Liquid Crystals and Polarisation

Introduction

To understand liquid crystals, we must first understand the polarisation of light. In this article, we will explain what light is, how it can be filtered by polarisers and how liquid crystals can achieve this with such low power consumption. Applications of liquid crystals include human-machine interfaces for automotive, medical and industrial devices as well as augmented reality near-eye displays.

What is Light?

Light is an electromagnetic wave and can be visualised as electric and magnetic fields, each perpendicular to each other, and both perpendicular to the direction of travel. In the diagram below, the electric field is shown on the y-axis (pointing upwards), the magnetic field on the z-axis (coming out of the page), and the direction of travel is on the x-axis (pointing to the right). Both the electric and magnetic fields are sinusoidal waves, with peaks that may coincide (meaning they are in phase), or peaks that do not coincide (they are out-of-phase), or any phase difference in between.

Electromagnetic wave with electric and magnetic fields perpendicular to each other, shown here in-phase

If you ‘look into’ the direction of travel of the wave, the electric field vector would appear as a vertical line, sometimes pointing upwards (at 0º from the vertical), like the minute hand of a clock at noon, or downwards (180º from the vertical), when the clock shows half past the hour. We also see in the above diagram an electric field vector at 10º from the vertical and one at 90º from the vertical. Now, daylight is produced by a random and spontaneous emission of electromagnetic waves from our closest star, the Sun, so we can expect the orientation of the electric field in daylight to also be random. And it is. In fact, the polarisation of light changes direction every 10E-8 seconds, as if the minute hand of the clock were randomly and rapidly changing position. It is the position of the electric field vector that defines the polarisation of light. If the tip of the electric field vector does not change over time (e.g. it is constantly pointing to 10 minutes past the hour) then the light is said to be linearly (or plane) polarised. Let’s not forget that a changing electric field induces a perpendicular magnetic field, and a changing magnetic field induces a perpendicular electric field, so we cannot simply ‘remove one of them’ by polarising light. We focus on the electric field here since it is of more relevance to the subject of liquid crystals.

What is a polarising filter?

A polarising filter only allows through light which is polarised in a particular orientation. It is a filter. It merely absorbs certain light polarisations and allows other polarisations to pass through. A polarising filter is composed of a network of infinitesimally small parallel lines, constructed at the molecular level by transparent chemical compounds. If we apply a vertical polarisation filter to daylight, light emerges vertically polarised. If we have a sequence of polarising filters which are ‘crossed’ (i.e. perpendicular with respect to each other), no light will emerge from the second filter, since the vertically-polarised light from the first filter cannot pass through the second (horizontal) filter.

Polarisation filters applied to light producing (a) vertically polarised light or (b) no light

The top portion of the diagram shows how the first (vertical) filter polarises light vertically. This light can pass through the second (also vertical) filter since it has the same orientation. From the right side, we would simply see light emerging. In the lower part of this diagram, the horizontally-polarised light from the first filter cannot pass through the second (vertical) filter, and no light emerges from this arrangement. The output looks opaque to an observer positioned on the right. This arrangement was first investigated by Étienne-Louis Malus (1775-1812), a French physicist, who created a mathematical formula to calculate how much light emerges through polarising filters depending on their orientation. I won’t bore you with the maths.

Elliptically and Circularly Polarised Light

If the tip of the electric field vector is not constant over time, but rather traces the outline of an elliptically shaped clock, then the light is said to be elliptically polarised. A special case of an ellipse is a circle, and light filtered by a circular polariser emerges as circularly polarised light (where the electric field vector traces the outline of a circular clock). If we were to ‘look into’ the direction of propagation of a circularly-polarised light wave (from the right side), we would merely see a circle, with the electric field vector moving like the minute hand around the clock. However when we take time into account, you can see from the diagram below that the circularly polarised light now traces out a helix.

Circularly polarised light traces out a helix over time

Furthermore, if the electric field vector is rotating clockwise, we call this ‘right circularly polarised’ light; if the vector is rotating anticlockwise, it is called ‘left circularly polarised’ light.

What is the ‘Order’ of a Liquid Crystal?

Liquid crystals sit somewhere between solids and liquids, that is, they have no positional order but they do have some orientational order:

• Positional order refers to molecules which are in certain positions with respect to each other. Think of pieces on a chessboard and how they move on an 8 x 8 matrix, always respecting their relative positions (according to the rules of chess).
• Orientational order is when molecules are constrained to point in certain directions. In our analogy, the chess pieces must always sit upright on the board. That is their ‘preferred’ orientation.

Solids exhibit both positional and orientational order, whereas liquids do not have positional or orientational order. Liquid molecules are randomly distributed. In a liquid crystal the molecules, on average, point in a particular direction. This ‘average direction’ is called the ‘director’ of the liquid crystal, which we can think of as a vector. The ‘order parameter’ of the liquid crystal takes on a number between 0 and 1. The image below shows how the order parameter varies with temperature for a typical liquid crystal. We can see that it is highly temperature dependent. On the x-axis, the value ‘Tc’ is the transition temperature when the liquid crystal turns into a liquid, at which point the order parameter goes to zero, confirming that liquids have no order.

