I'm looking for a precise expression for the strength of the transverse momentum correlations between signal and idler photons in parametric downconversion.
The scaling is easy to work out, but the precise factors not so clear (to me).
Anybody got a good reference to suggest ?
Hi Miles, Monken at al [PRA 57 3123 (1998)] show that the pump angular spectrum (the Fourier transform of the transverse field distribution) is transferred to the down-converted two-photon field. If "V" is the angular spectrum of the pump, then the two-photon state is proportional to V(p1+p2). The strength of correlations between p1 and p2 (momentum units) is then the width (whichever width you choose to use) of V.
To observe that, of course, one has to use a Fourier transform lens, such that the measured correlations at observation plane (position units) is (f/k) times the width of V.
That is how I always think of the momentum correlations. Does that answer your question?
Mr. Padgett, I noticed that there was a review about the correlations and entanglements in parametric down-conversion in 2010 (Phys. Rep. 495, 87–139).
Not sure whether it mentioned the expressions of transverse momentum correlation, but maybe some relevant information were indicated in the references.
Hope this could be helpful.
Hi Miles,
The scaling as you say it is easy to get doing some approximations, but if you want the exact factors you need to do them numerically. The typical approximations aer: considering the phase matching sinc function as an exponential, and assuming the indices of refraction of the three waves are the same.
If you have a particular problem you want to solve I am happy to share the program that we use with you (or for that matter for anyone interested ;-) )
Cheers,
Gabriel
- Badges
- Science topic