Roy Lewallen wrote in
:

The time phase angle between E and H is determined by the medium the
wave is propagating through. The (complex) ratio of E to H is called
the intrinsic impedance of the medium, and for lossless media, it's
always a purely real number (about 377 ohms for air or free space),
meaning that E and H are in phase. Only when propagating through a
lossy medium are E and H not in time phase, and then the maximum phase
difference is always less than 45 degrees.

If I understand this correctly, a field arrangement with E and H in time
and space quadrature is not propagating energy, but rather energy
exchange.

In very close to an antenna, the time phase relationship of E and H may
be close to quadrature due to the inductive or reactive field close to
the conductors, but that changes eventually to 'in-phase' in the far
radiation field in free space (as the induction field components decay
more quickly with distance than the radiation field components).

If that is the case, the complex value of E/H varies from very close to
the far field. I have seen plots of E/H vs distance that treated E/H as a
real number, but I suspect that it is more complex when all of the
components of E and H are included.

Thoughts?

Owen