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!