Physics Bootcamp

Another polarization of particular interest happens when electric field direction rotates in space and time as shown in Figure 46.16. For a wave traveling towards positive \(z\) axis, electric field direction will be in the \(xy\) plane. For linear polarized light, the electric field stays along one line in \(xy\) plane. But, if light is circularly polarized, the direction of polarization rotates in \(xy\) plane as shown in the figure.

There are two types of circularly polarized light as shown in Figure 46.16. One way to tell the difference is to use handedness. Point the thumb of your right towards the direction of propagation of the wave. Now, if you curl the other fingers and the electric field rotates in time in the same direction as curling of your other fingers of your right hand, then it is said to be right-handed circularly polarized and if it goes in the opposite direction, then you have left-handed circularly polarized. Sometimes clockwise and countecloskwise is also used, but they depend on whether you are looking from the direction of the source or the target.

Looking at \(E_x\) and \(E_y\text{,}\) you would notice that if the arguments of the cosines, i.e., the phases, of \(E_x\) and \(E_y\) were same, you would not get any rotation. The rotation of electric field, which is a vector sum of the \(x\) and \(y\) parts, comes from the lag of phase of the \(E_y\) wave, the full value of \(E_y\) occurs \(T/4\) later than it occurs for \(E_x\text{.}\)

Finally, if the direction of polarization of incident light is some angle \(\theta\) to the the polarization direction of the polarizer, then only some of the light is blocked. How much is blocked in this case? To analyze this general case, note that we need to think in terms of electric field to see what is let through and what is blocked.

Natural light such as the light from the Sun is unpolarized. It is generally a random mixture of various waves of different polarizations and frequencies. There are devices that act as filter of light and let through light with a particular type of polarization. These devices are called polarizers.

There are various types of polarizers depending on the polarization of the light that is emitted from the polarizer. For instance, if light emitted is linearly polarized, we call it a linear polarizer and light emitted is a circularly polarized light we call it a circular polarizer. Linear polarizers are easier to understand and we will mostly look at them.

There are some naturally occuring crystals, such as tourmaline, that have dichroic property of preferentially absorbing polarization light. Hence, such a crystal will let through light polarized in the perpendicular direction to the direction of polarization that the crystal absorbs. These crystals introduce some other artefacts such as absorption depending on wavelength also and they are not the primary means we obtain polarized light.

A majority of polarizers, such as use in sun glasses, are made from synthetic materials. For instance, in H-sheet Polaroid, clear polyvinyl alcohol (PVA) is stretched along its chains, and then dipped into iodine solution which imbeds into the plastic and arranges along the long hydrocarbon chains, essentially making molecular size wires of iodine. These Polaroids transmit electromagnetic waves whose polarization is perpendicular to the direction of "iodine wires". In a sense, these are synthetic dichroic materials, and that is why ther are also referred to as dichroic filters.

In Section 46.4, we have also seen that if we reflect light at Brewster’s angle, then P-wave does not have any reflection but S-wave does have reflection. Therefore, if we reflect an unpolarized light off a surface at the Brewster’s angle, then we will get only S-wave in the reflected direction. Now, S-wave is polarized perpendicular to the plane of incidence. This will give light polarized linearly in the direction perpendicular to the incidence plane and parallel to the interface.

We will discuss special types of crystals, such as calcite, that have refractive index that depends on the polarization direction of light with respect to a crystal axis. These crystals are called birefringent crystals This leads to separation of light of different polarizations and hence can also be used to produce polarized light.

By using an appropriate arrangement of linear polarizers, you can obtain polarized light that is polarized in any desired direction in the plane perpendicular to the direction of the wave. However, each polarizer reduces the intensity of light by blocking off the perpendicular components.

If you look back in Subsection 46.5.2, you will find that to produce right circularly polarized light moving in positive \(z\) axis, we need to introduce delay of \(\pi/2\) in the phase of the \(E_y\) wave relative to the \(E_x\) wave. And similarly for the left-circularly polarized light. Thus, we need polarization dependent wave velocity. Recall that wave velocity in a medium is \(v = c/n\text{.}\) This means we need polarization dependent refractive index. Birefringent materials have just such a property. Therefore, when a linearly polarized light is sent in appropriate direction and through appropriate thickness of a birefringent crystal, the crystal produces the desired delay. These devices are called retarders. There are commercially available quarter-wave and half-wave plates that do the appropriate retardations.

A retarder is constructed to retard the phase of one of the components by a set amount. You can buy full-wave, half-wave and quarter-wave plates. The cause relative retardations of the phase by \(2\pi\text{ rad}\text{,}\) \(\pi\text{ rad}\) and \(\pi/2\text{ rad}\) respectively. Also commonly available are compensators which can be used to produce retardation to a arbitrary degree.

The above describes how you can turn a linearly polarized light into a circularly polarized light. If you want to go the other way around, it is much simpler - you just pass the circularly polarized light through a linear polarizer!