Before seeing this paper, my understanding was that the distinction was nothing more than the difference between Rayleigh scattering (from molecules or nanoparticles) and scattering from a crystal. He seems to be arguing that there are two distinct microscopic scattering mechanisms. But that would imply that, just for the normal linear optics case, you could have Rayleigh scattering from a bulk crystal. That would be news to me, but maybe someone else can contradict me. My understanding is that every dipole in a solid scatters quasi-isotropically, but the periodicity of the solid prevents any scattering from persisting except in well defined directions. That argument should hold regardless of what microscopic mechanism you want to talk about. So the idea of getting isotropic scattering from a bulk crystal seems suspect.
I don't know how much faith I put in his argument at the moment. In the HRS part he is talking about microscopic scattering mechanisms, and in the SHG part he is talking about relating fields and their derivatives as if it's an independent mechanism. Reconciling these two pictures isn't easy, but they have to be fundamentally the same thing. You don't reference the individual dipoles when you solve Maxwell's equations, but obviously they are still responsible for everything the equations ultimately predict...
The central point of his argument seems to be that you can tell if a material is centrosymmetric only if the HRS goes away, because it can not exist in these materials. But then, when talking about the bulk quadrupole contribution to SHG he says that it can also give rise to HRS in centrosymmetric crystals. Did I miss something?
Besides that, he only briefly mentions surface second harmonic scattering, which you will get from every centrosymmetric crystal, because the symmetry is broken in the first few monolayers. Maybe someone else can clarify, but I would expect that to be isotropic if it only comes from a few atomic planes. If so then that kind of kills his argument as well.
Either he or I is confused! I hope it isn't me :)
