The Incremental Far Field and Degrees of Freedom of the Sinusoidal Current Filament

From where radiation originates for a specified current source or PEC boundary seems not to be as well-understood or agreed-upon as many other aspects of electromagnetics. Two propositions are explored in this article that relate to this issue. One is that if some incremental portion of a source distribution increases (changes) the total far field at any observation angle, then by definition radiation originates from that portion of the source distribution. The other is that the greater the number of degrees of freedom in a radiation pattern, the greater will be the proportion of the source distribution that actually radiates. These issues are explored here in terms of the radiation from a sinusoidal current filament.