Generally the far field distance is taken as 2d2/λ, but for antenna dimension in the sub-wavelength region, what should be the far field distance that can be used in measurements ?
For all electrically small antennas the reactive field reaches out to roughly the same diameter as for a half-wave dipole (so this is different for different frequencies). Inside this sphere the shape of the field patterns cannot be described by only propagating waves, evanescent wave modes are required, that store inductive or capacitive energy but don't radiate. If you look at the equations for the fields around a half-wave dipole these are the fields (electric field or magnetic field, not power) that fall off as one over r squared or one over r cubed. Look at the equations and see the value of r where the one over r term is bigger than the one over r squared and one over r cubed terms. Inside this sphere the field is mainly reactive, i.e. circulating electric and magnetic fields that exchange energy each half cycle with each other or with the tuning capacitors and/or inductors. There are several definitions of near-field, one is the region where reactive fields dominate, another is the region where the far-field radiation pattern has not yet formed. There are others ,too. For electrically large antennas the first is much smaller than the second (one sixth of a wavelength radius compared to hundreds of wavelengths for a satellite dish, for instance) , whereas for electrically small antennas the first can be larger than the second. However, in the reactive near field coupling will probably be mainly capacitive or inductive (e.g. like a transformer works) rather than by radiation, so the shape of the radiation pattern is not really relevant for interactions in the reactive near field.
For all electrically small antennas the reactive field reaches out to roughly the same diameter as for a half-wave dipole (so this is different for different frequencies). Inside this sphere the shape of the field patterns cannot be described by only propagating waves, evanescent wave modes are required, that store inductive or capacitive energy but don't radiate. If you look at the equations for the fields around a half-wave dipole these are the fields (electric field or magnetic field, not power) that fall off as one over r squared or one over r cubed. Look at the equations and see the value of r where the one over r term is bigger than the one over r squared and one over r cubed terms. Inside this sphere the field is mainly reactive, i.e. circulating electric and magnetic fields that exchange energy each half cycle with each other or with the tuning capacitors and/or inductors. There are several definitions of near-field, one is the region where reactive fields dominate, another is the region where the far-field radiation pattern has not yet formed. There are others ,too. For electrically large antennas the first is much smaller than the second (one sixth of a wavelength radius compared to hundreds of wavelengths for a satellite dish, for instance) , whereas for electrically small antennas the first can be larger than the second. However, in the reactive near field coupling will probably be mainly capacitive or inductive (e.g. like a transformer works) rather than by radiation, so the shape of the radiation pattern is not really relevant for interactions in the reactive near field.
to define the distant area in most books arises that the distance between the transmitting and receiving antenna must be much larger than the wavelength. this can be seen in detail in the Balanis and Stratton.
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