Output of down converted beam not proportional to input beam power?

[Spinnor]

There are optical crystals that can convert a small fraction of the incoming beam of light into light of different frequency. See the Wiki article,

https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

"Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a pump photon), into a pair of photons (namely, a signal photon, and an idler photon) of lower energy, in accordance with the law of conservation of energy and law of conservation of momentum. It is an important process in quantum optics, for the generation of entangled photon pairs, and of single photons."

In the article we are told the conversion fraction can approach 1 to 4 million, that is for every 4 million incoming photons one will convert into a pair of photons.

Question, is the above fraction a non-linear function of input beam power? These effects occur in non-linear crystals so I am guessing the answer is yes, conversion fraction is a non-linear function of input beam power, the effect is only significant with an intense input beam?

Thanks.

 

[Cthugha]

No, in first-order approximation the conversion efficiency is not expected to depend on the pump intensity under standard conditions. When looking into details, one finds some small effects due to, e.g., better phase matching in focused beam geometries when the pump intensity is increased (Open Access paper in Optics Express ).

Indeed, you are right that one expects some non-linearity as these are non-linear crystals. However, if you consider other non-linear processes such as stimulated emission, the non-linearity does not arise directly from the occupation of the pump beam, but from occupation of the target mode - the (n+1)-term in stimulated emission depends on the occupation of the light field mode stimulated emission goes to. You can get similar effects in parametric downconversion. If you additionally pump the output modes - signal and idler - you can get higher conversion efficiency. However, you will obviously not get single photons anymore in that case.

You could also pump the crystal so strongly that the mean photon number in the signal and idler modes becomes large due to pumping alone. However, as there is usually no cavity involved in standard SPDC, so this is not really how the operation of some SPDC crystal looks like.