= Matched-load scattering of a Hertzian dipole
{title2=$P_{\rm sca}=P_{\rm load}$}
For a lossless ideal <Hertzian dipole> driven by an incident wave, use its induced open-circuit voltage and its feed impedance $R_{\rm rad}+iX$. A conjugately matched load has impedance $R_{\rm rad}-iX$. The same induced current therefore delivers equal <power> to the load and to <radiation resistance>: $P_{\rm sca}=P_{\rm load}$. The scattered wave has the usual dipole angular pattern. In direction of gain $G$, its scattering cross-section is $G A_{\rm eff}$, since the load receives $S_{\rm inc}A_{\rm eff}$.
This ideal single-mode scattering is not the same as a signal that travels through an already matched antenna port, reflects from a mismatched terminating load, and returns. A zero port reflection coefficient removes that latter echo but does not make the physical dipole invisible to the incident field. Additional structural scattering, ohmic loss or a different load changes the result.
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