# Non reciprocal light propagation

In search for some explanation in why magneto-optical materials (like the one used in the Faraday rotator and, consequently, in the "optical diode") act in such a "strange" way, I saw that this kind of materials break the time-reversal symmetry and a different kind of reciprocity is applicable, the Rayleigh-Carson one.

What I cant figure out is how the interaction of the the light with the material can rotate de polarization vector depending on the direction? How can I visualizate it in a microscopic level (using Quantum Mechanics)?

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The faraday effect is a different index of refraction for clockwise or anticlockwise polarized light, when in presence of a static magnetic field.

In classical mechanics, the electric field of the light makes electrons oscillate in phase with the E field. As they have non-zero velocities, the B field acts on them through the Lorentz force, thus changing their trajectories. Their phase actually change so that the light they emit is slightly out of phase compared to the incident light. Either in advance or late, depending on their polarization (CW or ACW). As a whole, that corresponds to a medium with a different speeds of light for different poarizations.

In quantum mechanics, this is the same story. The photon gives angular momentum to the electron, CW or ACW depending on its polarization. But this momentum gets shifted differently for AC and ACW because of the B field (similar to the Zeeman effect). Thus the emitted photon gets a different phase. This means a different speed of light. And you have the same conclusion.

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