Introduction to Polarized Light


Figure 1 - Polarization of Light



The first clues to the existence of polarized light surfaced around 1669 when Erasmus Bartholin discovered that crystals of the mineral Iceland spar (a transparent, colorless variety of calcite) produce a double image when objects are viewed through the crystals in transmitted light. During his experiments, Bartholin also observed a quite unusual phenomenon. When the calcite crystals are rotated about a particular axis, one of the images moves in a circle around the other, providing strong evidence that the crystals are somehow splitting the light into two different beams.

Figure 2 - Bi-Refraction in Calcite Crystals

Over a century later, French physicist Etienne Malus examined images made with light reflected through calcite crystals and noticed that, under certain circumstances, one of the images will disappear. He incorrectly speculated that ordinary daylight is composed of two different light forms that were passed through the calcite crystal in separate paths. It was later determined that the difference occurs due to the polarity of the light passing through the crystal. Daylight is composed of light vibrating in all planes, whereas reflected light is often restricted to a single plane that is parallel to the surface from which the light is reflected.

Polarized light can be produced from the common physical processes that deviate light beams, including absorption, refraction, reflection, diffraction (or scattering), and the process known as birefringence (the property of double refraction). Light that is reflected from the flat surface of a dielectric (or insulating) material is often partially polarized, with the electric vectors of the reflected light vibrating in a plane that is parallel to the surface of the material. Common examples of surfaces that reflect polarized light are undisturbed water, glass, sheet plastics, and highways. In these instances, light waves that have the electric field vectors parallel to the surface are reflected to a greater degree than those with different orientations. The optical properties of the insulating surface determine the exact amount of reflected light that is polarized. Mirrors are not good polarizers, although a wide spectrum of transparent materials act as very good polarizers, but only if the incident light angle is oriented within certain limits. An important property of reflected polarized light is that the degree of polarization is dependent upon the incident angle of the light, with the increasing amounts of polarization being observed for decreasing incident angles.


Formula 1 - Brewster's Angle

n = sin(θi)/sin(θr) = sin(θi)/sin(θ90-i) = tan(θi)


Figure 3 - Brewster's Angle



As discussed above, bright reflections originating from horizontal surfaces, such as the highway or the water in a pool, are partially polarized with the electric field vectors vibrating in a direction that is parallel to the ground. This light can be blocked by polarizing filters oriented in a vertical direction, as illustrated in Figure 4, with a pair of polarized sunglasses. The lenses of the sunglasses have polarizing filters that are oriented vertically with respect to the frames. In the figure, the blue light waves have their electric field vectors oriented in the same direction as the polarizing lenses and, thus, are passed through. In contrast, the red light wave vibration orientation is perpendicular to the filter orientation and is blocked by the lenses. Polarizing sunglasses are very useful when driving in the sun or at the beach where sunlight is reflected from the surface of the road or water, leading to glare that can be almost blinding. Polarizing filters are also quite useful in photography, where they can be attached to the front of a camera lens to reduce glare and increase overall image contrast in photographs or digital images. Polarizers utilized on cameras are generally designed with a mounting ring that allows them to be rotated in use to achieve the desired effect under various lighting conditions.

Figure 4 - Action of Polarized Sunglasses

One of the first polarizing filters was constructed in the early nineteenth century by French scientist François Arago, who was an active investigator into the nature of polarized light. Arago investigated the polarity of light originating from various sources in the sky and proposed a theory that predicted the velocity of light should decrease as it passes into a denser medium. He also worked with Augustin Fresnel to investigate interference in polarized light and discovered that two beams of light polarized with their vibration directions oriented perpendicular to each other will not undergo interference. Arago's polarizing filters, designed and built in 1812, were made from a stack of glass sheets pressed together.

A majority of the polarizing materials used today are derived from synthetic films invented by Dr. Edwin H. Land in 1932, which soon overtook all other materials as the medium of choice for production of plane-polarized light. To produce the films, tiny crystallites of iodoquinine sulfate, oriented in the same direction, are embedded in a transparent polymeric film to prevent migration and reorientation of the crystals. Land developed sheets containing polarizing films that are marketed under the trade name of Polaroid (a registered trademark), which has become the accepted generic term for these sheets. Any device capable of selecting plane-polarized light from natural (non-polarized) white light is now referred to as a polar or polarizer, a name first introduced in 1948 by A. F. Hallimond. Because these filters are capable of differentially transmitting light rays, depending upon their orientation with respect to the polarizer axis, they exhibit a form of dichroism, and are often termed dichroic filters.

