Degrees of Freedom and Characteristic Modes

The number of degrees of freedom is a crucial parameter in many electromagnetic problems. In for example modern communication systems spatial diversity is often employed through multiple beams to enhance capacity and reliability. However, while the degrees of freedom can be computed, their connection to physical quantities is not as easily understood. To address this issue, this paper proposes a scattering-based formulation of characteristic mode analysis that can estimate the degrees of freedom of arbitrarily-shaped objects. The relation between the number of dominant characteristic modes and physical characteristics differs for electrically large and small objects. Specifically, for large objects, it is linked to the average shadow area, while for small objects, it is linked to their average polarizability through the forward scattering sum rule. Therefore, the average shadow area and polarizability are fundamental parameters that provide insight into the number of degrees of freedom for any object. These basic parameters also provide straightforward estimates of the minimum size of a device region required to support a desired number of electromagnetic degrees of freedom across a given spectral response.