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…