Polarized light microscopy was first introduced during the nineteenth century, but instead of employing transmission-polarizing materials, light was polarized by reflection from a stack of glass plates set at a 57-degree angle to the plane of incidence. Later, more advanced instruments relied on a crystal of doubly refracting material (such as calcite) specially cut and cemented together to form a prism. A beam of white non-polarized light entering a crystal of this type is separated into two components that are polarized in mutually perpendicular (orthogonal) directions.

One of the light rays emerging from a birefringent crystal is termed the ordinary ray, while the other is called the extraordinary ray. The ordinary ray is refracted to a greater degree by electrostatic forces in the crystal and impacts the cemented surface at the critical angle of total internal reflection. As a result, this ray is reflected out of the prism and eliminated by absorption in the optical mount. The extraordinary ray traverses the prism and emerges as a beam of linearly-polarized light that is passed directly through the condenser and to the specimen (positioned on the microscope stage).

Several versions of prism-based polarizing devices were once widely available, and these were usually named after their designers. The most common polarizing prism (illustrated in Figure 5) was named after William Nicol, who first cleaved and cemented together two crystals of Iceland spar with Canada balsam in 1829. Nicol prisms were first used to measure the polarization angle of birefringent compounds, leading to new developments in the understanding of interactions between polarized light and crystalline substances.

Figure 5 - Nicole Polarizing Prism

Presented in Figure 5 is an illustration of the construction of a typical Nicol prism. A crystal of doubly refracting (birefringent) material, usually calcite, is cut along the plane labeled a-b-c-dand the two halves are then cemented together to reproduce the original crystal shape. A beam of non-polarized white light enters the crystal from the left and is split into two components that are polarized in mutually perpendicular directions. One of these beams (labeled the ordinary ray) is refracted to a greater degree and impacts the cemented boundary at an angle that results in its total reflection out of the prism through the uppermost crystal face. The other beam (extraordinary ray) is refracted to a lesser degree and passes through the prism to exit as a plane-polarized beam of light.

Other prism configurations were suggested and constructed during the nineteenth and early twentieth centuries, but are currently no longer utilized for producing polarized light in modern applications. Nicol prisms are very expensive and bulky, and have a very limited aperture, which restricts their use at high magnifications. Instead, polarized light is now most commonly produced by absorption of light having a set of specific vibration directions in a filter medium (such as polarizing sheets) where the transmission axis of the filter is perpendicular to the orientation of the linear polymers and crystals that comprise the polarizing material.



Figure 6 - Transmission of Polarized Light Through an Analyzer

The amount of light passing through a crossed pair of high-quality polarizers is determined by the orientation of the analyzer with respect to the polarizer. When the polarizers are oriented perpendicular to each other, they display a maximum level of extinction. However, at other angles, varying degrees of extinction are obtained, as illustrated by the vector diagrams presented in Figure 6. The analyzer is utilized to control the amount of light passing through the crossed pair, and can be rotated in the light path to enable various amplitudes of polarized light to pass through. In Figure 6(a), the polarizer and analyzer have parallel transmission axes and the electric vectors of light passing through the polarizer and analyzer are of equal magnitude and parallel to each other.

Rotating the analyzer transmission axis by 30-degrees with respect to that of the polarizer reduces the amplitude of a light wave passing through the pair, as illustrated in Figure 6(b). In this case, the polarized light transmitted through the polarizer can be resolved into horizontal and vertical components by vector mathematics to determine the amplitude of polarized light that is able to pass through the analyzer. The amplitude of the ray transmitted through the analyzer is equal to the vertical vector component (illustrated as the yellow arrow in Figure 6(b)).

