Requesting Help Regarding the Cause of the Faraday Effect

[Archeon]

Hey everyone,

I seek help regarding the Faraday-effect (change of the polarization angle of a linearly polarized wave in an electric field). I have asked my professor about the topic and learned a lot, but I think I am still lacking one or some crucial points. Here is how I understand the cause of the effect to date, mind that I might have misheard some of the thing I've been told:

A linearly polarized wave traveling parallel to a magnetic field can be written as the superposition of $\sigma^+$ and $\sigma^-$ parts. These can be seen as transitions in the energy level diagram of the medium the wave is passing through, with the added constraint that the magnetic quantum number $m$ must change by $+1$ for $\sigma^+$ and $-1$ for $\sigma^-$ . The wave parts do not have enough energy for this transition, yet they still experience some "absorption" based on how close to the energy level they are. This effectively causes the wave to travel slower the narrower the gap to the next state is. When a magnetic field is present, the Zeeman effect alters the excited states differently. The gaps for $\sigma^+$ and $\sigma^-$ are of different height, thus they travel at different speeds, which in turn causes a change in the angle of polarization.

But what is meant by this absorption effect that causes the slowdown, and what does it have to do with absorption? And how does this explain that the effect is not inversed when the wave is traveling in the opposite direction?

Thanks in advance.

 

[Chandra Prayaga]

The Faraday effect is not because of absorption. It is because, in the presence of the magnetic field, the dielectric constant of the material is slightly different for left circularly polarized (LCP) and right circularly polarized (RCP) light. This gives rise to different speeds of LCP and RCP light. when you combine them to get linearly polarized light, you find that the direction of polarization rotates as the beam passes through the medium. The math for this is shown, for example, at: http://farside.ph.utexas.edu/teaching/em/lectures/node101.html.