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Is it possible for use to apply a potential or magnetic field to the surface of the media, so that the light being reflected out of the plane of incident?

i.e. Compare to an initial "vertical" plane of incident normal to the surface, the reflected beam also had a $\phi$ angle changes in terms of polar sphere coordinate.

(Please ignore diffraction for now, just simple reflection. Use a beam of single wavelength.)

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For sure when the fields are not too strong you always get that the reflected beam lies in the same plane containing the incident beam and the normal to the surface. With strong fields I am not sure you can take plane waves as a solution, there may be non negligible quantum corrections (see for instance the Euler-Heisenberg Lagrangian https://en.wikipedia.org/wiki/Euler%E2%80%93Heisenberg_Lagrangian).

Back on topic with the weak field, the result follows from the Maxwell equations written at the interface of the two media. You can find details here https://en.wikipedia.org/wiki/Snell%27s_law#Derivation_from_Maxwell's_Equations .

In order to violate this condition I think you need at least a non-homogeneous medium, or some other non linearity (an instance of this could be perhaps strong fields, which can also make the homogeneous medium approximation insufficient).

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  • $\begingroup$ I think you are missing the point. It doesn't matter weak/strong, none of your solution included interaction term, thus did not answer the question. In EMM, the description was through the changes of propagation vector $k$, in dynamics and quantum, you didn't explain why the momentum remain the same bases as well. $\endgroup$ – user9976437 Apr 2 at 14:04
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    $\begingroup$ @user9976437 What is "EMM"? If this answer misses the point, I would suggest clarifying the question. I'm no longer sure what you are asking. $\endgroup$ – garyp Apr 2 at 14:23
  • $\begingroup$ @user9976437 your comment is not clear, sorry; If you can, please edit it. I directed you to a source with good details about the computations. Since with extremely strong fields there is an effective interaction of the photons with the fields, the fact that the field is relatively weak does matter. Infact there is no guarantee that you still have plane waves propagating, when a very strong field is present. Check the wiki link about Snell's law that I wrote above, you should find all the details you need. Hope this helps $\endgroup$ – AoZora Apr 2 at 17:04
  • $\begingroup$ @france95 Unfortunately, the derivation of snell's law had an assumption that three rays lies in the plane of incident, but that not necessary the case. I couldn't find a good answer for reflection. But as to reject you comment of interaction, diffraction(which I didn't want to get into here) was an excellent case, and acoustic-optic effect allowed the addition of momentum. Basically, I want to proof the interaction of reflection, and proof that if it's possible to reflect the ray out of "usual incident plane". The first link was for transportation and did not have the boundary condition. $\endgroup$ – user9976437 Apr 3 at 14:51

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