1. Types of polarization>

Normally the electric vector of an electromagnetic wave is randomly orientated in a plane that is perpendicular to the direction of propagation.

However there are some situations where the direction of the electric vector has a definite behaviour – these are described as linear, circular and elliptical polarization.

linear polarization: the electric vector is restricted to a single plane that is parallel with the direction of propagaton

circular polarization: the electric vector has a constant magnitude, but its direction rotates in a plane perpendicular to the direction of propagation. In these exercises it will be defined as right-handed if the sense of rotation is clockwise as viewed by the receiver; left-handed if anti-clockwise. (Unfortunately there are two opposite definitions of the handedness; one as seen from the reciever, the other as seen from the source).

elliptical polarization: this is a more general case, where both the magnitude and the direction of rotation can vary.

1.1 The detection of polarisation

The visual systems of some animals are known to be sensitive to the plane of polarization; examples include social insects such as ants and bees, some spiders and some cephalopods. Alas the human visual system is usually not very aware of polarization. However with some training it is possible for many people to detect the plane of linear polarization under some conditions via the visual phenomenon known as Haidinger’s Brush.

In these experiments we will overcome these evolutionary deficiencies by using modern materials that allow us to detect easily the various types of polarization.

Detecting linear polarisation.

One possibility is to use polarizing sunglasses (e.g. Polaroid) - these preferentially transmit light with horizontal polarisation; we'll see why later on. Another possibility is to use the linear polarizing glasses used for some 3D movies - in these glasses the right and left hand hand lenses usually preferentially transmit light with polarisation at 45 degress to the right or left of vertical respectively. These linearly polarising glasses in cardboard frames can be purchased via the internet for less than A$1.

Detecting circular polarisation.

Here we can use the glasses used for many 3D movies that have analysers for circular polarisation - in these glasses the right and left hand hand lenses will block circularly polarised light with left and right handed polarisation respectively. Most cinemas will provide glasses with plastic frames for around A$1 a pair - versions with cardboard frames can also be purchased via the internet even more cheaply. Two, or even three pairs, can be most useful.

1.3 The production of polarised light

Now to investigate how we can produce different types of polarized light.

Producing linearly polarised light.

The easiest method is to pass randomly polarised light through use a linear polarisation filter. (These can be constructed using materials with long chain polymers that are streched when hot so that the polymers remain aligned when cooled).

Producing circularly polarised light.

The usual method is to start with linearly polarised light that is then passed through a quarter wave plate. A quarter wave plate is constructed from a material where the speed of light is different along two orthogonal axes and has a thickness so that light that travels along one axis will undergo a phase change of 90 degrees (i.e.a quarter wave). If you shine light from the inside of your 3D glasses to the outside, the light emerging from the front will be circularly polarised.

1.4 Combinations of polarisers

You can examine what happens with various combinations of linear, left-handed circular and right-handed circular polarisers.

1.5 Polarization and 3D movies

Polarization filters

Producing circular polarised light.

In circular polarization the electric vector has a constant magnitude, but its direction rotates in a plane perpendicular to the direction of propagation. It is defined as right-handed if the sense of rotation is clockwise as viewed by the receiver; left-handed if anti-clockwise.

The 3-D glasses

The analysers in your glasses have a quarter wave plate in contact with a linear polarizer that is closest to your eye. The quarter wave plate will shift the relative phase by 90 degrees. The linear polariser is arranged so that the x and y components are now in phase, i.e. linearly polarised, in a direction that will pass through the linear polarisation filter. The filter for the left eye is arranged so that the opposite occurs for the left eye.

Quarter wave plate will only shift exactly at one wavelength.

Look at a light source through left and right lenses.
Also try the glasses in reverse; they will produce cpl

Try linear in front of glasses. Or look at a screen, although it is easier to rotate a linear filter.
Try linear filter  between after glasses and eyes.

If you have two pair of glasses Hold one in front of the other.

Use one pair of glasses in reverse. Look at the light from the reversed right eye with both  left and right. Now look at the left eye.

Try place different objects in front of the left and right analysers. Alternately closing eyes you can confirm that each eye has a different view.

2.2 The law of Malus.

Hold two linear polarisation filters up to a randomly polarised light and change their relative orientation. When their polarisation axes are aligned they should transmit the maximum amount of light (I_max). When their axes are at ninety degrees the should transmit the minimum amount of light. (The cheap filters we are using in fact will always transmit a very small amount of light at the short wavelength end of the spectrum, hence rather than black you will usually see a deep purple.)

The intensity I the of transmitted light should follow the law of Malus, i.e.

I = I_max cosΦ

where Φ denotes the angle between the planes of polarisation. This can be tested by photographing your filters with different orientations. It is best if the aperture and exposure time of your camera can be controlled so the images are all made under the same conditions. If this is not possible (for example with a simple point and shoot camera), then you will need to have something in every image that will act as a control so you can correct for varying exposures from photo to photo.

Once the images are loaded into your computer, you can use software to determine the RGB levels in appropriate places in your image. (I used the ColorSync Utility, an integral part of the MAC OS operating system)

The photo below shows an arrangement where I use an LCD screen as a source of polarised light. Taping linear polarisation glasses onto the screen allows a number of angles to be investigated simultaneously.

Optical birefringence

In the example shown below, an injection moulded, plastic tray is illuminated by the linearly polarized light from an LCD screen. A small piece of linear polarizing material is attached to the camera lens. The colours reveal the stress lines frozen into the plastic as it cooled. If you flex the plastic you will change the stresses in the material and change the colours .

 

Here are some pictures with a tray in a different orientation.

The above photo was without the filter (some faint colours can be seen where the light passed through two layers of plastic).

 

This photo was taken with the linear filter in front of the lens.

2. Polarization by reflection.

When randomly polarised light is reflected off a planar surface, light that is reflected at the Brewster angle θ_B will be linearly polarised in the same plane as the reflecting surface, where θ_B is defined by

tan θ_B = 1/n

where n denotes the refractive index of the reflecting medium.

The photos below show the effect of viewing the reflected light from a window onto a piece of glass at close to the Brewster angle.

   No filter

   Filter passes horizontal polarization only

   Filter passes vertical polarization only

Looking at such reflections is often a convenient way of determining which plane of polarization is transmitted through your linear polarization filter.

Because water surfaces tend to be horizontal (unless there is a waterfall or a really good surf running), polarising sunglasses transmit only vertically polarised light and thus remove much of the reflected light from the water surface, allowing objects to be seen below the surface. You can see this effect in the photos above, the surface grain of the wooden desk can be seen clearly through the glass slab once the reflected light is removed.

3. Polarization by scattering.

3.1 Sunset in a glass of milk

Shine the narrow beam from a torch through a container of water - a container with rectangular sides is best. Add a very small amount of milk and stir well.

Using your linear polarising filter, look at the beam that has passed through the glass and also look at right angles to the beam.

Are they polarised? Slowly increase the amount of milk.

Does the degree of polarisation increase? Does the colour of the beams change?

3.2 Scattering in the atmosphere

View the sky on a day when it is blue. Look in different directions and try rotating your linear polarisation filter.

WARNING: Be careful not to look accidently at the sun whilst doing this.

You should notice a significant degree of linear polarisation in regions of the sky that are located around 90 dgrees to the position of the sun.

Do any regions of the sky show circular polarisation?

Are the clouds polarised?