Degrees of Freedom for Radiating Systems

Electromagnetic degrees of freedom are instrumental in antenna design, wireless communications, imaging, and scattering. A large number of degrees of freedom enhance control in antenna design, influencing radiation patterns and directivity, while in communication systems, it links to spatial channels for increased data rates, reliability, and resolution in imaging. The correlation between computed degrees of freedom and physical quantities is not fully understood, prompting a comparison between classical estimates, Weyl’s law, modal expansions, and optimization techniques. In this article, it is shown that the number of degrees of freedom for arbitrarily shaped radiating structures approaches the shadow area measured in squared wavelengths asymptotically as the wavelength decreases.