Hyper-Rayleigh Scattering vs. Second Harmonic Generation

[dentedduck]

I've been reading a bit recently on Second Harmonic Generation and came across a supposedly separate technique called Hyper-Rayleigh Scattering (HRS). Can anyone explain the difference? I came across this paper, but didn't understand the difference: http://www.minsocam.org/ammin/AM73/AM73_701.pdf

Thanks,

Dave

 

[johng23]

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 :)

 

[dentedduck]

Hey, thanks for your reply!

I'm glad to see that I'm not the only one confused. I checked out the paper he references by Chemla (http://iopscience.iop.org/0034-4885/43/10/001) a portion of which is attached. That one seems to be a pretty good review of the topic.
While he doesn't specifically mention HRS, if I'm understanding correctly, you're right in your statement "every dipole in a solid scatters quasi-isotropically, but the periodicity of the solid prevents any scattering from persisting except in well defined directions."
HRS is a result of the dipole interacting with the applied field and re-radiating in an incoherent manner. SHG results from this _same emission_ propagating in the material and because the dipoles are phase locked to each other and phase matched to the applied field, the emission adds coherently and can propagate out of the bulk crystal. The propagation in the nonlinear material is what brings in the spatial derivative (in the direction of the propagation) through Maxwell's equations. The reference made to the dipoles in Maxwell's equations is indirectly through P_NL.

Does that sound like a good reiteration of what your understanding is?


Dave

 

[johng23]

Yes, that sounds like how I understand it.

 

[dentedduck]

Great, thanks!