Degrees of freedom，sampling，and spatial geometry in electromagnetic information theory

Wireless communication, sensing, and imaging all rely on electromagnetic fields to carry information. As antenna systems move toward extremely large arrays, continuous apertures, and near-field operation, the number of antennas or the dimension of a channel matrix is no longer sufficient to describe their information capability. The central question becomes: under given frequency, aperture, distance, energy, and noise constraints, how many independent electromagnetic modes can be stably distinguished and used? Following the line of“Gabor’s information diagram—Shannon capacity—Wigner phase space—electromagnetic degrees of freedom—three-dimensional apertures”, this article explains the physical connection among degrees of freedom, sampling, and spatial geometry. It emphasizes that degrees of freedom are not port numbers, but usable electromagnetic modes; sampling is not the source of degrees of freedom, but an engineering representation of finite degrees of freedom in continuous fields; three-dimensional antennas or apertures do not break physical limits, but reorganize and access available modes more effectively. The article aims to provide an intuitive picture of how information is carried and extracted by electromagnetic fields.