When I watch this video* on Bell’s Theorem (in which a polarization approach is taken), I keep getting stuck on the fact that I don’t understand at all how polarizers actually do their thing. (And maybe therein lies some part of the “paradox” in the video’s title?)
I know I can’t hope to ever understand the underlying math and physics, but maybe I can get some intuition.
Again, I ‘understand’ what polarizers do; their effect. But, how do they do it?
*produced by the superb 3Blue1Brown channel
For a wave, it’s easy to understand. Picture you and a friend holding a long jumprope, and you’re wiggling your end to send waves down it. You’re wiggling it in some direction, up-and-down, or side-to-side, or some diagonal combination, or maybe you’re getting fancy and wiggling it in a circle (which could be a clockwise or counterclockwise circle).
Now picture that the jumprope is passing through the slits in a picket fence. If the pickets are oriented vertically and you’re wiggling the rope vertically, the waves will go right through the fence with no problem. If the pickets are vertical but you’re wiggling it horizontally, the waves can’t get through the fence at all. If you’re wiggling diagonally or in a circle, then part of your wiggling is vertical and gets through, and part is horizontal and doesn’t get through, so you end up with an all-vertical wave on the other side, but weaker than it was on your side.
Where it gets a bit harder to understand is when you think of light as particles. The “strength” or amplitude of a light wave corresponds to how many photons there are in it. So if you’re doing something to a light wave that decreases its amplitude, that means that you’re blocking some of the photons. In other words, when a diagonally-polarized photon hits a polarizer, it has a random chance of making it through, and a random chance of not making it through.
There are different types of polarizers that work in different ways.
Nicol prisms and similar devices make use of a birefringent crystal, which has different refractive indices for different linear polarizations, which allows them to separate the two different linear polarizations into beams going in two different angles.
A “Pile of Plates” polarizer takes advantage of the fact that light of different polarization is reflected with different intensities from a flat piece of dielectric material (such as a sheet of glass). You can use several such plates, at the same angle, parallel to each other to produce light with only one polarization pasing through. Alternatively, you can use one sheet of dielectric at Brewster’s angle to reflect only one polarization. This is how Malus did it when he discovered Malus’ Law and became the first person to us crossed polarizers to extinguish light.
Edwin Land came up with Polaroid by experimenting with polarization and truing to create cheap, large-area polarizers. His first sheet, made of microscopic crystas in a sheet of nitrocellulose, which he then stretched to orient them in the same direction. It worked similarly to “wire gird” polarizers (used in infrared light), where you preferentially absorb one polarization rather than the other. This is probably the most widely used type of polarizer, and the kind used in those 1950s through 2000s 3D movie glasses.
You can also use multilayer thin films deposited on a substrate to create custom polarizers. It;'s sort of a sophisticated version of the pile-of-plates polarizer.
Therte are others, but these are the main types.
As ever, I appreciate your answers.
There are a variety of types of polarizers but I assume that, ultimately, they work in the same manner?
Which leads me back to Chronos analogy with the picket fence. If you’re wiggling the rope in a circle, then only a component (a projection) of the original wave can make it through. Where does the light go that doesn’t make it through? Is it absorbed by the polarizer? If so, does that change the polarizer in any meaningful way? Maybe heat it up or blur its position in space? Does that invariably cloud any experimental results?
All polarizers work by taking advantage off the differences between the absorption, reflection, or transmission of the different polarizations of light. If you pull out a book on optics – one with all the math – you’ll find that the description of reflection and refraction at a dielectric interface is divided into two types – the case where the plane of vibration of the light is in the plane defined by the incoming ray, the outgoing ray, and the refracted ray (called p-polarization), and the case where the plane of polarization is perpendicular to this (called s-polarization). The coefficients are different in the two cases, so at the same angle of incidence the intensity of p-polarization reflected light is different from that of s-polarization reflected light.
So what happens to the light that isn’t transmitted? In the case of Polaroid sheets and wire grid polarizers, it’s absorbed by the polarizer. as a result, the polarizer gets a little hotter. This doesn’t matter in most cases, like 3-D movie glasses, but it can be a significant problem with, say polarizers for weapons-grade lasers.
In the case of pile-of-plates polarizers and multilayer stack polarizers, the unwanted polarization is reflected away. you can stop it with a beam block, or you might even want to use it for something else. If you’re building a 3D movie camera that uses polarization separation of the two images, you might want to use both polarizations.
In the case of a Nicol prism or Iceland Spar or the like , the two polarizations go off in different directiuons due to index of refraction differences, so, again, you get two beams that you have to deal with.
