Nematics in use: polarised light, electric fields and displays

Light vibrates in a direction, and a filter keeps only one

Intuition

Think of waving a rope. You can shake it up and down, or side to side. Light is like that. Its electric field shakes in some direction. A polarising filter is like a fence with vertical slats. Only the up and down shake gets through.

Polarisation is a property of waves that can oscillate in more than one orientation. In light, the direction the beam travels, the electric field and the magnetic field are all mutually perpendicular. If all the photons in a beam have their electric field in the same direction, the light is polarised. When many beams travel together they may not share a polarisation. That is unpolarised light, and almost all light sources produce it.

Light can be polarised by reflection, refraction, scattering or transmission. Filtering by transmission needs an anisotropic material. Reflection, refraction and scattering do not need anisotropy in the material, because of the different angles of incidence, surface and measurement. Crossed filters block all light. Filter 1 lets only one polarisation through, and filter 2 blocks it. The lecture notes a common analogy is passing through a grate, but the conducting direction is actually the direction that absorbs the light waves.

If two perpendicularly polarised beams are combined out of phase, the field vector spirals around the axis of travel. A phase difference of a quarter of a wave ($\pi/2$) gives a circular cross section, so it is circularly polarised. Any other phase difference gives elliptical polarisation. To work out how this meets filters or materials, treat the two components separately and add them at the end.

Aligned molecules slow the two directions of light by different amounts

A solution of a chiral molecule can rotate the plane of polarisation of light. In the same way, a chiral phase placed between crossed filters rotates the polarisation, so some light now passes the second filter. The cholesteric (chiral nematic) is the example, since its pitch can be on the order of the wavelength of visible light.

For an achiral phase, the electrons oscillate and together carry the electric field wave more slowly (a higher refractive index). The oscillation is different for each polarisation, one across the molecules and one along them. So the two components travel at different speeds and drift out of phase. This is birefringence.

Birefringence gets more interesting when the beam is not at right angles to the surface. The angle of refraction depends on the refractive index, so the two polarisation components of one beam are split into two beams. The amount of birefringence also changes with wavelength, so different colours drift out of phase by different amounts. That is why mesophases between crossed polarisers look so colourful.

Exam detail

Know the chain: aligned (anisotropic) molecules, two polarisation components, different speeds, out of phase, birefringence. Know that a chiral phase rotates polarisation and an achiral aligned phase is birefringent.

An electric field turns the rods and switches the light

Intuition

Hold a small bar magnet near a compass needle and the needle swings round to line up. Each molecule feels a tiny twist like that from the electric field. One twist is small. A billion of them add up and the whole pattern turns.

The charge distribution or polarisability of the molecules means an external electric field can alter the structure of the mesophase. Even a small torque on every molecule adds up to realign the director. The new equilibrium can be set up very quickly, although the speed depends on temperature and molecular interactions. In the no-field case, the molecular alignment can be chosen by structural patterns on the upper and lower surfaces.

Together with polarised light, this gives tunable or switchable transmission. Slide 13 shows a cell between a polariser and an analyser. With $E = 0$ the rods are aligned by the surface patterns and light emerges polarised. With the voltage on, the rods reorient along $E$ and the analyser passes no light.

Cholesterics pick out colours, and a field can tune which one

The periodic helix of a cholesteric reflects some wavelengths and transmits others. That selects colours out of white light. The lecture compares it to the Bragg reflection from earlier in the course. The slide 14 reflection spectrum is for a pitch of $p = 0.427\ \mu\text{m}$ and a layer thickness of $21.0\ \mu\text{m}$. The measured reflection plateaus near 80% and the calculated one near 100% across a band of about 0.62 to 0.65 µm (read from the axis).

An applied field changes the cholesteric structure, so it tunes the selective reflection. Slide 15 shows a heliconical cholesteric whose helix unwinds as the field rises. The micrographs go from dark at 4 V/µm to blue at 1.5, green at 1.4, orange at 1.2, red at 1.1, dark red at 0.9, dark at 0.8 and textured at 0 V/µm. Finally in a display device, each pixel has transparent addressable electrodes on either side, so it can be switched. The lecture calls this “the most important action”.

Pitfall

Do not say a field “removes” the light. The field only reorients the molecules. It is the crossed filters plus the changed alignment that make the cell go dark.

Optional aside

The lecture has no displayed equations. The values $p = 0.427\ \mu\text{m}$ and $21.0\ \mu\text{m}$ come from the slide 14 caption, and the field values on slide 15 are read from the figure.

Recall

How does an LCD pixel go from bright to dark?

A voltage across the pixel’s electrodes turns the rods along the field. With polariser and analyser crossed, the new alignment stops the light reaching the analyser.