Above all answers are assuming that the original question is "What is the near field of an antenna?". However, I try to answer the original one.
I'd like to regard some antennas which we take advantage of their near field to transmit power and signal as near field antennas. Someone may refuse such kind of "definition". Try to review the definition of "antenna" on the first page of C.A.Banasis' "Antenna Theory" and think about the electrically small antenna, we will find exciting issues.