# As for four wave mixing

## Main Question or Discussion Point

Is there three wave mixing, or two wave mixing?

why it starts with four?

i am confused.

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Cthugha
Yes, there are also other orders of wave mixing. In nonlinear optics you can model the response of the system to incident fields in terms of a power series:

$$\vec{P}=\chi^{(1)}\vec E + \chi^{(2)}\vec E \vec E+ \chi^{(3)}\vec E \vec E \vec E$$

(P: polarization, $$\chi$$: susceptibility tensor, E: em field)

$$\chi^{(3)}$$ is the domain of four wave mixing. The fourth wave is produced as a result of the nonlinear response of the system to the three other fields.

$$\chi^{(2)}$$ is the domain of three wave mixing. You might know sum frequency conversion or the special case of second harmonics.

The term two wave mixing is usually used for processes, where two waves are interacting in a photorefractive crystal, so that one becomes weaker, while the other gets stronger, where no third wave is produced.

The problem with three wave mixing is, that the components of the second order susceptibility tensor are nonzero only for materials with inversion symmetry while four wave mixing is not really limited by symmetry.

Yes, there are also other orders of wave mixing. In nonlinear optics you can model the response of the system to incident fields in terms of a power series:

$$\vec{P}=\chi^{(1)}\vec E + \chi^{(2)}\vec E \vec E+ \chi^{(3)}\vec E \vec E \vec E$$

(P: polarization, $$\chi$$: susceptibility tensor, E: em field)

$$\chi^{(3)}$$ is the domain of four wave mixing. The fourth wave is produced as a result of the nonlinear response of the system to the three other fields.

$$\chi^{(2)}$$ is the domain of three wave mixing. You might know sum frequency conversion or the special case of second harmonics.

The term two wave mixing is usually used for processes, where two waves are interacting in a photorefractive crystal, so that one becomes weaker, while the other gets stronger, where no third wave is produced.

The problem with three wave mixing is, that the components of the second order susceptibility tensor are nonzero only for materials with inversion symmetry while four wave mixing is not really limited by symmetry.
Thank you very much!

people working on BEC are also talking about four-wave mixing.