## Tuesday, 31 August 2010

### A few notes on polarization, and the construction and use of a home-made polarimeter

The Theory

Light consists of electric and magnetic fields at right angles to one another. Polarized light is light where the electric field has a particular orientation.

Linearly polarized light has an electric field oriented in one fixed direction, while circularly polarized light is light where the electric field continually rotates either clockwise or anti-clockwise. Circularly polarized light can be thought of as two linear polarization states, where one state is out of phase with the other by half a wavelength.

Circularly polarized light itself is a particular example of elliptically polarized light, where the electric field describes an ellipse, and this can be thought of as waves at right angles with differing intensities, half a wavelength out of phase.

The Experiments

To study the light with an electric field oriented in a specific way, the first requirement is a source of such so called polarized light. There are many readily available sources of linearly polarized light, that is, light where the electric field is aligned in a particular direction. Polaroid driving sunglasses allow linearly polarized light through, blocking light where the electric field is not oriented vertically. In normal use, this reduces glare, as sunlight reflecting off a road is mostly polarized horizontally. From our point of view, wearing these glasses allows quick and easy viewing of light to assess its polarization state.

Most LCD displays make use of two crossed linear polarisers, with a material in between to rotate the plane polarization when a potential is applied to it. Looking at an LCD monitor through polaroid lenses, you will see that tilting your head to a certain angle will blot out the image, while holding your head 90 degrees to that angle will allow you to see the image. Such an arrangement qualifies as a basic polarimeter.

This image shows the view at three different angles of an LCD screen set to show a white background with RGB values 255, 255, 255.

Placing various items between the glasses and the screen will show whether they have the ability to rotate the plane of polarization of light. Such materials are wave plates. Try placing a strip of sellotape between the glasses and the screen. At a certain angle, it will cause light to pass through the crossed polaroids. Essentially this is what is happening already within the screen, but with a material that rotates polarization when a potential is applied to it.

Holding a plastic item in this arrangement will show an interesting array of colours, highlighting any areas of stress in the item. Often, this arrangement is good enough. You can see stress patterns in a variety of transparent objects, and see how they change as the objective polaroid is rotated.

A transparent plastic hatchery for hatching brine shrimp and other aquatic microbeasts.

A pair of 3D circularly polarized glasses, with a strip of sellotape in the middle.

A plastic ruler.

I zoomed the camera in to show a close up of the screen.

Here you can see the white quarter with all three pixels illuminated, and three sections with 255 in red, green, and blue.

This reveals the problem with using an LCD screen as source of polarized light. Polarization effects are often frequency dependant, but the colours you see on screen are a composite of three basic pixels. Moreover you can look at the spectrum from a screen where only one pixel type is illuminated through a diffraction grating. The following image shows the spectra of just the green pixels from my LCD screen.

The pixel colours are themselves composites of various spectral lines, rather than a continuous spread of colour. While an LCD may serve to highlight stresses in materials, for polarization work where you need a frequency dependence, a smoother light source is needed.

A polarimeter with a smooth spectrum light source is not hard to build. The light source can be any incandescent light, which will give out a close approximation to black body radiation. Work at specific frequencies can be performed by interposing optical filters that work at specific frequencies, by using lights that give specific known spectral lines, such as sodium lights, or by diffusing laser light.

This polarimeter is suitable for examining small samples, and is fitted with a scale for measurement of the polarizing angle. A light tight housing with a source of polarized light at the bottom passes through the sample. A top polaroid can then be rotated, with a means to measure the angle by which any change in polarization takes place. The design here uses polaroid film. I acquired mine from curiousminds.co.uk, in the UK, but many such stores exist that supply worldwide. In the event that you have no access to polaroid, a viable and interesting alternative is to make the device in the style that pre-dated ready access to polaroid film.

Light striking a sheet of glass is partially reflected, and partially transmitted at a refracted angle. The refracted light is caused by the transparent material oscillating to emit the photons. When the refracted ray is at right angles to the reflected ray, the reflected ray is totally polarized, with the electric field parallel to the interface's surface. This angle is about 58 degrees from the normal in a glass/air interface. This provides a source of polarized light. Allow the incident light to strike a glass plate at 32 degrees, and the reflected light is polarized. To amplify this effect, a stack of glass plates are typically used. Microscope slides work quite well for this purpose. Allow incoming light to reflect off your stack of glass plates, up into your polarimeter. The use of glass plates has the added advantage that you immediately know the direction in which your light is polarized.

My polarimeter used an MDF housing, with a 'push lamp' as the light source. The source light is passed through a diffusing filter, and then on to the lower polaroid. The central part of the polarimeter supports any samples. I cut away a section of the housing, and used it as a removable door. This allowed me to place smaller samples completely inside the device, and remove it entirely to view larger objects.

The layout of parts for the polarimeter, roughly cut. Thee were filed smooth, then guide holes were drilled for the nails. The top and bottom had the edges filed down to a recess so they could slot into the main housing.

The top polaroid is mounted in a disc, with an external tab to rotate it. A hole was drilled in the top using a hole saw drill attachment. This is then glued to a larger circle of wood, and a hole is drilled through both parts to fit the polaroid. The measuring tab passes by degree markings, created by printing out a large image of a protractor, backing it onto card, then using a compass, marking out the radius of the support to remove it with a craft knife. This allows measurements of the degree of polarization. More sophisticated polarimeters allow significantly more accurate readings with vernier scales. These can be added as an improvement to this basic design. Calibrate the polarimeter by rotating the top polaroid until you block out as much of the light as possible.

There are many samples you can try in the polarimeter. When set to the zero point, half wave plates rotate the plane of polarization 90 degrees. Quarter wave plates convert light to circularly polarized light. Due to the wave nature of light, something that behaves as a half wave plate may actually be a 1½ wave plate, or more. Changing the wave by a full phase has no net effect.

One of the more interesting samples I tried in the polarimeter is a sample of Calcite. Calcite is birefringent, and the appearance in the polarimeter depends not only on the orientation of the top polaroid, but also the orientation of the sample itself.

The optical rotation displayed by sugar solutions is difficult to determine in a polarimeter such as this, as light has to pass through quite a quantity of dissolved sugar to be appreciably rotated. A different design of polarimeter is better for this application. I made up a 1 molar glucose solution, by dissolving 180g of sugar (1 mole, to the accuracy of my kitchen scale) into a litre of water. Even passing through 10cm of this liquid, the change in polarization was small, and difficult to detect.

Refinements
The angular measurement is done by a basic scale. Most polarimeters use Vernier angular scales, which can measure much more accurately.

Much polarization is heavily frequency dependent. A specific frequency light source would allow you to study frequency dependence of polarization, and rotation of polarization states. I've designed this polarimeter so that specific frequency filters can easily be placed between the light source and lower polaroid.

The linear polarizers could easily be replaced with circular polarizers, one clockwise, one anti clockwise. These filters are somewhat easier to get hold of, being the lenses in the 3d glasses available at the cinema.

A large scale lower polaroid would make viewing large objects far easier. The polarimeter as built is best for small samples, but a better design would be a large light box type design with a large polaroid film, and an elevated eyepiece polaroid with a fine angle measurement. It may be possible to strip large polaroid sheets out of second hand broken LCD screens, but I've not yet had time to investigate this.

A polarimeter for measuring the concentration of sugar solution and other optically active solutions would be designed somewhat differently, with a longer region to hold the liquid. Ideally, a glass tube with T connection, with adjustable polaroids at either end, and a known frequency light source.

Bibliography
Scientific American – The Amateur Scientist Jan 1978, Dec 1977, Jul 1974