The differential radiated power of a sinusoidal filament of electric current

The authors consider a sinusoidal filament of current I(z)=u/sub z/I/sub m/ sin(k(H-|z|)), -H/spl les/z/spl les/H along the z-axis. The time dependence e/sup jwt/ is implicit, u/sub z/ is the unit vector in the z-direction, I/sub m/ is a complex constant, and k is the wavenumber in free space. From their analysis the differential radiated power appears to be identical to the differential input power and there seems to be no z-directed time-average power flow along the filament. The differential radiated power is the time-average power radiated per unit length along the filament. The differential input power is the time-average input power per unit length along the filament. The differential input power is negative for some values of z. The sections of the filament at these values of z absorb power radiated by other sections of the filament.