Durham University Physics Department: National Science and Engineering Week 2010

Polarimetry

Polarisers

Most typical light sources (the sun, light bulbs, strip lights etc.) emit unpolarised light - each individual photon emitted from the source is randomly polarised, leading to zero net polarisation. Polarised light can be obtained from this unpolarised light by passing it through a linear polariser: this simply a sheet of material arranged to block light polarized along one axis, but transmit light polarised along the other, orthogonal, axis. At longer wavelengths (e.g. for microwaves) a grating of metal wires is a reasonably effective polariser.

By a combination of more complex optical elements it is also possible to generate light with specific circular or elliptical polarisations, but we will concentrate on linear polarisers since they are far more common. The polarimetry we will be conducting in the experiment involves using a linear polariser (the polaroid sheet in our case) to analyse the polarisation of light. A key concept in understanding how this works is Malus' law:

Malus' Law

Consider a stream of completely vertically polarised light (as obtained by passing unpolarised light through a linear polariser with the polarisation axis oriented vertically) of intensity I₀ incident on a sheet of linear polariser with its polarisation axis rotated away from the vertical by an angle θ:

Malus' law tells us that the intensity I of the light transmitted by the rotated polariser depends upon the angle of rotation θ as

Now, given a beam of light linearly polarised along an unknown axis, we can use a linear polariser and Malus' law to find that axis: simply rotate the polariser to find angle of minimum (or maximum) transmission, and this tells us the axis of the original polarisation.

You can see Malus' law in action in real life in our interactive demo, and plotted out with graphs in the polarimetry applet below:

Polarimetry applet

In the polarimetry applet below the polarisation of the input light is shown in the Lissajous figure at the top and controlled by the first four sliders — exactly as it was in the polarisation applet. The graph below the Lissajous figure shows the relative intensity of light that will be transmitted by a linear polariser oriented with its polaristion axis at an angle θ relative to the x-axis. The fifth slider allows you to set a specific value of θ: the blue line in the Lissajous figure indicates the angle of the polariser's polarisation axis, and the blue dot on the transmission graph indicates the transmission that will be observed.

Lissajous Figure: Plot of (E_x,E_y)
over an entire period

Relative transmission as a function
of polariser angle

Use the following sliders to adjust the figures above:

Ellipticity vs. depolarisation

After using the applet above, you may have noticed that the amplitude of the intensity variation goes to zero for circularly polarised light: the graph on the right becomes a completely flat line. While this is the true result for circular polarisation, you may remember that this is also the result we would expect for completely unpolarised light (light made up of rays polarised in many different directions). To show the effects of depolarisation, try using this slider to control the percentage of the incoming light that is randomly polarised in the applet above:

Clearly, distinguishing elliptically (circularly) polarised and partially (completely) depolarised input light apart is a problem with using a rotating linear polariser as an analyser. Fortunately in many cases (including our experiment) we can tell which one we are measuring simply by thinking about the physics of how the light we are analysing is generated. You can jump to the interpreting the data activity to read more about this in our experiment.