The Polarization of Light by Reflection

by Michael C. Fink – thin film scientist, Kirk Winchester – astronomy product manager, Gary Carver, and Robert L. Johnson – president and technical director.

It is now two hundred years since Étienne-Louis Malus, a French mathematician, discovered the polarization of light by reflection. Malus’s discovery was made using a birefringent mineral. Birefringence occurs when light of different polarizations travel at different speeds through a material. The result of looking through birefringent material is a double image because light of different polarizations is bent or refracted by different amounts. One such material that carries this property is a clear crystal from Iceland known as Iceland Spar. (See Fig.1)

Fig. 1: Malus made this discovery while looking through a clear piece of calcite crystal from Iceland, known as Iceland Spar, which produces a strong double refraction of light, as seen here.

Since then, our understanding of polarization of light has led to countless advances in science and technology.

While the majority of the western world uses these polarization-based advances in technology on a daily basis (polarized sunglasses, LCD displays, fiber-optic based telecommunications), few realize that, were it not for the polarizability of light, these technologies would not be possible.

To understand why light can be polarized, we have to refer back to our conventional schematic of an electromagnetic wave. (See Fig. 2)

Fig. 2: An electromagnetic wave has an electric field component and a magnetic field component. The two components cannot exist independently of each other.

A single photon creating a light ray has an oscillating electric wave component and perpendicular to that, an oscillating magnetic wave component. The two components cannot exist independently of each other and the angle that separates them is always 90o. While the angle between the two oscillating components is fixed, they can collectively be rotated. This becomes particularly important when light interacts with atoms, molecules and surfaces – all of which have an impact on the orientation of the polarization of the light.

Linear vs. Random Polarization

When a light ray is made of photons that have the same orientation of their electric and magnetic fields relative to each other, the light is said to be linearly polarized. If the waves have an orientation of their fields that is random relative to each other, the light is randomly polarized or unpolarized.

Fig. 3: This image shows the orientation of the electric fields of two examples of linearly polarized light. Both waves are linearly polarized, but they are polarized in different planes.

Partial polarization of light occurs when one orientation of the EM fields is preferential, but not exclusive. The figure below shows the orientation of the electric fields of two examples of linearly polarized light. Both waves are linearly polarized, but they are polarized in different planes. (See Fig. 3)

When Do We Expect to See Polarized Light?

Whenever light and matter interact, the polarization of the light will be altered. For example, if we collect light coming directly from the sun, it looks randomly polarized, but if we look at the sky or the reflection of the sun on a lake, the light is polarized. The light from LEDs is unpolarized, but light from a laser is polarized. Light from an LCD monitor is polarized, but light from a cathode-ray tube (TV-like monitor) is unpolarized. Why is this? There are several different reasons you might expect to see polarized light.

First, depending on the mechanism by which the light was created, it may be polarized or not. For example, if there is a group of fluorescent molecules that are all oriented with their emissive transition dipole in the same direction, the fluorescence produced by that group of molecules will all have the same orientation of electric field in their emitted light. In the case of the laser, the light is being produced by a process called stimulated emission. During stimulated emission, the emitted photons have the same polarity as the ‘stimulating’ incident photon, so the light amplification that occurs in a laser will have a preferred polarization.

In other cases, light is polarized because it has undergone a process that has preferentially removed light of a certain polarization. For example, when light reflects off of a surface, those light waves that have their electric field oriented in the plane of reflection (in the plane defined by the incident and reflected rays) is more likely to be refracted (light with this orientation of electric field is often referred to as p-polarized light). Light waves that have electric fields oriented perpendicular to the plane of reflection (s-polarized light) are more likely to be reflected.

It is possible to use reflection off a surface to isolate s-polarized light. If the orientation of the incident ray of light and the surface are adjusted carefully, one can find an angle at which all of the reflected light is s-polarized and none of it is p-polarized. This angle at which no p-polarized light reflects is called Brewster’s angle and can be found for any pair of media forming a surface (See Fig. 4) where n₁ and n₂ are the indices of refraction for the two mediums:

Fig. 4: The following graph shows that at Brewster’s angle (shown here for an air-fused silica interface, about 55 degrees and about 77 degrees for an air-silicon interface), none of the p-polarized light is reflected.

Polarized sunglasses take advantage of the fact that most of the light reflecting off a surface is s-polarized. The lenses in the sunglasses include a thin-film polarizer that selectively absorbs light with s-polarization. The result is that glare from reflections off water or ice is greatly reduced. Of course, if the wearer chooses to orient their head sidewise, they will selectively attenuate the p-polarized light and allow s-polarized light (including the reflections) to pass.

