Here’s an update to the lasercut Poincare sphere I made previously. I was very happy with it as a desktop ornament, but it wasn’t quite the tangible intuition pump I was hoping for.

I decided to remake it with the coordinates on the outside and a clear ball on the inside, so that you can ‘fidget’ and rotate the sphere by hand to figure out what series of operations will move polarizations the way you want them.

Poincare Sphere, with the waveplate’s rotation axis in green

I’ve also included parts to show the behaviour of probably the three most common optical tools. A waveplate, a Faraday rotator, and optical rotation (which I’ve called a ‘sugar rotator’ as it’s more memorable). You can see how moving orientations of the waveplate, or using left-handed sugar instead of right-handed sugar will change the behaviour.

The waveplate (green arrow) rotates the polarization through an axis which always passes through the ‘equator’ of the sphere.

The Faraday rotator rotates the polarization through the ‘North/South’ axis of the sphere, and is proportional to the strength of the field, so you could reverse the magnet to reverse the rotation:

Faraday Rotator

The Optical Rotator (Sugar rotator) rotates the polarization around the same axis as the Faraday rotator, but the rotation is due to the subtle difference in the way light propagates through molecules of different chirality. Ordinary glucose we get from plants is all right-handed, and makes a Dextro-rotation on the polarization of the light.

Optical Rotation, or a “Sugar Rotator”

If you were to synthesise glucose in the lab, (being careful not to use any ingredients or catalysts of a particular handedness to start), you’d end up with an equal mixture of right and left handed glucose molecules, and the resulting mixture wouldn’t have any net effect on the polarization.

I’m pretty happy with it as a model. I’ve had to use it extensively as a reference while designing another project, and it’s quick and simple to play with.

Files here for anyone that wants to make their own:

https://www.thingiverse.com/thing:3076318

(The ball you’ll need is an 80mm Christmas ornament, with the top cut off. )