Polarisation Optics - Demonstrate a Channelled Spectrum With Fruit Boxes

The channelled spectrum is an optical effect useful in several metrological techniques. It appears as a more or less sinusoidal periodic intensity variation modulating a broad continuous spectrum. It can be produced using interferometric or polarimetric techniques. Here we demonstrate the effect using polarised light and commonly available household materials.

PC or laptop with LCD screen.

Small pieces of polariser, big enough to look through.

Spectrometer, such as assembled from CDs or DVDs

White light source - small filament bulb or LED and power supply.

Ultra-clear adhesive tape.

DVD you're happy to ruin.

Clear plastic food containers.

On the internet you can find colourful pictures of transparent objects like plastic rulers, CD cases, pieces of clear adhesive tape and crumpled Cellophane sheet, viewed between crossed polarisers. The plastic items are birefringent, modifying the state of polarisation (SOP) of transmitted light, giving wavelength dependent absorption in the second polariser. Even thin plastic sheets show this effect, although the low level of birefringence of a typical single sheet gives rather weak coloration.

The effect can be multiplied by overlaying several sheets - See the Instructable: Polarisation Optics - Pocket Polarisation Detector. For this Instructable we describe two ways to easily fabricate high birefringence materials and how to use them to demonstrate a channelled spectrum.

Bring up a blank white page in your word-processor or Notepad editor and expand it to fill the whole screen. Look at the white screen through a piece of polariser and rotate it for minimum intensity. Now hold the sticky tape at about 45° to the polariser axes in front of the screen. You will typically see light with some weak coloration. This is the basis of what follows, but to see the colours in more detail we need a spectrometer.

To see what is going on you will need to find/build a spectrometer. This could be a commercial instrument, but a home-made version is good enough. The internet abounds with spectrometer designs based on the use of CDs (track-spacing 1.6 µm) and DVDs (track-spacing 0.74 µm) used as diffraction gratings. I used a minimal DVD design as in the photo. The source is a white LED, but a small filament lamp or hand-torch is fine too. Position it about 120 mm directly above the DVD. Underneath the LED is a diffuser (tissue paper) and a slit (0.5 mm, parallel to the DVD tracks, made from two pieces of black tape). You can use a whole DVD, or just cut a 20 mm wide segment out of one. For best results use scissors to bisect the DVD and then peel apart the two layers. Use a segment of the reflective side with the coating undamaged.

I like to operate at about 10° incidence angle on the DVD with the diffracted light on the same side of the normal. This is roughly the camera position for the above photo. The center of the cut segment of DVD points towards the observer. By adjusting your viewing position you should be able to see a bright, full spectrum.

We showed above that a single piece of sticky tape only gives a low level of birefringence, and very weak modulation of the colours of the spectrum. This certainly isn't a convincing channelled spectrum. Looking around in the kitchen we found two good examples of high birefringence materials. First - sticky tape again. We could layer dozens of pieces of sticky tape on top of each other to get a strong effect, but life is too short for that. Instead, from a brand new reel of glass-clear sticky tape, using a scalpel or other sharp knife, cut a slab a mm or so thick. It's probably about forty layers of tape. Stick this, oriented at 45°, onto one piece of polariser to flatten it out. Now place a second, crossed polariser on top. This is your "birefringent sandwich".

Switch on your light source and adjust your position so that you can see a good spectrum "in" the DVD. Then place the plastic sandwich in front of your eye. You should see maybe five, six or more dark bands across the visible spectrum - a channelled spectrum!

The figure above was photographed in this way. The source light has to pass though the birefringent sandwich and the spectrometer to your eye, but the order is not important. The sandwich can equally be placed between light source and DVD.

In order to avoid trashing a reel of sticky tape to make our sample we also tested many plastic objects like bags, overhead foils, Cellophane and food containers in this way for large values of birefringence. Most of these showed some effect, but not convincingly. However, one type of container stood out. This was a deep box used to protect grapes and other fruit, shown above. We cut samples from areas of these boxes and tested them. The sidewalls of our grape boxes provided the best samples. The surfaces are fairly flat and of good optical quality, and probably due to the high levels of stretch required to form the sidewalls, as opposed to the base and rim, a higher stress-birefringence is frozen in. Like most drinks bottles, these containers are often made from PET, well known to produce high levels of birefringence. Try to recycle any you don't need for science.

As above, make a sandwich from two pieces of polariser, crossed for minimum transmission of light, with the PET sample in between and rotated to about 45°. It's much easier to handle than thick sticky tape. View the full spectrum in your DVD spectrometer as before and place the birefringent sandwich in front of your eye. We obtained the channelled spectrum shown in the introduction above, with ten dark bands.

Let's look at how our birefringent sandwiches work. Most sheet plastics are linearly birefringent. This is because they are manufactured as large rolls, with quite different mechanical treatment (molecular alignment and stretching) in the "long" direction compared with perpendicular to it. So these samples often exhibit just two values of refractive index, one for the light's electric vector (E-vector) oriented along the direction of manufacture, one for E-vector perpendicular to it; i.e. two "special directions".

When linearly polarised light is incident on such a material at an arbitrary angle, the light acts as though the E-vector splits into two components, one in each of the two special directions. Because of the different refractive indices seen, the two components travel at different speeds. Hence at the output of the plastic there is a time delay between the two E-vectors. When they add together again, they no longer trace out the straight line of a linear polarisation state, but perhaps a circle or an ellipse, or a line at a quite different angle.

If the light now passes through a second polariser, the transmitted intensity will depend on the details of the linear, circular or elliptical state of polarisation (SOP). For instance, circularly polarised light would pass only half the intensity of the original, crossed linearly polarised light almost none at all. If you need more detail on the calculation, look into Jones-matrix methods or the Poincaré sphere.

The distance by which one component leads or lags the other is called the retardance (R). It is a real, measurable distance, perhaps 50 nm for a thin plastic sheet.

Further, the transmitted intensity depends not really on the retardance alone, but actually on the phase shift, which is a combination of retardance and the light's wavelength. Phase = 2 pi R/wavelength. As the transmission is dependent on wavelength, most plastics between crossed polarisers show some colour - different wavelengths are attenuated differently. If R = 200 nm blue light at 400 nm might be blocked completely, while deep red light is hardly affected.

When R is very large, say several times the light's wavelength, the SOP will cycle several times through states, in our case, horizontal linear, left circular, vertical linear, right circular, horizontal linear again and so on as a function of wavelength. In the case of our high birefringence sandwiches, let's say R is 5 µm and the phase will vary by about 5 times 2pi radians. That's five cycles and we get five dark bands across the spectrum.

The channelled spectrum is an interesting and useful phenomenon of optics. It appears when broadband light passes through a highly birefringent object placed between crossed polarisers. Dispersing the light in a spectrometer we see quasi-periodic dark bands. However, the demo requires many wavelengths of birefringent retardance, such as that of a thick uniaxial crystal. This is only rarely available outside optics R&D labs.

We have shown that sufficient retardance can be had from a slab of transparent adhesive tape, not unrolled but cut in one piece from the roll. Alternatively certain deep-drawn PET fruit boxes also exhibit sufficiently large levels of retardance. Combined with a simple DVD spectrometer we have a way to demonstrate this optical effect in the kitchen (I mean the classroom), and to explain it using the model of two speeds of light in uniaxial birefringent materials.