On the relationship between the transmitting and receiving properties of an antenna

The response of a linear, passive antenna in free space to an incident plane wave is related to its far-field radiation in the reverse direction by
\bar{h}^{r}
=
\bar{h}^{t}
. The vector effective height
\bar{h}^{r}
characterizes the voltage across the open-circuit antenna terminals induced by an incident plane-wave field, and the corresponding
\bar{h}^{t}
characterizes the far-field radiation of the antenna when driven by a current injected into the same terminals. This relationship, which is shown to follow from the well-known reciprocity principle, both includes phase and makes mathematically explicit the polarization relation involved in the identity of the transmit and receive patterns of an antenna.