Say you have a beam or pulse of light with known polarisation which then gets perturbed by something which causes that polarisation to rotate slightly, how could you measure this and what would be the smallest measurable change in angle? I'm aware of beam splitters but they have a limit on angle resolution. Is there anything better?
With the right experimental setups, nanoradian rotations are measurable.
The ability to measure nanoradian polarization rotations, $\theta_f$,, 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 principal be used in this limit with near equivalent figures-of-merit (FOM). In practice a bridge to PCP/Sagnac source noise rejection ratio of $1/4 \theta^2_f$ 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.
Briefly, they're comparing three methods:
(TGG creates the test rotation) The top is the traditional Partially Crossed Polarizer (PCP) approach. The sensitivity comes from having them partially crossed.
The center one is a Sagnac interferometer. Those are normally used to sense global rotations, like a gyroscope. But an optical rotation can be sensed too. Light going in the two directions around the path is rotated in opposite ways, affecting the end-point interference.
The third approach is called a "Polarising Bridge". The Partial Beam Splitter (PBS) allows the two detectors to look at the X and Y coordinates of the rotated beam, allowing a better comparison (less noise) than the PCP approach, at least in theory.
The experimental result is a comparison of measuring a 3 nanoradian ($3 \times 10^-9$ radian, less than a thousandth of a second of arc) rotation of visible light. That’s the effect due to 25mm of material in a 0.9nT magnetic field, about 1/10,000 of Earth’s field.
You could use a slab of transparent material with a known index of refraction such that the specular reflection corresponds to Brewster's angle for the polarization perpendicular to the desired polarization. That is, in the ideal case, the laser pulse is incident on the surface with p-polarization, and the specular reflection is zero. See the picture below. Your laser pulse should be polarized parallel to the plane of incidence. If everything is aligned correctly, there will be no reflected ray.
This way, you can measure the variation in polarization with a light meter placed to intercept the reflected light. Deviations from zero power are much easier to measure than deviations from maximum power.
I have not done the math to figure out the smallest polarization angle defect this could measure.
Image from wikipedia article.