## Tuesday, November 15, 2016

### Explanation of "Cool tricks with polarized light" video

I saw a cool YouTube video yesterday. Let me warn you, if you don't like being barefoot, then I suggest you invest in a pair of sock garters before you watch this next video, cuz without them, this video will knock your socks off.

Wow. The guy in the video repeatedly says he doesn't know what's going on. I suspect he knows a bit more than what he let on. But just in case he didn't know the physics behind this, I decided to write this blog.

Polarized light

Let's start with a little bit on polarized light. Light can be thought of as a rope that wiggles to and fro. It might be wiggling up and down, or right and left, or maybe at angle. The orientation becomes important if the light goes through a picket fence, as shown in the diagram below. If the wiggle direction aligns with the direction of the pickets (as shown on the left), the wiggle is not obstructed by the pickets. If the wiggle runs perpendicular to the  pickets, the energy doesn't go through. if the wiggle angle is somewhere in between, then some energy passes through.

Dreaming of a place with a white picket fence and a wiggly rope

That's all we need to know about picket fences and polarized light to explain the video. Well, maybe something else will come up. I dunno.

Extruded films

A lot of people I know would say that their favorite line from The Graduate is "Mrs. Robinson, you are trying to seduce me... Aren't you?" That is a great line, but for me, it's when Mr. Braddock whispers the key of the future into Dustin Hoffman's ear: "Plastics." This line, by the way, is listed as number 42 in the American Film Institutes 100 best movie quotes. "Plastics" became a movie symbol of the era, a symbol of fake eyelashes, fake relationships at cocktail parties, and aspirations to the fake nirvana promised by consumerism. At least that's what my seventh grade teacher (Mr. Mattke) told us about The Graduate.

Plastics are made up of molecules (monomers) that have chained themselves up into a conga line known as a polymer. These very long lines of connected molecules are what give plastics their unique combination of strength and flexibility.

Monomers polymerizing into a conga line

Here is where I come up with an extremely clever analogy that brings these two thoughts together. Picket fences are a social symbol of the aspirations of one era, and plastics are a social symbol of that of another. But they are connected in another way... a way that involves polarization of light, especially when it comes to thin films of extruded plastics.

Imagine if you will, a dance floor with multiple conga lines kinda winding around at random. Imagine further that the head person in each conga line suddenly gets mesmerized by the evil villain The Extruder. The Extruder induces these charismatic people to suddenly start running due north. What happens to the conga lines? It is easy to visualize that those conga-regants who hang on will one by one start heading north. In the end, each conga line will be running basically north to south, and the lines will be close to parallel.

I haven't spent much time actually in an extruder nozzle, but this is what happens when molecules in the chamber of an extruder accelerate as they head out the nozzle. The homogeneity of orientation depends (I would guess) on the amount of acceleration that the material experiences when it exits the nozzle, the viscosity of the polymer in it's liquid phase, and the amount of time it takes for it to harden. But I'm just guessing. I am not a polymeric chemist. Nor do I play one on TV.

Here comes the important part where I draw this all together. For a wave of light, the two symbols of the aspirations of the generations (picket fences and plastics) look kinda the same. So, any extruded polymer film is inherently polarized, at least to some extent.

Example - cellophane

Cellophane is a polymer of good ol' glucose. The polymer is formed into sheets by extruding it through a slit. For whatever reason, cellophane seems to have a lot of this polarizing effect that I just predicted. I investigated a bunch of thin films for this blog post, and cellophane seems to be the most pronounced.

(Interesting trivia: If you remove the letter a from cellophane, and move the o to where the a was, you get the word "cellphone". If that's not proof of a conspiracy involving Reagan and ray guns, then I don't know what is!)

For the next three pictures, I used my KindleFire as a backlight. The KindFire, like many displays, emits polarized light. The first picture is just a piece of cellophane that I tore from a box of Lipton tea. Nothing exciting here. Move on to the next image, please.

Boring image of cellophane on my tablet

For the next picture, I put a polarizing filter between the camera and the cellophane. Wow. There are two interesting things happening here. First, the black area shows that the light emitted from the Kindle display is indeed polarized, just like I said in the last paragraph. (All this time, the news articles you have been reading on your Kindle were polarized, and you didn't even realize it! Yet another conspiracy? I dunno. You be the judge.)

A polarizing element has interjected itself into the picture

But the odd part is what happens to the light that was emitted from the Kindle through the cellophane and then though the polarizing filter. That light does not seem to be polarized. Did the cellophane scatter the light so that it was now randomly polarized??? (Note the use of multiple question marks. This could be a sign that this "answer" to the befuddlement is tentative, and may not actually be correct.)

Just based on the picture above, I am thinking that perhaps the cellophane is not truly scattering the polarization of the light. You see, polarizing filters will attenuate randomly polarized light. Some of the light doesn't pass through. But the gosh darn cellophane appears almost as bright as the Kindle light that does not pass through the cellophane or the polarizing filter.

The following picture proves that the cellophane does not randomize the polarization. For this picture, the polarizing filter was rotated by around 70 degrees. Heavens to Betsy! The cellophane has rotated the polarization by about 70 degrees! So, the conga lines in the extruded glucose polymer (the cellophane) are not acting like a typical bouncer at a nightclub, only allowing photons with certain orientations to pass. The bouncer at the Cellophane nightclub is actually twisting the orientations of the photons as they come in the door! I will refrain from political commentary about whether this is appropriate behavior for a bouncer.

A simple twist of the filter, and Holy Buckets!

