The Faraday effect rotates the plane of linearly polarized light travelling through a transparent medium that sits 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.
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)
- Field B and rod length L — set the two factors that multiply the Verdet constant; watch the twisted "ribbon" of arrows along the rod wind up faster and further.
- Material — swaps the Verdet constant; terbium gallium garnet (TGG) is roughly 10× water, which is why real isolators use rare-earth garnets, not glass.
- Analyzer axis — rotate it to trace out Malus's law on the transmitted-intensity readout; "Align" finds the angle of maximum transmission, "Cross" finds extinction.
- Round-trip mode — unlike ordinary optical activity (sugar solutions, quartz), the Faraday rotation does not reverse when the light's direction reverses — it is non-reciprocal. A mirror sends the beam back through the same rod and the rotation doubles to 2θ instead of cancelling to 0°. That one-way-only behaviour is exactly what makes a Faraday rotator the core of an optical isolator, protecting lasers from back-reflections.