Is the momentum conservation law correct in parametric conversion process?

[Torero]

In optical parametric conversion process, such as second harmonic generation,the conversion efficient is determined by function sinc(ΔkL),where L is the length of the crystal,and Δk is the phase mismatch condition. When the sum of wave vectors of the two fundamental photon,equals to that of the second harmonic photon, that is Δk=0, the conversion efficient is maximum.That is the usually called momentum conservation law of parametric conversion.But here comes the question,when Δk≠0,this process can still take place.Then momentum of the fundamental photons and second harmonic photons won`t conserve.

 

[kith]

I would guess that something like Raman scattering is involved here, i.e. momentum is exchanged with the lattice.

 

[Torero]

I would guess that something like Raman scattering is involved here, i.e. momentum is exchanged with the lattice.

thank you.yes,maybe there is something we miss.In the parametric process,there is no virtual level involved,and total energy of photons never change. how could momentum exchanged?

also there is another question, consider a photon incident into a medium,such as quartz, from vacuum, its momentum changes for the refractive index of the medium is larger than 1.
When it exit to the vacuum again, its momentum recovers. i just can not imaging how the momentum exchanges.