Nonlinear Optics: third-order susceptibility

[IcedCoffee]

Hi. I've just learned about enumerating the second-order susceptibility (rather blindly) by

3^3 * (3*2*1) * 2 = 324.
(tensor size * 3 frequency permutation * negative frequency)

I'm guessing that for the third-order susceptibility would similarly yeild

3^4 * (4*3*2*1) * 2 = 3888?

I couldn't find any book or reference that bothered to do this calculation, but I need to give a presentation about this by tomorrow. Is there anything wrong with my logic?

 

[sophiecentaur]

Hi. I've just learned about enumerating the second-order susceptibility (rather blindly) by

3^3 * (3*2*1) * 2 = 324.
(tensor size * 3 frequency permutation * negative frequency)

I'm guessing that for the third-order susceptibility would similarly yeild

3^4 * (4*3*2*1) * 2 = 3888?

I couldn't find any book or reference that bothered to do this calculation, but I need to give a presentation about this by tomorrow. Is there anything wrong with my logic?

I read this, first time through but I thought someone else could chip in better than I can - however. . . .
I can't speak for the tensor element in this but the formation of intermodulation products under a third order nonlinearity can only give resultants at all possible combinations of three frequencies f₁, f₂ and f₃. (Some of the coefficients could be zero, of course, depending on the actual law.) Whether a medium is isotropic or not, I can't see that it can affect that combination calculation. In the absence of any other responses, perhaps you could look at your result and see if what I say would modify the result of your attempt to extrapolate on the second order result.