Faraday Rotation & Verdet Constants
Faraday rotation θ = VBL in TGG, TSAG, CeF₃ and fused silica, with the Verdet constant's dispersion from published fits, the field or length for a 45° isolator rotator, and YIG's saturated rotation at 1550 nm.
paramagnetic; Vojna et al. 2019, Table 2; fit range 400–1100 nm.
Verdet constant V
-130.6 rad/(T·m)
paramagnetic: negative
Faraday rotation θ = V·B·L
-74.818°
non-reciprocal: a return pass doubles it, so an isolator's 45° becomes 90° and the input polarizer blocks the return
Field for 45° at this length
0.3007 T
Length for 45° at this field
12.03 mm
Verdet constant against wavelength
Materials at 633 nm
| Material | V (rad/(T·m)) | Kind | Range | Source |
|---|---|---|---|---|
| TGG (Tb₃Ga₅O₁₂) | -130.6 | paramagnetic | 400–1100 nm | Vojna et al. 2019, Table 2 |
| TSAG (Tb₃Sc₂Al₃O₁₂) | -156.4 | paramagnetic | 400–1100 nm | Vojna et al. 2019, Table 2 |
| CeF₃ | -123.6 | paramagnetic | 300–700 nm | Vojna et al. 2019, Table 1 |
| Fused silica (SiO₂) | 3.809 | diamagnetic | 300–1100 nm | Tran et al. 2024 |
| YIG (Y₃Fe₅O₁₂) | — | ferrimagnetic | 1550 nm only | Vojna et al. 2019, Table 3 |
Click a row to select the material.
Model
θ = V B L
Sign convention (Vojna et al.): V < 0 when the medium rotates the polarization clockwise for light propagating along B. Tb³⁺ and Ce³⁺ paramagnets are negative, diamagnetic glass is positive. The rotation does not reverse with the beam, so a round trip doubles it.
|V| = F λ₀²/(λ² − λ₀²) + G
Single-transition fit of Vojna et al. 2019: TGG F 820.3 rad/(T·m), G −6.2, λ₀ 239.3 nm; TSAG F 756.7, λ₀ 262 nm; CeF₃ F 743.6, λ₀ 239 nm, stopped at 700 nm because it underestimates 1064 nm by 15 %. Fused silica uses V = α/(λ² − λ₀²) + β (Tran et al. 2024), fitted to 310 ± 3 °/(T·m) at 532 nm.
YIG is ferrimagnetic: its rotation saturates (304 rad/m at 1550 nm) and stops growing with B, so the field input has no effect on it.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
θ = VBL is exact for a uniform field. V(λ) at room temperature comes from published fits inside their ranges: the single-transition model for the Tb³⁺ and Ce³⁺ paramagnets (Vojna et al.), a dispersion fit for fused silica (Tran et al.). YIG is ferrimagnetic, so only its saturated rotation at 1550 nm is given.
- Vojna D., Slezák O., Lucianetti A., Mocek T. (2019). Verdet constant of magneto-active materials developed for high-power Faraday devices. Appl. Sci. 9, 3160. Eq. 13 and Tables 1–3. doi:10.3390/app9153160
- Tran D.-B.-A., Edwards E., Tew D. P., Peverall R., Ritchie G. A. D. (2024). Continuous-wave cavity ringdown for high-sensitivity polarimetry and magnetometry measurements. J. Chem. Phys. 160, 054201. Fused silica Verdet dispersion, eq. 2. doi:10.1063/5.0187832