Faraday Rotation — Magneto-Optical Polarization Rotator (2D)

Magneto-Optic Medium

Axial field B 0.60 T

Rod length L 50 mm

Material

Analyzer

Transmission axis 45°

Show round-trip (isolator mode)

Readouts

One-way rotation θ0.0°

Transmitted intensity0%

θ vs (B·L) — linearity check

θ (deg) vs B·L (T·m) — 28 sampled points

Non-reciprocity

Faraday round-trip: θ + θ =0.0°

Normal optical activity control: θ − θ =0.0°

How it works

The Faraday effect rotates the plane of linearly polarized light travelling through a transparent medium sitting inside an axial magnetic field. The rotation angle is:

θ = V · B · L

V = Verdet constant  [rad / (T·m)]
B = field along the propagation axis  [T]
L = path length through the medium    [m]

Physically, the field Zeeman-splits the medium's left- and right-circularly-polarized refractive indices (n₊ ≠ n₋). A linear wave is a superposition of the two; the small index difference makes them accumulate phase at different rates, so the recombined linear polarization comes out rotated — this engine draws that rotation progressively, arrow by arrow, along the beam's path through the crystal, not as a single jump.

The rotated beam then hits a second polarizer (the analyzer). Its transmitted intensity follows Malus's law for the angle between the beam's polarization and the analyzer axis:

I = I₀ · cos²(θ − θ_analyzer)

Linearity check — the scatter chart samples 28 fresh (B, L) pairs every time you change the material, computes θ = V·B·L for each, and fits a real least-squares regression line through those points. The fitted slope (deg per T·m) should match V·180/π for the selected material — that is the numerical proof θ is linear in B·L.
Round-trip mode — unlike ordinary optical activity (sugar solutions, quartz), Faraday rotation does not reverse when the light's direction reverses — it is non-reciprocal. Sending the beam back through the same rod adds the same rotation instead of undoing it, so the round trip totals 2θ. A normal (reciprocal) optical-rotation control is computed alongside it and always cancels back to 0°, exactly the contrast that makes a Faraday rotator the core of a real optical isolator.

Entrance polarization Forward twist / exit Analyzer axis Return pass (round-trip)