Degrees of Freedom and Sampling Representation of Electromagnetic Fields: Concepts and applications

This article reviews the development of the concept of the number of degrees of freedom (DOF), or NDF, of radiated or scattered fields and of optimized sampling expansions for their adequate representation, highlighting their impact on the amount of information that a communication system exploiting electromagnetic fields can transmit. After summarizing and discussing the concept of DOF and its relationship with the mathematical properties of the radiated fields, the concept of spatial bandwidth of the electromagnetic field is reviewed. Then, the approximation of the field using band-limited functions is discussed, clarifying the convenience of sampling representations and including a new analysis of their redundancy with respect to the NDF. Finally, we provide an updated overview of their application in many fields of practical interest, both in classical areas of applied electromagnetics and in the emerging electromagnetic information theory sector.