Order Parameter vs Temperature for a typical liquid crystal

Liquid Crystals and Electric Fields

A dipole is a charged molecule with a ‘positive end’ and a ‘negative end’ (much like a magnet has a North pole and a South pole). The image below shows a ‘point dipole’ (a theoretical object of infinitesimally small size with no separation between the two equal and opposite charges), and a ‘physical dipole’ (a real world object) with two equal and opposite charges, separated by some distance.

Point dipole vs. physical dipole, image attribution

When an electric field is applied to the dipole, a dipole will align with the electric field. If the molecule did not originally have a dipole, then one is induced when the field is applied. The electric field needed to accomplish this is pretty minimal in liquid crystals, whereas for solids, it has little effect because the molecules are held by very strong bonds. In liquids, electric fields have no influence over the molecules, since they possess a lot of kinetic energy. By the way, only alternating (AC) voltages can be used to switch liquid crystals, as a direct (DC) voltage would electrolyse (i.e. decompose) the liquid crystal. Furthermore, if we drive the liquid crystals with a direct voltage, the transparent indium tin oxide (ITO) electrodes would be reduced to indium tin, which is opaque and the device would rapidly fail. Hence, the drive circuitry must be AC with a zero average DC level, in order to ensure the correct operation of the liquid crystals.

Liquid Crystals and Birefringence

Since liquid crystals are anisotropic (any measured parameter depends on the direction of measurement), light entering at a point on the surface of the crystal will interact with different refractive indices, depending on the density of molecules in the direction of travel of the electromagnetic wave. When the refractive index depends on the direction of travel and the polarisation of the incoming wave, the material is considered to be ‘birefringent’. One value of refractive index corresponds to light polarised parallel to the director, and the other to light polarised perpendicular to the director.

Birefringence in liquid crystals, leading to multiple wave paths through the crystal

In a birefringent material, these two light waves will propagate through the liquid crystal at different speeds and may arrive out of phase when they exit the crystal, sometimes producing colours and other visual effects.

Liquid Crystals and Polarisation

A liquid crystal molecule is a dipole and hence will align itself with an applied electric field, which is exactly what happens in a liquid crystal display (LCD). LCDs can be found in handheld calculators, digital clocks, computer monitors, aircraft cockpit displays, petrol station fuel indicators and passenger announcement displays at train stations. The elements of a LCD are shown below:

Liquid Crystal Display with polarisers, Image attribution

This LCD is based on twisted nematic (TN) liquid crystals, with the following features:

1. Vertical filter to polarise incoming daylight.
2. Glass substrate with indium tin oxide (ITO) electrodes. The electrodes form the dark shapes that will appear when the LCD is activated. There are vertical ridges etched on the surface so the liquid crystals are aligned with the polarised light.
3. Twisted nematic liquid crystals.
4. Glass substrate with common electrode film (ITO) with horizontal ridges to line up with the horizontal filter.
5. Horizontal filter to block/allow through light.
6. Reflective surface to send light back to the viewer.

Each pixel of an LCD can be switched on or off, depending on whether a voltage is applied to it. The liquid crystals are sandwiched between two transparent electrodes of indium tin oxide (ITO) and have two crossed polarising filters. The third ‘polarising filter’ is of course the liquid crystal itself, controlled by our applied voltage. In a twisted nematic liquid crystal, the molecules arrange themselves in a helix structure, like a spiral staircase. It is the helix that rotates the incident light. When not activated, twisted nematic liquid crystals feature a naturally occurring 90º twist, which polarises light. Incoming light is first vertically polarised by the outer filter before being horizontally polarised by the liquid crystal layer (when unactivated), whereupon this horizontally polarised light is passed by the second horizontal filter unperturbed, and reflected by the mirror back out to the user. When the liquid crystal is activated, it will not polarise the light, which will then not pass through the second (horizontal) filter. That pixel will then appear dark. By controlling the voltage applied across each liquid crystal pixel, light can thus be controlled to switch an LCD user interface. It must be remembered that liquid crystals are light modifiers, not light producers. This factor allows for a very low power consumption, typically 1 to 300 microwatts of power per square centimetre.

Outlook

There is plenty of life left in liquid crystal technologies, despite their existence since the late 19th century. Current and active research is leading us into territories new and bold, with applications in pharmaceuticals, medical, smart windows and augmented reality displays. Rest assured you can expect more from us on this topic in future articles.

References

1. Liquid Crystal, MIT Media Lab, URL 2. Colour and the Optical Properties of Materials, Richard Tilley, ISBN: 978-1-119-55468-4, URL 3. Computer Peripherals, Nanyang Technological University of Singapore, URL