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Modeling a Kerr Effect

Hello.

I want to model a material with birefringence that depends on the electric field inside the medium, similar to the Kerr effect where the index depends on the square of the field. This is complicated by the fact that:

1. The field is not uniform.
2. The index dependence on the field is slightly different than a power of 2 (perhaps 1.5).
3. There is an added continuous spatial modulation to the birefringence.

How can this can be done? I suspect the easiest way to just throw the electric field into the differential equations. Is that possible and how can I do that?

Thank you.

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