the utility of partial functions in the electrodynamic calculation of a longitudinally inhomogeneous EL is provided.