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

In summary, the Wiki article discusses spontaneous parametric down-conversion (SPDC), a process in quantum optics where one photon of high energy is converted into a pair of lower energy photons. The conversion efficiency can reach up to 1 to 4 million for every 4 million incoming photons. This efficiency is not expected to depend on the pump intensity, although some small effects may arise with an intense input beam. However, if the output modes are also pumped, higher conversion efficiency can be achieved. Pumping the crystal too strongly can also result in a large mean photon number in the output modes, but this is not typically seen in standard SPDC operation as it does not involve a cavity.
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Spinnor
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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.
 
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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.
 
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Related to Output of down converted beam not proportional to input beam power?

What is the cause of the output of a down converted beam not being proportional to the input beam power?

The output of a down converted beam not being proportional to the input beam power is caused by a phenomenon known as non-linear conversion. This means that the relationship between the input beam power and the output beam power is not a simple linear one, and is influenced by other factors such as the intensity of the input beam and the properties of the down conversion material.

How can non-linear conversion affect the output of a down converted beam?

Non-linear conversion can cause the output of a down converted beam to be either higher or lower than expected based on the input beam power. This can be due to factors such as saturation of the down conversion material or non-uniform distribution of the input beam intensity.

What are some ways to improve the proportionality between input beam power and output of a down converted beam?

One way to improve the proportionality between input beam power and output of a down converted beam is to carefully select and optimize the down conversion material. This can involve choosing a material with higher non-linear coefficient or adjusting the thickness of the material. Another approach is to use techniques such as beam shaping or spatial filtering to achieve a more uniform input beam intensity.

Can the non-proportional output of a down converted beam be corrected?

In some cases, the non-proportional output of a down converted beam can be corrected by using post-processing techniques such as amplification or filtering. However, these methods may not always be effective and it is important to carefully consider the factors contributing to the non-linearity before attempting to correct it.

Are there any potential applications for non-linear conversion in down converted beams?

Yes, there are several potential applications for non-linear conversion in down converted beams. One example is in frequency conversion for laser sources, where non-linear conversion can be used to generate new frequencies from the input beam. Non-linear conversion can also be used in optical parametric amplifiers and oscillators for amplifying or generating specific wavelengths of light.

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