Faraday effect
Rotation of the polarization of light propagating through a magnetically biased medium, with rotation sense set by the field direction rather than the propagation direction. The basis of optical isolators.
When linearly polarized light propagates through a medium parallel to a magnetic field , the polarization vector rotates by an angle proportional to field strength and propagation length:
where is the Verdet constant of the material (units: rad/(T·m)), is the magnetic field strength along the propagation direction (T), and is the physical length of the medium along the field (m).
The Faraday effect is non-reciprocal: the rotation sense is set by the magnetic field direction, not by the light's propagation direction. Light traversing the same medium in opposite directions experiences cumulative rotation in the same sense, totaling for a round trip. This contrasts with reciprocal rotators (e.g., half-wave plates), where reverse propagation undoes the forward rotation.
The non-reciprocity is what enables optical isolators. An isolator cannot be built from linear, time-invariant reciprocal optical elements alone.
Typical Verdet constants at room temperature:
| Material | (rad/(T·m)) | Wavelength |
|---|---|---|
| Terbium gallium garnet (TGG) | 40 | 1064 nm |
| TGG | 19 | 1550 nm |
| Yttrium iron garnet (YIG) | 200 (much higher, ferrimagnetic) | 1310 / 1550 nm |
| Fused silica | 4.0 | 633 nm |
| Heavy flint glass (SF57) | 23 | 633 nm |
| Water | 3.7 | 633 nm |
Ferrimagnetic vs paramagnetic and diamagnetic. YIG and similar iron garnets are ferrimagnetic, with intrinsic magnetization. They require only a small bias field to align internal magnetic moments and produce rotation through their full magnetization. TGG is paramagnetic and silica is diamagnetic: in both, rotation scales linearly with applied , requiring much stronger external fields for the same rotation.
Standard isolator design. A 45° rotation Faraday element placed between polarizers at 0° and 45° passes forward light fully (45° rotation aligns with output polarizer) and blocks reverse light fully (45° + 45° = 90° rotation makes light perpendicular to input polarizer).
Wavelength dependence. Verdet constants decrease with wavelength, typically following a dependence in paramagnetic materials, which takes TGG from 40 rad/(T·m) at 1064 nm to about 19 at 1550 nm. Practical isolators are specified for a specific wavelength range: single-wavelength designs achieve dB isolation; broadband designs cover 30–40 nm with reduced isolation.
The Faraday effect was discovered by Michael Faraday in 1845 and was the first experimental evidence of a connection between electromagnetism and light.