Nonlinear susceptibility with loss

I want to calculate a third order nonlinear effect such as self focusing and bistability etc.

From the examples, I can get information. However, I can’t find an example for nonlinear susceptibility with losses.

I want to calculate the nonlinear effect of Ag. The nonlinear susceptibility of Ag is 2.5^-8 + i7.2*10^-8.
How can I apply imaginary part of nonlinear susceptibility ?

Thank you

Dear @kimmh1028

You can’t directly implement a complex valued chi3 because we are solving the fields in the time domain where E(t) is real-valued.

However, one possible option is to use Chi3 Raman Kerr model. There are a few things to note about this model:

  1. While chi3 term in the model may predict harmonic generations, the Raman section accounts only for the material susceptibility. This model will still predict self focusing and bistability.

  2. You have freedom on choosing 4 parameters (Chi3, α, ωRaman, and δRaman), and hopefully you can come come up with a simple way to use these 4 parameters to model the nonlinear susceptibility of interest ( 2.5^-8 + i7.2*10^-8).

  3. The Raman part is frequency dependent and material will be dispersive. This means that in principle the set of parameters you chose for the Raman term will be valid only for one frequency only. Therefore, this would work for single frequency (or narrowband) simulations only.

You can read more about different models for nonlinear materials here:

I hope this answered your question.

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I considered the chi3 raman kerr model. However, I don’t know how to find the 4 parameters.

For example, If I set the nonlinear susceptability 3.47710^-16 + i9.99710^-17 m^2/V^2 in wavelength of 440 nm, what is value of 4 parameters (Chi3, α, ωRaman, and δRaman) ?

Is there any example that 4 parameters corresponding to a certain susceptability value are shown.
Thank you.

Dear @kimmh1028

Can you please elaborate more on the application example that you are interested in? Are you looking to study harmonic generation or want to add to add nonlinearity as material susceptibility? If you are interested only in nonlinear susceptibility, we can set α=0.

This is being said that I have not done any simulation with nonlinear susceptibility, but I think it can be simulated using Chi3 Raman Kerr model.