I am familiar with the Faraday Effect, but I remain confused as to why the electric and/or magnetic components of light do not naturally align themselves with a magnetic or electric field (in a vacuum) and thereby become polarized.
[Physics] Why Does Light Not Become Polarized In A Magnetic and/or Electric Field
electromagnetic-radiationelectromagnetismpolarization
Related Solutions
Materials, and certainly materials transparent to light , have few magnetic properties. They are not composed out of atoms that have strong ferromagnetism. But all atoms have strong electric fields. This means that light, as it goes through a transparent medium has small probability to interact with its magnetic field component with the medium, which is mainly transparent to it.
Take the wire grid polariser as a more simple example
It consists of a regular array of fine parallel metallic wires, placed in a plane perpendicular to the incident beam. Electromagnetic waves which have a component of their electric fields aligned parallel to the wires induce the movement of electrons along the length of the wires. Since the electrons are free to move in this direction, the polarizer behaves in a similar manner to the surface of a metal when reflecting light; and the wave is reflected backwards along the incident beam (minus a small amount of energy lost to joule heating of the wire).
A wire-grid polarizer converts an unpolarized beam into one with a single linear polarization. Coloured arrows depict the electric field vector. The diagonally-polarized waves also contribute to the transmitted polarization. Their vertical components are transmitted, while the horizontal components are absorbed and reflected.
The magnetic component in this setup cannot interact to affect the absorption of the light the way the electric can with the free electrons in the metal of the wire.
But if you adopt the different sign convention you have just got the same result!
The E-field is a vector; by making the incident and reflected waves have opposite signs on the LHS in your revised formula you have started off by assuming that the reflected E-field is in the opposite direction to the incident E-field. Then when you find that the reflection coefficient is positive, you have merely confirmed your assumption.
Whichever way you do it, if $n_2>n_1$, then the incident and reflected fields are in opposite directions. It really does help if you write these equations down as vector expressions.
Best Answer
The Faraday effect is dispersive, so it is coherent and reversible. It tweaks the evolution of the light but doesn't cause "relaxation". In general, a system cannot reach a ground state, like becoming aligned to a magnetic field, without some sort of dissipation (e.g., absorption).
The linear algebra way to think about this is as follows: consider orthogonal states of light, such as $H$ and $V$ linear polarizations. After coherent evolution, they remain orthogonal, or else the evolution would not be reversible (given the final state, the initial state can be uniquely determined). This logic shows us the range of possible options for coherent evolution. The polarization can rotate (like the Faraday effect), it can go from linear to elliptical or circular (like a quarter waveplate), or it can undergo a mirror reflection (like a half waveplate). Of course, any combination of those options is also valid. But it can't align without ''losing information'', which would require a absorptive polarizer. (What I've just described is the $U(2)$ group of unitary matrices on $2\times 2$ complex vectors.)
Note: when I say "reversible", I mean coherent or unitary. I'm not referring to time reversal symmetry, which the Faraday effect breaks.
Edit If we're looking for a way for light to align to the magnetic field, we need the information on the original polarization of the light to be lost. The Faraday effect is off-resonant and cannot achieve that. One way to realize this is through dichroism, where one polarization (usually circular) of light is absorbed. This process is clearly not coherent/unitary because it erases the information on what the incoming polarization is. After absorption, with the right setup, the light can become aligned with the magnetic field. (I can give an explicit example with atoms, if you'd like.)
Sorry if this repeats my comment.