Near-Field Matching and Universal Limits on Electromagnetic Energy Transfer

This article introduces the concept of near-field (NF) matching as a continuum-mode generalization of port matching in circuit theory suitable for field-theoretic electromagnetic energy transfer scenarios, with a focus on spatio-frequency processes in coupled systems. The concept is rigorously formulated using the full electromagnetic Green's function of a generic receiving surface interacting with arbitrary illumination fields where the Riemannian structure and the electromagnetic boundary condition of the problem are encoded into the tensor structure of a Green's function on a manifold. After a carefully selected combination of proper function spaces for the various field quantities involved, we utilize exact methods to estimate the sizes of various operator quantities using the appropriate function space norms. A field-theoretic measure of power transfer efficiency in generalized NF matching scenarios is introduced, and exact upper bounds on this efficiency are derived using Young's inequality for integral kernel operators. This theoretical study complements and generalizes the largely empirical and problem-specific literature on wireless energy transfer by providing an exact and rigorous mathematical framework that can guide and inform future optimization and design processes.