# Quantum Optics: 4-wave mixing

1. Jun 11, 2015

### marco1235

Hi all, I've some questions for you which challenge my brain a lot!

I'm dealing with a Photonic course and our professor introduced us a little bit of Non-Linear Optics. We spoke about Four-Wave-Mixing (4wm for brevity) and we said that when we shine a material with $\chi ^{3}$ with two frequencies $\omega_1$ and $\omega_2$ they mix to produce a downshifted (Stokes) wave at $\omega_3 = 2\omega_1 - \omega_2$ and an upshifted (anti-Stokes) wave at $\omega_4 = 2\omega_2 - \omega_1$. The frequencies have equal spacing, that is, $\omega_1 - \omega_3 = \omega_2 - \omega_1 = \omega_4 - \omega_2$. That's ok like in fig1 of the attached files. Now in our discussion in class the professor showed the second picture, where the process is a little bit different in my opinion (is this the well-known Degenerate Four-Wave-Mixing??). He sad that also this second process is a 4wm, and that we must think that $\omega_1$ and $\omega_2$ are now the same frequency $\omega_p$ of the pumping laser. But if they are identical I don't get $\omega_3$ and $\omega_3$ as from the formula above, because if $\omega_1 = \omega_2 = \omega_p$ then by substituting I get $\omega_3 = \omega_4 = \omega_p$. There's something wrong in my head of course!! XD

The last question is how is it possible with a degenerate-4wm to create a frequency comb!
I think that if I could undestand the first part, everything it would be (a little bit) more clear!
Thank you in advance and have a beautiful day!

Greetings from Italy!!

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2. Jun 16, 2015