A Random Field Theory of Electromagnetic Information

As a rigorous and comprehensive foundation for electromagnetic information theory (EIT), we develop a general theory that elucidates the universal stochastic structure of radiated electromagnetic (EM) fields and induced currents in generic EM information transmission systems. The framework encompasses arbitrary random scatterers, input information fields, and EM mutual coupling. The system is modeled as a multiply connected, arbitrary Riemannian manifold within the language of differential geometry. Our approach exploits exact Green's functions (GFs) on manifolds to construct a novel electromagnetic random field theory (EM-RFT). Interpreted as response functions localized on the surfaces of transceivers and scatterers, the GFs allow us to treat the internal physical details of the EM system as a black box, redirecting analytical attention toward external input-output relations in line with signal processing and communication theory. This integration of random fields (RFs), electromagnetics, and GFs yields a unified framework for deriving and characterizing the stochastic structure of arbitrary EM information transmission systems. We rigorously establish that EM random fields satisfying Maxwell's equations can always be constructed using system GFs driven by external information fields. The theory further decouples stochastic input RFs from random fluctuations associated with the communication medium (e.g., scatterers), and introduces general correlation propagators valid for arbitrary EM links. Using the Karhunen-Loève expansion, all EM random fields are represented as sums of random variables, providing both a simulation framework for arbitrary EM RFs and a basis for evaluating mutual information between input and output spatial domains at arbitrary locations in the system.