Electromagnetic energy from a dipole antenna

Looking for references on previously done analytical development of the radiated field very close to a dipole antenna. I am not interested in a spherical coordinate system-based analysis, because that predetermines a certain kind of answer that is only valid when far enough away that the dipole is an oscillating doublet (point source). I want to see the analysis when the separation from the dipole is short relative to the dipole's length. I would like to see this analysis both for a center-fed, tuned half-wave dipole, and an electrically short dipole much smaller than a wavelength. This latter is like a Hertzian dipole, except in close.

This kind of problem should have been worked out decades ago, but all I find in textbooks is the Hertzian treatment, when the point of observation is far enough away from the dipole that it is an oscillating doublet and a spherical coordinate system-based analysis is performed, where the answer is invalid approaching the origin. I want to see what happens when the origin is approached.

• It is usually solved in cylindrical coordinates with the axis along the dipole. Look for near field, since radiated field is by definition far from the antenna. Oct 14 at 6:22