Cecil, W5DXP wrote:
"Assuming the source signal is a pure sine wave, if the standing wave
current "isn`t in general sinusoidally shaped (as Roy said)", then the
antenna would have to be introducing harmonic radiation that doesn`t
exist in the source signal."

Standing waves are produced by forward and reflected traveling
soinusoidal waves produced by the same generator. Coherent signals on a
transmission line and antenna of the same frequency are correctly
represented by phasors.

The term phasor is preferred over vector for an arrow which indicates
phase separation and magnitude of an electrical unit. Phasors are used
to represent sinusoidal voltages and currents. They are also used to
represent reactances and impedances.

Like vectors, phasors can be "added" by the head-to-tail method or by
the component method.

If a phasor represents an alternating current:
I = Io cos omega t,
then the sum of the two phasors representing forward and reflected
sinusoidal components is another sinusoid of the same frequency.

Point is the components are amenable to phasor representation. All the
old authors do it. This amenability is proof the standing wave is a
sinusoid too.

Best regards, Richard Harrison, KB5WZI