Fundamentals of Light & Optics

Properties of Light - Polarisation

Polarisation is a wave property that describes the orientation and direction of oscillation of the electric fields that make up a light wave. Ordinary unpolarised light, the wave vibrations (which occur at right-angles to the direction in which light waves travel) are randomly distributed around the axis of propagation, i.e. the directions of oscillations are in all directions.

Random (unpolarised) Light
Fig 2.22 - Random (unpolarised) Light

There are three main states of polarisation of a wave: linear, circular and elliptical.

Linear polarisation is said to be when the electric field is orientated in a single plane or direction. If the electric field rotates as the wave travels, this is said to be either circular or elliptical polarisation.

Lets take a closer look at linear polarisation to gain a better understanding of the phenomenon.

Linear Polarisation of light
Fig 2.23 - Linear Polarisation of light

Fig 1.23 demonstrates the basic principle of polarisation of light. Unpolarised light (i.e. the direction and oscillation of the electric field is random), strikes the first polarising filter, which in turn have been designed to allow light through the filter at the same time selecting (only allowing) a single plane of polarisation of the electric field to pass through the filter. In the case above, the filter's rotation is in the horizontal (x-axis), therefore selecting only the electric field that is oscillating in the horizontal plane.

The light emerging from the first filter is now linearly polarised. We can demonstrate the polarised nature of light by adding a second polarising filter, and rotating this through 180°. When the second filter's rotation is inline, i.e. 0° with respect to the first filter, this will allow light through the filter. As we rotate the filter, we see a decrease in transmitted light, at which point where the second filter's rotation is 90° with respect to the first filter, no light will be transmitted.

Circular and elliptical states of polarised light behaves in the same way, with filters designed to filter these states of polarisation. An interesting aspect of these two states, is the ability to resolve them into two linearly polarized waves, of equal amplitude, in phase quadrature (90 degrees apart) and with their planes of polarization at right angles to each other.

The example shown in Fig 2.23 is a fundamental method in-use in everyday life including: Liquid Crystal Displays (LCD), polarising sunglasses, polarising filers placed in front of a camera lens and also polarising glasses used to watch 3D-movies.

Polarisation By Reflection

As we have just learnt, unpolarised light is actually made up of random polarisation of the electric fields. Unpolarised light incident at the boundary of a transparent material with a different refractive index will be transmitted as well as a small percentage of the incident light being reflected.

At a specific angle of incidence (polarisation angle), the electric fields of the incident light will be separated into parallel and perpendicular components with respect to the surface normal (plane of incidence). Light with the electric field vectors parallel, are said to be p-polarised, and light with the electric field vectors perpendicular, are said to be s-polarised (derived from the German word, senkrecht for perpendicular).

This angle is known as Brewster's angle, θB, named after the Scottish physicist, Sir David Brewster. At Brewster's angle, the electric field component of the light wave that are parallel with the plane of incidence (i.e. p-polarised component), cannot be reflected, therefore are transmitted (refracted) through the material and the electric field components that are perpendicular (i.e. s-polarised component), are reflected.

Brewster's Law states the maximum polarisation of a ray of light ocurrs when the reflected ray makes an angle of 90° with refracted ray. We can express this as follows:

From Snell's law;

n1 sin θ1 = n2 sin θ2

We can rewrite;

n1 sin θ1 = n2 sin (90 - θB) = n2 cos (θB)
θB = arctan (n2 / n1)

Brewster's Angle
Fig 2.24 - Brewster's Angle

Fig 2.24 shows the principle of polarisation resulting from an incident ray of light at the boundary of a material with a higher index of refraction at Brewster's angle. An everyday application that uses the principles of Brewster's angle is the polarising sunglasses and also the polarising filters used in photography. In both applications the aim is to reduce the glare resulting from reflections of the sun and increase contrast. In the above case, the refractive material is positioned (rotated) at Brewster's angle.

With the aid of Fig 2.24, we can demonstrate another important application, in optics, a component called a Brewster Window is used to seal the plasma tube of a gas laser and allow the laser beam to leave the tube. As the s-polarisation is reflected, the gain for this polarisation is reduced, although there is no effect to the p-polarisation. The net result is the laser's output is p-polarised and allows the laser to operate without loss at the windows.

Brewster Window
Fig 2.25 - Brewster Window

Fig 2.25 is a photo of one of the ends from an Argon-Ion gas laser tube, showing the Brewster window as attached to the tube stem. Typically, windows are made from fused silica.

This concludes our journey through the properties of light.

In the next chapter, we will investigate the basic lenses which form parts of more complex optical systems..

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