Durham University Physics Department: National Science and Engineering Week 2010

Polarisation and polarimetry

Electromagnetic waves

Visible light is just one part of the wide spectrum of electromagnetic (EM) waves. EM waves are transverse waves — the oscillations in the electric and magnetic field are directed perpendicular to the direction of wave propagation (unlike, for example, sound waves, which are longitudinal). An EM wave propagating along the z-axis of some coordinate system consists of electric and magnetic fields which are directed in the x-y plane and vary sinusoidally both space and time. This is illustrated in the figure below: the upper image shows the electric and magnetic fields as a function of position along the z-axis at a given time, while the lower image shows the variation of electric and magnetic fields as a function of time at a single point on the z-axis.

Note that the electric and magnetic fields in the figure above are shown to be orthogonal: for waves propagating in free space (or a material with a sufficiently low refractive index, such as air) this is always the case, and the exact magnetic field can be calculated directly from the electric field and the propagation direction. The magnetic field is also many orders of magnitude smaller in amplitude than the electric field, and doesn't usually need to be considered when studying the interaction of an EM wave with matter.

However, the wave shown in the figure above is linearly polarised in the y-direction: the electric field oscillates entirely in the y=0 plane. In general the electric field is free to vary in both the x- and y- directions, and different patterns of electric field variation define a whole range of polarisations for the wave.

The most general solution for the electric field of an EM wave of angular frequency ω in free space, propagating along the z-axis with wavevector k, can be written as

where A_x and A_y are amplitudes obeying the relation

,

and δ_x and δ_y are dimensionless phase shifts. The combination of amplitudes A_x, A_y and phases δ_x, δ_y associated with a given EM wave lead to polarisations which can be grouped into the three categories shown in the figure below: linear polarisation (left), elliptical polarisation (center), and circular polarisation (right).

You can see how the choice of amplitudes and phases creates these different polarisation states using the interactive applet.

Polarisers

Thermal light sources such as the sun or a simple light bulb emit an incoherent stream of light which, just as it is made up of light of many colours, is made up of light of many different polarisations (actually, daylight here on earth tends to be partially polarised by scattering processes in the atmosphere, but we won't worry about that here!). We usually refer to light with such a random mixture of polarisations as unpolarised light.

We can create linearly polarised light from a source of unpolarised light by passing that light through a linear polariser; this is a device that only admits light polarised in one plane. At radio/microwave wavelengths, a grid of parallel metal wires acts as an effective linear polariser: any component of an incoming wave's electric field parallel to the wires will induce a current and thus lose energy to electrical resistance, whilst an electric field component perpendicular to the wires will pass through undamped. Although polarisers working at optical wavelengths, such as the polaroid sheet we will use, don't look like a grid of wires, the picture is a good one to have in mind. The set-up for generating linearly polarised light in this way is shown schematically below:

Polarimetry

We can also use a linear polariser to analyse light of an unknown polarisation — a process known as polarimetry. We accomplish this by passing the light through a rotating linear polariser and recording the transmitted intensity as a function of the rotation angle. If the input light, with intensity I₀ is linearly polarised as in the following figure

then the transmitted intensity I follows Malus' law:

where θ is the rotation angle. You can learn more about Malus' law and the polarimetry of light — including light that is not linearly polarised, or even partially unpolarised — using our polarimetry applets and demos.