An interesting detail about this is that if you extinguish beams using a Nicol prism you get different results than when you use crossed polarizers. Crossed polarizers are a potent tool in mineralogy, crystallography, and measuring stress in glass. Two polarizers mounted so that one can rotate, with a space in between to place something is called a Polariscope. If the two polarizers are permanently fixed perpendicular to eachj other, it’s called a colmascope (which is one of those trademarked names that effectively crossed over to become generic, like Kleenex). Colmascopes were invented and sold long before Edwin Land invented sheet polarizers – they originally used Nicol prisms. The thing is, they didn’t completely extinguish the light pasing through. Instead, you got circular “rings” called “Landolt Fringes” that got wider the better your polarization got, but never got wide enough to cover your complete field of view (unlike Polaroid sheets, which did work over everything you could see). I just had an article about this published in Optics and Photonics News.
Just to add to the confusion – there are other polarization states besides linear. The most general type of polarization is elliptical, and a special case of elliptical polarization is circular polarization. There are filters that only transmit circular polarization of one type (there’s Left Hand Circular Polarized light and Right Hand Circular) and either absorbs or reflects the other kind. One way to make this kind of filter is to combine a linear polarizer with a quarter wave plate (don’t ask – that’s another thread). The “Real 3D” glasses used in many 3D cinemas use circular polarizers, whereas some 3D cinemas use linear polarizers. I notice now that many are using glasses that don’t rely on different polarization to separate the images, but which use liquid crystals or other technology to alternately opaque one “lens” alternately.
Some varieties of Mantis shrimp can actually see in circularly polarized light. Many animals – ants, bees, horseshoe crabs - can detector linearly polarized light. Include in this latter group human beings, although our ability to detector linearly polarized light is pretty wimpy compared to horseshoe crabs. Look up Haidinger’s Brush some time.
And it’s really a puzzle why mantis shrimps would be able to see circular polarization, because circularly-polarized light is really rare in nature (at least, under Earthly conditions). What benefit could that possibly provide for them?
It’s speculated that light reflected from the carapaces of a mantis shrimp predator is circularly polarized. I’m not sure if that’s been verified.
And it’s only one variety of mantis shrimp that can see circularly polarized light, so it’s not as if this is a widespread capability.
Linearly polarized light has some utility in navigation, apparently even under water.
OK, sure, maybe some predator’s skin acts like a quarter-wave plate or something, but that just pushes the question back one layer. A quarter-wave plate is not the sort of thing you’d expect to just happen randomly.
Linear polarization, sure. Probably especially so underwater, in fact, given that all light underwater had to first pass through a dramatic index-change interface to get there, so you’ll naturally end up with more polarization underwater.
No, but I could see it as an unexpected byproduct of something else. Considering that many creatures actually derive their color from what amounts to interference effects, I wouldn’t be surprised if some carapace had a waveplate effect, as well.
It’s not as if it needs to be a quarter waveplate to produce a noticeable effect – the most general form of light polarization is elliptically polarized light. The ability of mantis shrimp to detect a predator’s elliptically polarized reflection – not looking for truly circularly polarized light – could mean a statistically significant difference between life and death.
Very informative, thanks.
So, at the end of the day, polarizers are ultimately based on an interaction between photons and matter, i.e. whatever the polarizer is made out of. And this leads to where I’m stuck. Wouldn’t the interaction of light with the polarizer introduce noise (both thermal and quantum-random) to the extent of masking the ‘true’ state of the post-polarizer exit photon? And thus make the precise measurements required to test Bell’s Theorem impossible? Or is that the basis of the need for a statistical approach in the relevant experiment?
An interesting set of questions. But I believe that when you create an entangled pair of photons (and papers such as this show how they can set the polarizations – A source of polarization-entangled photon pairs interfacing quantum memories with telecom photons - IOPscience ) you need only detect the state of a single photon, which will be either horizontal or vertical. Noise, whether quantum or thermal or of some other type, isn’t going to change the polarization state from vertical to horizontal, or even to the point of ambiguity. If this were a case where I only looked at the classical electromagnetic features I might worry about such things, but in he quantum world you can actually take advantage of the way it “locks” the system into only certain states.
It’s sort of like the way the Mossbauer effect keeps recoil effects from contributing to emission linewidths. – Mössbauer effect - Wikipedia
Gotcha. And, yes, the Mossbauer effect helps me see it in another instance (although there is still a bit of recoil energy lost if I understood the link correctly).
Maybe what I was asking is basically the same as asking what happens to the extra energy when an electron ‘sees’ a little more or a little less than what’s necessary for it to become excited (which I am not asking)
Ordinary matter will do a fairly good job of randomizing polarization. But polarizers can be pretty precise.