# Nonlinear Optics: third-order susceptibility

• A
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
Gold Member
2020 Award
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.