# Is the Near-Field Regime the Result of the Velocity Field?

Gold Member
My understanding is that the radiation field produced by an accelerating charged particle has two distinct components: the acceleration field (~1/r) and the velocity field (~1/r^2) (Griffiths' terminology). Am I right to believe that far-field optics is the regime in which the acceleration field due to accelerating molecular charges dominates, whereas near-field optics is where the corresponding velocity field dominates? If so, what does that make evanescent waves, since they die off exponentially, faster than 1/r^2?

This could be completely off, but my best guess is that evanescent waves would be like the multipole expansion of the propagating disturbance of molecular/crystalline dipole moments in the scattering medium (that would give the higher powers of 1/r needed to get the exponential), in the same way that the velocity field is like the coulombic field due to a moving charge. My only argument for this is that it would explain why the Fresnel equations aren't accurate for evanescent waves. It seems plausible, but I would like to see the math behind it worked out before I go and make a fool of myself. Does Jackson or anyone do a mathematical investigation of evanescent waves from an EM radiation point of view? I'm honestly not comfortable at all with my understanding of evanescent waves. If I'm spouting total nonsense, please post a solid treatment for me to read. Thanks!

tech99
Gold Member
My understanding is that the radiation field produced by an accelerating charged particle has two distinct components: the acceleration field (~1/r) and the velocity field (~1/r^2) (Griffiths' terminology). Am I right to believe that far-field optics is the regime in which the acceleration field due to accelerating molecular charges dominates, whereas near-field optics is where the corresponding velocity field dominates? If so, what does that make evanescent waves, since they die off exponentially, faster than 1/r^2?

This could be completely off, but my best guess is that evanescent waves would be like the multipole expansion of the propagating disturbance of molecular/crystalline dipole moments in the scattering medium (that would give the higher powers of 1/r needed to get the exponential), in the same way that the velocity field is like the coulombic field due to a moving charge. My only argument for this is that it would explain why the Fresnel equations aren't accurate for evanescent waves. It seems plausible, but I would like to see the math behind it worked out before I go and make a fool of myself. Does Jackson or anyone do a mathematical investigation of evanescent waves from an EM radiation point of view? I'm honestly not comfortable at all with my understanding of evanescent waves. If I'm spouting total nonsense, please post a solid treatment for me to read. Thanks!
There is frequent confusion with terminology. It is also easier perhaps to think of lower frequencies, where we use antennas, as the operation is more easily visualised. If we consider an antenna such as a dish, we can see three regions. At large distances, the beam diverges at a small angle and the fields fall off as 1/r. This is the Far Field, or Fraunhofer Region. The antenna pattern does not change with distance.
At distances roughly closer than the Rayleigh Distance, D^2/(2 lambda), distance to an observation point from each point on the aperture now varies with distance. Roughly speaking the beam remains parallel in this region, but with hot spots. This is called the Radiation Near Field, or Fresnel region.
At positions very close to the metalwork of the antenna, we can observe fields caused by the currents and voltages on the structure. The magnetic field is the velocity component you mention, and the electric field seems to be the driving force which accelerates the electrons.
This region is called the Reactive Near Field. The fields here can fall off at various rates depending on whether they are E or H and how large the structure is compared to the distance. For instance, if an antenna uses a long conductor in the structure, the magnetic field initially falls off with 1/r, becoming much faster when the distance is more than the length of the wire. These fields are energy stores. Very often, if the antenna is a resonant structure, the stored energy is much greater than the radiated energy. With stored energy, the waves are taking energy away from the structure and then returning it. There is no phase shift in the wave, other than an abrupt 180 degrees at antinodes. There is no real magic here, because the fields are the same as we see from any wire carrying low frequency AC.
May finally I mention that an antenna does not necessarily have all three regions. For instance, a small antenna does not exhibit a Radiation Near Field and a travelling wave antenna does not have stored energy to form the Reactive Near Field.

Twigg