# Nonlinear Optics: third-order susceptibility

• IcedCoffee
In summary, the conversation discusses enumerating the second-order and third-order susceptibilities and the potential calculation for the latter. The speaker is unsure if their logic is correct and expresses difficulty finding references on the topic. They ask for feedback on their approach. The responder suggests considering all possible combinations of three frequencies and notes that the medium's isotropy may not affect the calculation.

#### 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?

IcedCoffee said:
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.

## What is the third-order susceptibility in nonlinear optics?

The third-order susceptibility is a measure of the nonlinear response of a material to an applied electric field. It describes the change in polarization of a material as a function of the electric field strength, and is an important parameter in understanding the behavior of materials in nonlinear optics.

## How is the third-order susceptibility different from the first and second-order susceptibilities?

The first and second-order susceptibilities describe the linear response of a material to an applied electric field. The third-order susceptibility takes into account the nonlinear effects that occur at higher field strengths. In other words, it describes how the material's response changes as the electric field becomes stronger.

## What factors affect the value of the third-order susceptibility?

The third-order susceptibility depends on the material's composition, structure, and properties such as its electronic and molecular structure. It can also be influenced by external factors such as temperature, pressure, and the intensity and wavelength of the incident light.

## How is the third-order susceptibility measured in experiments?

The third-order susceptibility is typically measured using techniques such as third-harmonic generation, four-wave mixing, or pump-probe spectroscopy. These methods involve applying a strong electric field to the material and measuring the resulting change in polarization or light emission.

## What are some applications of nonlinear optics and the third-order susceptibility?

Nonlinear optics and the third-order susceptibility have many practical applications, including in telecommunications, optical computing, and medical imaging. They are also used in the development of new materials, such as nonlinear crystals for frequency conversion, and in the study of fundamental physical phenomena.