# Polarisation

## Definition

Polarisation is a wave property which refers to the nature of the plane or planes in which the wave oscillates.

• For EM waves, the direction of polarisation is defined as the direction in which the electric field is vibrating, for example along the y-axis in the following figure:

• Light can be unpolarised, whereby the EM wave is a superposition of waves vibrating in many different directions
• Light is linearly polarised if the electric field vibrates in the same direction at all times at a given point. This is as opposed to elliptical or circular polarisation
• The plane formed by the span of the electric field's direction of oscillating and direction of propagation is called the plane of polarisation

## Polarisation by Selective Absorption

• Selective absorption is the most common method:

• A material, known as a polaroid, transmits waves whose electric field vectors are parallel to a certain plane of polarisation, and absorbs all others, resulting in a linearly polarised wave
• The direction of the plane of polarisation in this case is also referred to as the transmission axis
• An ideal polariser transmits all light with electric field parallel to the transmission axis and absorbs all light with electric field perpendicular to the transmission axis. For the purpose of homework problems assume an ideal polariser reduces the intensity of incident light by 50%
• The intensity of the polarised light after passing through both the polariser and the analyser varies by I = ImaxCos2θ where θ is the angle between the two transmission axes. This is known as Malus' law
• In examination questions be careful to note whether you are being asked to calculate intensity relative to the incident light or the transmitted light as the transmitted light through the first polariser has already lost 50% of the incident light's intensity

## Polarisation by Reflection

• When an unpolarised beam is reflected from a surface the reflected light may be polarised to differing degrees based on the incident angle
• For θ = 0° there is no polarisation, while for a certain angle, the polarising angle θp, there is complete polarisation
• Brewster's law states that Tan θp = n where n is the refractive index
• As a result θp can also be called Brewster's angle

## Polarisation by Double Refraction

• In certain crystalline structures, called double-refracting or birefringent materials the speed of light is not constant in all directions
• These materials have two indices of refraction

• There are two refracted rays, polarised in perpendicular directions
• One ray is known as the ordinary ray or O-ray and is characterised by an index of refraction no which is constant in all directions
• The other ray is called the extraordinary ray or E-ray which travels at different speeds depending on direction and is characterised by an index of refraction ne which varies with direction
• There is a direction known as the optic axis along which the ordinary and extraordinary rays have the same speed as no = ne
• The speed difference is maximised in the direction perpendicular to the optic axis
• Some materials become birefringent when under structural stress, which allows for a process called optical stress analysis which can assist in engineering design. For an image of such an object under stress click
here.

## Polarisation by Scattering

• Scattering is a process whereby incident light on a material causes electrons to absorb and reradiate part of the light
• The most common example of polarisation by scattering is the fact that white light from the sun is partially polarised to appear blue, except at sunrise and sunset where the angle of incidence results in predominantly red light being visible
• Optical activity is a property of materials in which they rotate the plane of polarisation of any light transmitted through it. It is determined by molecular asymmetry