is it crystal structure or some thing else that make polarization of daughter photon orthogonal in type 2 and parallel in type 1?
Hi Arsar,
Nonlinear crystals can typically support both type-I and type-II phase matching conditions, depending on the specific wavelengths and the propagation directions of the pump and down-converted photons. I think it's easier to imagine the reverse process (second harmonic generation), in which two photons are annihilated in the presence of a nonlinear crystal and a new photon is created, preserving the original combined photons energy (its frequency is the sum of the two photon frequency) and momentum (its momentum vector is the vector sum of the two photon momentum vector, when we also need to consider the refractive indices of all the photons involved in the process). The polarization direction of the newly-generated photon is limited upon creation to one of the crystal's polarization normal modes (that can be calculated using the index ellipsoid), and the specific polarization mode is chosen so that the phase-matching conditions are satisfied. Since each polarization normal mode propagates with a different refractive index, it is clear why for a chosen process only one of the normal modes is possible (the other will have a photon momentum that is either higher or lower with respect to the momentum of the two original photons). This only means that the polarization direction of the photons is not conserved in this process, as opposed to the photons' energy and momentum.
I hope it helps,
Assaf
It's all about phase-matching. kp = ks + ki has to be satisfied. In many birefringent crystals this condition may be satisfied both for type-I DPC (for certain wavelengths and directions) and for type-II DPC (for certain other wavelengths and directions).
Hello,
as for practical applications there is difference. Actually you cannot effectively run parametric process for both cases even if you can rotate ( or heat ) crystal to reach phase matching angles. Lets use for example BBO crystal. There is one more (often not shown) angle which defines effective nonlinearity for the process. For BBO pumped 800nm both Type I and II are available. Theta(type I)~20deg and Theta(type II)~29deg. However other angle Fi(type I)=90deg, Fi(type II)=0deg. This is not a general case, but it explains what happens in practice. Effective nonlinearity is maximal (parametric process most efficient) for Type I Theta~20deg and Fi=90deg. By changing Fi from 90 to 0 deg effective nonlinearity from max drops to 0 and parametric process vanishes. And vice versa for Type II Theta~29deg and Fi=0deg are best conditions. By changing Fi from 0 to 90 deg effective nonlinearity from max drops to 0 and parametric process of Type II vanishes.
Therefore if BBO crystal is cut for Type I (by default Fi=90deg and highest nonlinearity) it will not work as Type II even if you would rotate these 9 degree Theta difference. And opposite is correct.
I need to mention once again that effective nonlinearity is of complex dependence on crystal structure. Info can be found in handbooks of nonlinear optics and optical materials. Present example of complete cancelation is not a general case. I am lazy to look at data of all crystals but I do not remember any practically used crystal where Fi angle would be the same for both processes and with biaxial crystals situation is even more complex...
"What happens inside?" - do not have an answer as all quantum physics. There is no explanation by reasoning to normal understanding. Just happens when you solve case using quantum physics. Actually you can try to explain first what photon is which should split into two - no chances using common sense. Amplification can be obtained classically but spontaneous down conversion - not.
Thanks Gintaras Tamosauskas
you have explained really well.....i would say perfect ans for the question (from my point of view). can you tell about the reference (of information you mentioned above so that i can see it in literature too) ?
Hello,
David N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey
Data on refraction index and nonlinearity for different types of interaction is available.
Some copies of this or similar handbooks by Nikogosyan are available online.
For example BBO type II:
deoe = doee = d22*cos(2θ)*cos(3φ); d22=2.2pm/V
You can see that for φ=90 cos(3φ)=0 and dooe=0; for φ=0 cos(3φ)=1 and nonlinearity value depends now on θ angle but goes 0 only for θ=90. In practice θ angle you cannot choose freely - it defines phase matching, but φ can be any when you are cutting crystal. So, proper cutting orientation and specification of both angles is really important.
@Gintaras, what I understand is that both type I and II cannot be obtained from the same crystal because of the difference in the angle Fi. If we were to change Fi as well as theta, is it possible to go from type I to II or vice versa?
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