Spontaneous parametric down-conversion: Should this be a three-wave mixing?

[Ameno]

Hi

I am currently reading through a semiclassical approach to nonlinear optics. I learned about effects of second-order nonlinear optics like second harmonic generation and three wave mixing. I understand three-wave mixing as a process in which you send two (or three) monochromatic beams through a nonlinear medium in which those beams "interact" (via the medium) if they are phase-matched, the net result being a third beam generated (and / or changes in the intensities of the individual beams).

At the end of the treatment of second-order nonlinear optics that I'm reading, spontaneous parametric down-conversion is mentioned as an example. I don't understand how this is an example for second-order nonlinearity. In the description, a pump beam is sent into a nonlinear medium (note: just one monochromatic beam). What comes out of the crystal is the weakened pump beam, together with a family of idle and signal beams, arranged in a cone (since there are many solutions for those two beams to be phase-matched with the pump beam).

How can this be an effect of second-order nonlinear optics? If I send one single monochromatic beam through a second-order nonlinear medium, the only effect is the generation of the second harmonic and a constand polarization, none of which correspond to idler and signal beam, right? And if this should be a three-wave mixing, there should be at least one more monochromatic beam entering the medium, right? So can anyone explain to me how this should be an example of second-order nonlinear optics?

Thanks in advance.

 

[eljose79]

Hello, thank you for your question. I can understand your confusion regarding spontaneous parametric down-conversion (SPDC) as an example of second-order nonlinear optics. Let me try to explain it to you in simpler terms.

First, it is important to understand that SPDC is a nonlinear optical process, meaning it involves interactions between light and a nonlinear medium. In this case, the nonlinear medium is usually a crystal. Now, in second-order nonlinear optics, the intensity of the incoming light plays a crucial role in determining the behavior of the light as it passes through the medium. When the intensity of the light is high enough, it can cause the nonlinear medium to behave differently than it would with lower intensities.

In SPDC, the pump beam that is sent into the crystal is usually a high-intensity beam. As it passes through the crystal, it induces a nonlinear effect, causing the crystal to emit two photons in different directions. This is where the idler and signal beams come from. These beams are created due to the nonlinear effect of the high-intensity pump beam on the crystal.

Now, you are correct in saying that in second-order nonlinear optics, sending a single monochromatic beam through a nonlinear medium would only result in the generation of the second harmonic and a constant polarization. However, in SPDC, the high-intensity pump beam induces a nonlinear effect that creates two new beams, the idler and signal beams, in addition to the second harmonic. This is why it is considered an example of second-order nonlinear optics.

I hope this explanation helps clarify your understanding of SPDC as an example of second-order nonlinear optics. If you have any further questions, please don't hesitate to ask.