The magneto-optical phenomena

When a linearly polarized beam strikes a medium, its electric field modifies the electron distribution, creating electric dipole moments.  The linearly-polarized light is composed of left-circularly polarized light (LCP) and right-circularly polarized light (RCP). The orientation of light polarization (the electric field) determines which way the charges move toward.dipole moment

Now, if a magnetic field is added to this setup, the moving charge-distribution will experience an additional force (Lorentz force).

Lorentz Force

The force orientation can be found from right-hand rule. Since the electron has negative charge, the force is exerted in opposite direction of what the right-hand rule determines.  Let’s see how the Lorentz force influence electrons in both cases of the first figure.

Force on dipoles

The velocity vector (yellow) shows the path of charge distribution under the influence of the light’s electric-field. The Lorentz forces along this path, in the right case, shrink the charge distribution whereas the left case where the charge distributions experience an expansion.

Expansion of charge distribution means a larger electric dipole moment.eqn1d is displacement vector and shows the length of the dipole moment or the distance that the charge distributed over it.eqn1Where N is number of dipoles per unit volume and P is net electric dipole density or the electric polarization. The electric polarization, on the other hand, is proportional to dielectric constant.eqn3Where ℇ0 is vacuum permittivity, Χe is electric susceptibility andeqn4and ℇr is the dielectric constant which is proportional to the medium magnetization.

To be continued…

Faraday effect

Faraday effect states that magnetic field can affect the polarization of a linearly-polarized light.

Consider a linearly-polarized (LP) light passing through a pair of Helmholtz coils (along the direction of the magnetic field). Let’s decompose the LP light into its components: Left- and right-handed circular beams (LHC and RHC).

The electric field of each component exert a force on electrons which leads to their circular motion (how?). This motion creates a magnetic field in or against the direction of the applied magnetic field. This means different interaction of LHC and RHC beams with the applied magnetic field which results in a different refraction index and consequently a different propagation speed for LHC and RHC beams.

Combining back the two components (LHC and RHC) of the beam after the coils, produces a linearly-polarized light with a polarization angle different from the beam entered the magnetic field. This change in polarization angle is called “Faraday rotation”.