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I understand that if a light wave passes through either an electric or a magnetic filed when it comes out the other side of the field there is no change to the wave.

But what happens to the light wave while inside the field. For example is the wave amplified at all? or is it reduced? Are there any other effects to it while in the field that disappear when the field is gone?

I'm a complete layperson with regards to physics so forgive me if the question is not very clear.

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In purely classical physics, electromagnetic fields obey the principle of superposition. This means that, if source one produces field $({\vec E_1}, {\vec B_1})$ and source two produces field $({\vec E_2}, {\vec B_2})$, then if you have the two sources, the field will be $({\vec E_1} + {\vec E_2}, {\vec B_1} + {\vec B_2})$.

Since a constant electric or magnetic field is the field due to one distribution of charge, and a wave is the field due to another distribution of charge, when they overlap, the fields will just add, and not otherwise be affected by each other.

In quantum field theory, light can scatter light, which means that a strong enough field, which is just made up of photons in the QFT picture, will be able to scatter light too, and you can therefore get (small) interactions, but this effect is second-order in QFT, and will not be observable under ordinary circumstances.

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  • $\begingroup$ Has it ever been observed? $\endgroup$
    – user137289
    Commented Jan 31, 2019 at 22:55
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    $\begingroup$ @Pieter Some evidence is reported here: "Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC," nature.com/nphys/journal/v13/n9/full/nphys4208.html. For a more recent report, see "Evidence for light-by-light scattering and searches for axion-like particles in ultraperipheral PbPb collisions at $\sqrt{s_{NN}}= 5.02$ TeV," arxiv.org/abs/1810.04602 $\endgroup$
    – Chiral Anomaly
    Commented Feb 1, 2019 at 1:12
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The first premise is not entirely true.

Light is an excitation of the Electromagnetic field. In a linear medium, this excitation will not couple with any other fields due to the property of linear functions: f(aE1+bE2) = af(E1)+bf(E2)

However in a nonlinear medium there is coupling between light and the field and the light is changed. Terms in E1E2 can give rise to sum and frequency generation and a lot of other awesome effects. E.g. A BaBO crystal can be used to turn an Argon laser operating at 488nm in the blue into a UV laser operating at 244 nm due to frequency doubling.

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  • $\begingroup$ Interesting. But what's a 'BaBO crystal'? $\endgroup$
    – Gert
    Commented Jan 31, 2019 at 22:44
  • $\begingroup$ Barium Borate. Most nonlinearities are weak, eg in glass the crystal structure symmetry cancels out the even orders, making the third order nonlinearity the first one observed. In a non-centrosymetric crystal the second order (quadratic term in the field) is non zero, which allows nonlinear effects to be stronger at weaker field strengths $\endgroup$
    – Paul Childs
    Commented Feb 1, 2019 at 2:24
  • $\begingroup$ Ah, OK. That's Ba(BO2)2. $\endgroup$
    – Gert
    Commented Feb 1, 2019 at 14:50

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