Continued rotation of the analyzer transmission axis, to a 60-degree angle with respect to the transmission axis of the polarizer, further reduces the magnitude of the vector component that is transmitted through the analyzer (Figure 6(c)). When the analyzer and polarizer are completely crossed (90-degree angle), the vertical component becomes negligible (Figure 6(d)) and the polarizers have achieved their maximum extinction value.


Formula 2 - Malus's Law

I = I(o) • cos2θ

where I is the intensity of light passing through the analyzer (and the total amount of light passed through the pair of crossed polarizers), I(o) is the intensity of light that is incident upon the polarizer, and θ is the angle between the transmission axes of the polarizer and analyzer. By examining the equation, it can be determined that when the two polarizers are crossed (θ = 90 degrees), the intensity is zero. In this case, light passed by the polarizer is completely extinguished by the analyzer. When the polarizers are partially crossed at 30 and 60 degrees, the light transmitted by the analyzer is reduced by 25 percent and 75 percent, respectively.

Polarization of Scattered Light

Gas and water molecules in the atmosphere scatter light from the sun in all directions, an effect that is responsible for blue skies, white clouds, red sunsets, and a phenomenon termed atmospheric polarization. The amount of light scattered (termed Rayleigh scattering) depends upon the size of the molecules (hydrogen, oxygen, water) and the wavelength of light, as demonstrated by Lord Rayleigh in 1871. Longer wavelengths, such as red, orange, and yellow, are not scattered as effectively as are the shorter wavelengths, such as violet and blue.

Figure 7 - Polarization of Scattered Sunlight

Atmospheric polarization is a direct result of the Rayleigh scattering of sunlight by gas molecules in the atmosphere. Upon impact between a photon from the sun and a gas molecule, the electric field from the photon induces a vibration and subsequent re-radiation of polarized light from the molecule (illustrated in Figure 7). The radiated light is scattered at right angles to the direction of sunlight propagation, and is polarized either vertically or horizontally, depending upon the direction of scatter. A majority of the polarized light impacting the Earth is polarized horizontally (over 50 percent), a fact that can be confirmed by viewing the sky through a Polaroid filter.

Reports have surfaced that certain species of insects and animals are able to detect polarized light, including ants, fruit flies, and certain fish, although the list may actually be much longer. For example, several insect species (primarily honeybees) are thought to employ polarized light in navigating to their destinations. It is also widely believed that some individuals are sensitive to polarized light, and are able to observe a yellow horizontal line superimposed on the blue sky when staring in a direction perpendicular to the sun's direction (a phenomenon termed Haidinger's brush). Yellow pigment proteins, termed macula lutea, which are dichroic crystals residing in the fovea of the human eye, are credited with enabling a person to view polarized light.

Elliptically and Circularly Polarized Light




The ordinary and extraordinary light waves generated when a beam of light traverses a birefringent crystal have plane-polarized electric vectors that are mutually perpendicular to each other. In addition, due to differences in electronic interaction that each component experiences during its journey through the crystal, a phase shift usually occurs between the two waves. Although the ordinary and extraordinary waves follow separate trajectories and are widely separated in the calcite crystal described previously, this is not usually the case for crystalline materials having an optical axis that is perpendicular to the plane of incident illumination.

Figure 8 - Elliptically and Circularly Polarized Light Waves




Applications of Polarized Light

One of the most common and practical applications of polarization is the liquid crystal display (LCD) used in numerous devices including wristwatches, computer screens, timers, clocks, and a host of others. These display systems are based upon the interaction of rod-like liquid crystalline molecules with an electric field and polarized light waves. The liquid crystalline phase exists in a ground state that is termed cholesteric, in which the molecules are oriented in layers, and each successive layer is slightly twisted to form a spiral pattern (Figure 9). When polarized light waves interact with the liquid crystalline phase the wave is "twisted" by an angle of approximately 90 degrees with respect to the incident wave. The exact magnitude of this angle is a function of the helical pitch of the cholesteric liquid crystalline phase, which is dependent upon the chemical composition of the molecules (it can be fine-tuned by small changes to the molecular structure).

