Author: Jan (Jack) Beda, University of Edinburgh, UK
Let’s begin with polarized sunglasses. You may have them. Why did you get such a fancy pair? Maybe you’ve been told they reduce glare? They do, in fact. All the light that bounces around in our universe has a polarization. A “direction” in which the electromagnetic fields wiggle. Light can wiggle up-down or left-right (and in a few other ways). It turns out that when light is reflected off of water and other substances, it becomes “partially horizontally polarized” (1). That is to say, more of the light wiggles left-right than up-down. Your fancy polarized sunglasses include a polarizer that only lets through the up-down light, and so all of the horizontally polarized light (the glare off the water) gets cut out.
Now, you can probably already figure out what happens if I take two polarizers and put them perpendicularly on top of each other. Let’s say the first one blocks the up-down light, then the second one blocks the left-right light, and so if you put them together, all of the light is blocked, and you see nothing. As you rotate the polarizers with respect to each other, you are able to change how much light gets through. The transmission of light depends whether the polarizers are aligned in parallel (maximum transmission) or perpendicular (minimum transmission) to each other.
Fig. 1: Various pieces of packing tape placed between a computer, and polarized sunglasses. (Image created by the author).
Now, we can take these two perpendicular polarizers and slide a piece of transparent tape between them. Better yet, we slide a big mash-up of pieces of tape in between. What happens? Suddenly the polarizers fill with colour (Fig. 1 and 2). In fact, I encourage you to do this right now! You might not have polarizing sheets lying nearby, but if you have polarized sunglasses and a computer screen, you can do it. Most computers produce polarized light, and your sunglasses act as the second polarizer. Just zoom your computer screen into some white section of this article, increase the brightness, throw some pieces of tape together, and look at them between your computer and polarized sunglasses (nearly all tape will work, but some work better than others). You should see a stained-glass window-like array of colours which changes as you rotate the tape.
Fig. 2: A more involved piece of art by physicist Aaron Slepkov [5, p. 619]
What in the world is going on here? The tape demonstrates the phenomena of birefringence. When light passes through the back polarizer (or your computer screen), it has one polarization. Then the tape does something very neat, and rotates this polarization of light by some amount. Importantly, the amount by which the light is rotated depends on both the wavelength of the light, and the thickness of the tape. For example, in the centre of Fig. 2, we see a bright green section. The polarised light is rotated by just the right amount as it passes through the tape so that the resulting polarisation is perfectly aligned with the second polariser to pass through unchanged. Perhaps the red light, on the other hand, was rotated just enough to be completely cut out by the second polarizer. The amount that the light gets rotated depends on the thickness of the tape as well, meaning that places with more layers of tape will display different colors than places with fewer layers. By varying the number of layers, we can get a wide array of colours.
Now, how do birefringent materials rotate light? When light passes from one medium to another, the light refracts, and its direction changes as a result of a difference in index of refraction across the mediums. Some objects, like the tape, are birefringent, and due to their molecular structure, the index of refraction is different depending on the polarization of the light incident (2). When unpolarized light is passed through a birefringent object for a long enough time, the beam can split into two separate beams, each with perpendicular polarization. In many cases, the light does not travel for long enough in a birefringent material to fully split the incident beam. Instead, the different indices of refraction will create a phase shift in the two polarizations of light resulting in a change in the polarization of the exiting light. This often results in partially elliptically polarized light but can be approximated as a net rotation of the polarized light.
The world of birefringence is far and wide. This technique of viewing birefringent objects between two polarizers can be used to analyse stress patterns in plastic ( look at your plastic ruler between two polarizers) (3) and in geology (a number of rocks are birefringent) (4). Most importantly, we can create some beautiful pieces of art: birefringence is a fascinating concept to study..
Works Cited
1. Halliday D, Resnick R, Walker J. Fundamentals of Physics. 10th ed. Wiley; 2014. p. 997–998. ISBN 978-1-118-23061-9
2. Belendez A, Fernandez E, Frances J, Neipp C. Birefringence of cellotape: Jones representation and experimental analysis. European Journal of Physics. 2010;31(3):551-561.
doi:10.1088/0143-0807/31/3/012
3. Redner AS, Hoffman BR. Measuring residual stress in Transparent plastics. mddionline.com. 2017. https://www.mddionline.com/news/measuring-residual-stress-transparent-plastics
4. Alderton D. Other Silicates: The Al2SiO5 Polymorphs, Cordierite, Staurolite, Epidote, Chlorite and Serpentine. Encyclopedia of Geology. 2nd ed. Academic Press; 2021. p. 368-381. ISBN 9780081029091. https://doi.org/10.1016/B978-0-08-102908-4.00186-7
5. Slepkov AD. Painting in polarization. American Journal of Physics. 2022; 90 (617): 617-624. https://doi.org/10.1119/5.0087800