Significance of Polarization Sensitivity in Astronomy

For a long time, the effect of polarization in astronomy has been largely neglected. If you collect light from the entire surface area of a star, the light is almost completely unpolarized. In fact, the light from a distant star is so unpolarized that it can be used as a standard for unpolarized light.

The presence of polarized light in astronomy can tell us something about how the light was created. In the remnants of some supernovae, the emitted light is not unpolarized. Depending on the part of the remnant you look at, one can see a different polarization. It is also apparent that there is an interesting symmetry to the polarization. In the image below the polarization is color-coded so the blue regions have the same polarization and the reddish regions have the same polarization. (See Fig. 5) This information on the polarization of light from the different regions of the nebula can give researchers clues on the location of the obscured star.

Fig. 5: The Boomerang Nebula as seen here with color-coded, polarized light. Image courtesy of Hubble Heritage Team and NASA.

In other cases, the presence of polarized light can reveal information about an entire part of a galaxy that is otherwise hidden from sight.

In Astronomical Polarimetery by Jaap Tinbergen, the author refers to a study done in 1985 by Antonucci and Miller in which Antonucci and Miller were able to deduce the Seyfert galaxy core structure even though they couldn’t see it directly. The core of this galaxy is obscured from observation from our vantage point, but light from the core is scattered by electrons outside the galaxy’s core that Miller and Antonucci could collect. Because the light scattered by the electrons will be linearly polarized, Miller and Antonucci could separate out the scattered light they were looking for from all the other starlight from the galaxy.

One other use of polarization-sensitive measurements in astronomy is to detect the presence of magnetic fields. By examining the circular polarization of very specific colors of light coming from the sun’s corona, scientists have elucidated information about the strength of the magnetic field in those places. It is apparently a very difficult measurement to make unless the magnetic field is very strong, but some scientists have measured magnetic field strengths as small as 10 G on our own sun by using polarization sensitive measurements.

As our polarization measurement techniques become more and more precise, it is likely that we will see more astronomers considering polarization when making measurements.

Other Interesting Uses of Polarizations in Science and Technology

There are many potential uses of polarization sensitive measurements in the biomedical field. For example, there are many compounds in our bodies that are optically active, that is, they can rotate the polarization of light that passes by them. Different optically active compounds can rotate the polarization of light by different amounts and in different directions. Some optically active chemicals are present in higher concentrations during the early stages of eye disease. Doctors could potentially use this knowledge to diagnose eye diseases in the future. One might imagine a doctor shining a polarized light source into a patient’s eye and measuring the polarization of the light reflected off the retina as a non-invasive method of testing for such an eye disease.

The telecommunications industry uses polarized light to cram more information in to a single fiber optic. Different wavelengths of light can be used in the same fiber optic to send more information along the same fiber. Because of this, telecom companies would like to try and send as many different wavelengths through the same fiber.

Unfortunately, when the used wavelengths are too close together, the messages they carry can be difficult to separate when they get to the other end of the fiber. One way to get the wavelengths as close together as possible with out having the interference between wavelengths is to use different polarizations for adjacent wavelengths. With this method, it is possible to transmit (and more importantly, receive) much more information.

The telecom industry also has to be concerned with the problems posed by polarization. For example, most fibers will transmit light of different polarizations at slightly different speeds (polarization mode dispersion). This means that even if a pulse of light containing different polarizations all starts at one end of the fiber at the same time, when it reaches the other end the different polarizations will arrive at different times. Over lab table-sized distances the effect is negligible, but over thousands of kilometers, it must be considered and remedied.

Physical chemists can use the polarization of light to examine how quickly molecules rotate in solution. By exciting fluorescent molecules with one particular polarization of light, the scientists know that all the molecules that become excited will share one particular spatial orientation. When the molecules fluoresce, the polarization of their fluorescence is measured. Because the time that it takes for the absorption and re-emission of light is well known, the amount that the molecules have rotated can be inferred from the polarization of their emission signal. New polarization experiments may be able to determine how much molecules rotate and translate at the same time.

Polarization Bias of Instruments

Regardless of the field of science or engineering, nearly all optical instruments have some polarization bias. Sometimes this bias is negligible and can safely be ignored, but often the effect is significant enough to cause an erroneous result. As Tinbergen mentions in Astronomical Polarimetry, “…and astronomers now realize that, even as ‘common users’, they neglect polarization at their peril: wherever there is appreciable asymmetry in an astronomical situation, there is likely to be polarization at some level.”

For more information, visit: www.omegafilters.com