A terbium gallium garnet (TGG) rod of length 20 mm sits in a longitudinal magnetic…
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Polarisation and anisotropic media
What an Instrument Can See, Ch Modulating light: electro-optic, acousto-optic and magneto-optic devices
Problem
A terbium gallium garnet (TGG) rod of length 20 mm sits in a longitudinal magnetic field, Verdet constant VV=134radT−1m−1 at 633 nm. The field is set so that light travelling once through the rod, left to right, has its plane of polarisation rotated by exactly 45∘. A mirror is placed after the rod, perpendicular to the beam, so the light retraces the same path: it is reflected, crosses the rod a second time from right to left, and exits back through the entrance face. The magnetic field is not altered between the two passes. Someone argues: "Rotation of the plane of polarisation is the same physical effect whichever way the light runs through the rod, so the second pass undoes the first, exactly as a return pass undoes optical activity in a sugar solution. The light must emerge with its original polarisation, at 0∘ to where it started."
((a)) Explain what is wrong with this argument, using the sign rule for the gyration vector.
((b)) State the net rotation, relative to the incoming polarisation, after the double pass.