EM: When can you replace del, d/dt with ik, -iω?

[Cadaei]

I tried googling a good resource for this but it was difficult to think of good keywords. Are we always allowed to do this, or is it just for plane waves, linear media, conductors, etc? My intuition is that it's fine in all circumstances since we can Fourier decompose most any function into exponentials, but I'm not sure if that's right.

Thanks.

 

[Khashishi]

This works when the electromagnetic equations are linear and you are using Cartesian coordinates. In this case, you can decompose the solution into a sum of plane waves.
In media, the conductivity tensor is generally NOT linear, but it can be approximately linear for small amplitudes of electromagnetic waves. In plasma physics, we often solve for small amplitude plane wave solutions using this technique, but it isn't valid for large amplitudes.

 

[Cadaei]

This works when the electromagnetic equations are linear and you are using Cartesian coordinates. In this case, you can decompose the solution into a sum of plane waves.
In media, the conductivity tensor is generally NOT linear, but it can be approximately linear for small amplitudes of electromagnetic waves. In plasma physics, we often solve for small amplitude plane wave solutions using this technique, but it isn't valid for large amplitudes.

Thanks so much, that makes sense.