Engineering & Science
Faraday Magneto-Optic Rotation Angle & 45-Degree Optical Isolator Formula
Calculate non-reciprocal linear polarization rotation theta = DEGREES(V * B * L) from Verdet constant V (rad/(T*m)), axial magnetic field B (Tesla), and crystal length L (m), plus the exact field required for a 45° laser optical isolator.
Build one-way optical diodes that protect high-power lasers from back-reflections!
In 1845, Michael Faraday proved for the first time that light and electromagnetism are unified: passing linearly polarized light through a transparent crystal of length L (meters) immersed in an axial magnetic field B (Tesla) rotates the polarization plane by angle theta_rad = V * B * L, where V is the material's wavelength-dependent Verdet constant in rad/(T*m)!
Crucially, unlike chiral sugar solutions whose optical rotation cancels out on a mirror round-trip, Faraday rotation breaks time-reversal symmetry (NON-RECIPROCAL!): a 45° forward rotation PLUS another 45° backward rotation in the SAME lab sense adds up to 90°, allowing an entrance polarizer to block 100% of dangerous laser back-reflections! Using Terbium Gallium Garnet (TGG, V = 134 rad/(T*m) at 633 nm) of length L = 0.020 m in a NdFeB magnet of B = 0.50 T rotates light by 76.78°—requiring just B_45 = (PI() / 4) / (V * L) = 0.293 Tesla for an exact 45° optical isolator!
| Magneto-Optic Crystal (L = 20 mm, B = 0.50 T) | Verdet Constant V (rad/T*m) | Rotation Angle theta (deg) | Required B for 45° Isolator |
|---|---|---|---|
| TGG Crystal at 633 nm | 134 rad/(T*m) | 76.78° | 0.293 Tesla (Compact NdFeB magnet!) |
| TGG Crystal at 1,064 nm (Nd:YAG) | 40 rad/(T*m) | 22.92° | 0.982 Tesla |
| Invalid Crystal Length L <= 0 | Division by Zero Guard | Guarded Input Error | "Invalid Isolator Inputs" |
Faraday Polarization Rotation Angle theta = DEGREES(V * B * L)
Converts radians V * B * L to degrees via DEGREES(...).
=IF(OR(B2 = 0, B4 <= 0), "Invalid Isolator Inputs", ROUND(DEGREES(B2 * B3 * B4), 2))Required Axial Magnetic Field B_45 for a 45° (PI()/4 rad) Optical Isolator (Tesla)
Solves |V| * B_45 * L = PI() / 4 for the permanent magnet flux density needed in a laser optical diode.
=IF(OR(B2 = 0, B4 <= 0), "Invalid Isolator Inputs", ROUND((PI() / 4) / (ABS(B2) * B4), 3))Try the example
Use the original values or change them to test your understanding.