On the Methods of Further Generalization of Nyquist–Shannon sampling theorem

It is shown that the modernized Nyquist-Shannon theorem, which establishes the theoretical limit for the amount of information that can be obtained based on the analysis of a wave field existing in a bounded region of space, may be generalized to the case of vector electromagnetic fields. The proposed approach is based on the proof that it is possible to describe the propagation of electromagnetic waves in free space without using Green's functions (fundamental solutions of the wave equation). This description is constructed based on the correct definition of the spatial frequency spectrum of a monochromatic electromagnetic wave, proposed in this work, and the analysis of its transformations during wave propagation in space. This approach makes it possible to prove that the classical Huygens-Fresnel principle can be brought to a discrete form, as well as to show that an electromagnetic wave converter of arbitrary nature (including those based on metamaterials) can be represented by an equivalent circuit involving discrete elements. The practical applications of the proposed approach are discussed, including the creation of secure communication channels for transmitting commands from an operator to a swarm of Unmanned Aerial Vehicles (UAVs).