The ability to measure nanoradian polarization rotations, , in the photon shot noise limit is investigated for partially crossed polarizers (PCP), a static Sagnac interferometer, and an optical bridge, each of which can in principle be used in this limit with near equivalent figures-of-merit (FOM). In practice a bridge to PCP/Sagnac source noise rejection ratio of enables the bridge to operate in the photon shot noise limit even at high light intensities. The superior performance of the bridge is illustrated via the measurement of a 3 nrad rotation arising from an axial magnetic field of 0.9 nT applied to a terbium gallium garnet. While the Sagnac is functionally equivalent to the PCP in terms of the FOM, unlike the PCP it is able to discriminate between rotations with different time (T) and parity (P) symmetries. The Sagnac geometry implemented here is similar to that used elsewhere to detect non-reciprocal () rotations like those due to the Faraday effect. Using a Jones’ matrix approach, novel Sagnac geometries uniquely sensitive to non-reciprocal (e.g. magneto-electric or magneto-chiral) rotations, as well as to reciprocal rotations (e.g. due to linear birefringence, TP, or to chirality, ) are proposed.
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If had been chosen, the CCW beam would see a rotation given by , the same as the CW beam. In effect the time dependent Faraday rotator is made to behave as a chiral object.
If had been chosen, the CCW beam would see a rotation given by . The LC modulator then behaves as a Faraday rotator.