Also note that the light that passes through both the cellophane and the polarizing filter is not neutral gray or black; it's brown. This shows that the reorienting of the the polarization is not the same at all wavelengths. Here I am telling you just a bit more than what I know, but it seems to me that the width of the conga lines must be on the order of the size of the wavelength of light, so that (for example) larger photons (longer wavelength photons, like red) tend to be too big to experience this effect. Smaller photons are a bit more likely to be intimidated by the bouncer.

The video demonstrates that we can get some bizarre effects when we start mixing things up a bit.

But I see there are some questions in the audience...

Why did the color change as we rotated the Roscolux filters?

The distance between the conga lines depends on the orientation of the polarized light, as shown below. Since we have decided that the distance between polymer strands is in the neighborhood of the wavelength of visible light, we would expect to see different wavelengths effected differently as this distance changes.

Effective distance between conga lines depends on the angle you hit them at

Why does an individual filter show changes in color along its length?

Here is my conjecture: the thicker the film, the more rotation of the orientation of polarization. In the image at the left (below), there is a small difference in the effective thickness of the film, probably due to either the film not being perfectly flat, or due to manufacturing tolerances in the thickness. At the left, I have pinched the ends of the film together so that the effective thickness changes dramatically along the filter. As can be seen, the rainbow has been squashed together.

When films turn into inchworms

Why does stacking the filters cause such cool stuff to happen?

I'm gonna say "read the previous explanation". If you put one filter overneath another, you have something like twice the thickness, so there is more opportunity to rotate.

Why do some of the filters not show this effect?

I dunno, but I have an educated guess. According to the Roscolux website: the filters are "comprised of two types of body-colored plastic filters; extruded polycarbonate and deep dyed polyester". The fact that they use two different materials for the filters might explain why some exhibit this bizarre behavior, and some do not?

But I dunno, there is also (perhaps) an effect caused by the colorant. It seemed to me that higher amounts of colorant tend to suppress anything fun and interesting.

An introspective comment on the nature of science

When my kids would ask me science questions, I would usually have a pat answer. "Why is the sky blue?" "It's not blue, it's cyan, and it's because of Rayleigh scattering." "What is electricity?" "It is the flow of electrons through a wire."

Sometimes, but not always, they would ask a follow up question like "what's Rayleigh scattering?" or "What are electrons, and why do they flow in wire but not in wood?" Eventually, they just stopped asking questions. Maybe they lost interest, or maybe they realized that I was just kicking the can further down the road.

I have given what I think is a reasonable explanation of why polymeric chains have a tendency to align during the extrusion process. I dunno if this is truly the case. Maybe if I finally get that electron microscope I have been begging Santa for, I will be able to find out?

I have given my supposition that these aligned polymeric chains can cause polarization effects and that they can further effect the orientation of the polarized light. I realize that I neglected to explain just why that might happen.

I have noted that some films show this effect, and some do not. I didn't follow up on this or suggest anything substantive on why cellophane and some of the Roscolux filters do this.

Another mystery to me... I know that most display devices emit polarized light because they use liquid crystals to modulate the light. A weak electric field causes the liquid crystals to align one way or the other, so that the polarization changes. What I can't figger is why my KindleFire emits polarized light. I have been told that it has a layer of quantum dots that selectively absorb light from below, and then re-emit it (fluoresce) in a fairly narrow wavelength range. In this way, the light emitted can be closer to monochromatic. This gives the device a wider color gamut without the normal loss of power from a purely absorptive filter. But... I would think that the re-emission would be randomly polarized.

I was gonna pat myself on the back for a great explanation of a really cool effect, but all I have done is kick the can a bit further down the road.

1. The behavior of the cellophane probably has less to do with the alignment of the polymer chains (as they're not conductive, so as you point out shouldn't be able to act as a polarizer). What the alignment does give you, however, is an index of refraction depending on the direction of light propagation (and therefore polarization) - a.k.a. birefringence. The extrusion process leaves residual stresses in the cellophane, and the stress affects the refractive index (and thus the phase delay imparted to transmitted light) of the material as described here: https://en.wikipedia.org/wiki/Photoelasticity
Birefringent materials find applications in waveplates - a half-wave plate, for example, rotates by 90 degrees the polarization of light as you saw with your cellophane. If you want to see stress-induced birefringence in action, compare a piece of extruded acrylic to cast acrylic, or extruded acrylic that has been annealed, between crossed polarizers.

Your Kindle Fire most likely uses quantum dots in the individual subpixels, before the attenuating liquid crystal/polarizer pair. An ordinary LCD uses a white backlight, which is attenuated by the color filter in each subpixel. So even with an ideal backlight, only a maximum of 33% of emitted light makes it through - and the color filters aren't ideal either, causing spectral leakage and limiting the color gamut. By using quantum dots as phosphors for a blue LED, you get a much more spectrally pure emission (because quantum dots emit narrow wavelength ranges) at higher power efficiencies (because almost all the blue light is converted to red or green for those subpixels).

1. Trevor,

I greatly appreciate the correction to my hypotheses!

As I pondered your explanation, I realized one glaring error in my analysis. The image captioned with "Boring image of cellophane on my tablet" shows that cellophane does not polarize the light as I have suggested.

Your explanation of the KindleFire display makes sense. Thanks.

2. If you think that's a cool application of polarization, take a gander at this: http://alumni.media.mit.edu/~dlanman/research/polarization-fields/

1. This link only partially works. There are some images at the top with a lengthy caption, but the .mov file can't be found, and the link to the SIGGRAPH presentation is forbidden.

3. My apologies! Here's a link to the video on YouTube: https://youtu.be/mt3qBPENpno I think if you Google the paper title you can find a preprint.