Figure 9 - Seven-Segment Liquid Crystal Display (LCD)

An excellent example of the basic application of liquid crystals to display devices can be found in the seven-segment liquid crystal numerical display (illustrated in Figure 9). Here, the liquid crystalline phase is sandwiched between two glass plates that have electrodes attached, similar to those depicted in the illustration. In Figure 9, the glass plates are configured with seven black electrodes that can be individually charged (these electrodes are transparent to light in real devices). Light passing through polarizer 1 is polarized in the vertical direction and, when no current is applied to the electrodes, the liquid crystalline phase induces a 90 degree "twist" of the light that enables it to pass through polarizer 2, which is polarized horizontally and is oriented perpendicular to polarizer 1. This light can then form one of the seven segments on the display.


The phenomenon of optical activity in certain chemicals derives from their ability to rotate the plane of polarized light. Included in this category are many sugars, amino acids, organic natural products, certain crystals, and some drugs. Rotation is measured by placing a solution of the target chemical between crossed polarizers in an instrument termed a polariscope. First observed in 1811 by French physicist Dominique Arago, optical activity plays an important role in a variety of biochemical processes where the structural geometry of molecules governs their interactions. Chemicals that rotate the vibrational plane of polarized light in a clockwise direction are termed dextrorotatory, while those that rotate the light in a counterclockwise direction are referred to as levorotatory. Two chemicals having the same molecular formula but different optical properties are termed optical isomers, which rotate the plane of polarized light in different directions.

Asymmetric crystals can be utilized to produce polarized light when an electric field is applied to the surface. A common scientific device that employs this concept is termed a Pockels cell, which can be utilized in conjunction with polarized light to change the polarization direction by 90 degrees. Pockels cells can be switched on and off very rapidly by electrical currents and are often used as fast shutters that allow light to pass for very brief periods of time (ranging in nanoseconds). Presented in Figure 10 is a diagrammatic representation of polarized light passing through a Pockels cell (yellow wave). The green and red sinusoidal light waves emanating from the central region of the cell represent light that is polarized either vertically or horizontally. When the cell is turned off, the polarized light is unaffected as it passes through (green wave), but when activated or turned on, the electric vector of the light beam is shifted by 90-degrees (red wave). In situations where extremely large electric fields are available, molecules of certain liquids and gases can behave as anisotropic crystals and be aligned in the same manner. A Kerr cell, designed to house liquids and gases instead of crystals, also operates to change the angle of polarized light.

Figure 10 - Anatomy of the Pockets Cell

Other applications for polarized light include the Polaroid sunglasses discussed above, as well as the use of special polarizing filters for camera lenses. A variety of scientific instruments utilize polarized light, either emitted by lasers, or through polarization of incandescent and fluorescent sources by a host of techniques. Polarizers are sometimes used in room and stage lighting to reduce glare and produce a more even degree of illumination, and are worn as glasses to bestow an apparent sense of depth to three-dimensional movies. Crossed polarizers are even utilized in space suits to dramatically reduce the chances of light from the sun entering the astronaut's eyes during naps.

Polarization of light is very useful in many aspects of optical microscopy. The polarized light microscope is designed to observe and photograph specimens that are visible primarily due to their optically anisotropic character. Anisotropic materials have optical properties that vary with the propagation direction of light passing through them. In order to accomplish this task, the microscope must be equipped with both a polarizer, positioned in the light path somewhere before the specimen, and an analyzer (a second polarizer), placed in the optical pathway between the objective rear aperture and the observation tubes or camera port.

Image contrast arises from the interaction of plane-polarized light with a birefringent (or doubly-refracting) specimen to produce two individual wave components that are polarized in mutually perpendicular planes. The velocities of these components are different and vary with the propagation direction through the specimen. After exiting the specimen, the light components are out of phase and sweep an elliptical geometry that is perpendicular to the direction of propagation, but are recombined through constructive and destructive interference when they pass through the analyzer. Polarized light microscopy is a contrast-enhancing technique that improves the quality of the image obtained with birefringent materials when compared to other techniques such as darkfield and brightfield illumination, differential interference contrast, phase contrast, Hoffman modulation contrast, and fluorescence. In addition, use of polarized light allows the measurement of optical properties of minerals and similar materials and can aid in the classification and identification of unknown substances.

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Introduction to Polarized Light