near field power density formula for a dipole antenna
It is accepted that an EM wave doesn't properly form in the near field because the E and H fields are not properly aligned. Therefore you cannot consider a near field signal as a power. Here's a simple illustration: -



As for trying to understand or predict the E and H fields closeby, this is quite difficult. Here is an article from wiki that might help you understand. Here is an extract concerning the near field: -


  Near-field diffraction
  
  In contrast to the far-field, the diffraction pattern in the
  near-field typically differs significantly from that observed at
  infinity and varies with distance from the source. In the near-field,
  the relationship between E and H becomes very complex. Also, unlike
  the far-field where electromagnetic waves are usually characterized by
  a single polarization type (horizontal, vertical, circular, or
  elliptical), all four polarization types can be present in the
  near-field. The "near-field" is a region in which there are strong
  inductive and capacitive effects from the currents and charges in the
  antenna that cause electromagnetic components that do not behave like
  far-field radiation. These effects decrease in power far more quickly
  with distance than do the far-field radiation effects. Non-propagating
  (or evanescent) fields extinguish very rapidly with distance, which
  makes their effects almost exclusively felt in the near-field region.
  Also, in the part of the near-field closest to the antenna (called the
  "reactive near-field", see below), absorption of electromagnetic power
  in the region by a second device has effects that feed-back to the
  transmitter, increasing the load on the transmitter that feeds the
  antenna by decreasing the antenna impedance that the transmitter
  "sees". Thus, the transmitter can sense when power is being absorbed
  in the closest near-field zone (by a second antenna or some other
  object) and is forced to supply extra power to its antenna, and to
  draw extra power from its own power supply, whereas if no power is
  being absorbed there, the transmitter does not have to supply extra
  power.