Evanescent fields do contribute to the far field

By rigorously verifying the exact expressions for separate homogeneous waves and evanescent fields in the far field of dipole radiation, it is shown that (1) the homogeneous waves alone in the angular spectrum representation of the dipole field do not generate the far field; (2) the contribution of the evanescent fields to the far field is as 1/r, or as the inverse distance from the dipole, and thus cannot be neglected; and (3) only with the combination of the two parts, i.e. the complete angular spectrum, can the far field be precisely retrieved.