THE LIGHT that enters your eyes is a wave pattern of oscillating electric and magnetic fields that are perpendicular to the direction of travel of the light. Most of the light by which you see is unpolarized, that is, the fields oscillate along all possible directions perpendicular to the direction of travel of the light. Some of the light, however, is linearly polarized and thus has electric fields that oscillate along a single axis perpendicular to the direction of travel. For example, light directly from the sun is unpolarized whereas the sunlight reflected from a road surface can be polarized (with the electric field oscillating primarily horizontally).

Probably the most convenient modern way to convert unpolarized light from the sun or some other light source is with a polarizing filter such as a Polaroid filter. If initially unpolarized light passes through such a filter it becomes linearly polarized. In other words, the filter transmits light with electric fields that oscillate alone a single axis perpendicular to the direction of travel of the light. This selective transmission can be helpful. If a motorist wants to eliminate the glare from a road surface, he can wear polarized sunglasses that pass light with electric fields that oscillate vertically, thereby stopping the glare from ray with electric fields that oscillate primarily horizontally.

Standard polarizing filters are made by stretching sheets of the plastic polyvinyl alcohol. Initially the long-chain molecules in the sheets are in random orientations and show no preference for one polarization or another. When the sheets are warmed and then stretched however, the long molecules tend to align themselves in the direction of stretch. When unpolarized light passes through such a sheet of oriented molecules, the component of the light's electric field that lies along the molecules is absorbed by them. The electric field perpendicular to the length of the molecules is not absorbed. Hence when the light emerges, its electric field is along single axis and is linearly polarized. The polarizing sheet is called dichroic be cause its absorption is different for different polarizations of the incident light Two polarizing filters aligned in the same way will transmit light whereas two filters aligned with perpendicular senses of polarization will block it.

In other materials, such as certain crystals, both of the different senses o polarization for the incident light will b transmitted, but they will have different effective speeds. Such materials, which are called birefringent or doubly refracting, have two perpendicular axes the speed of light is higher along on axis than along the other.

Suppose linearly polarized light is incident on a birefringent material in such a way that the sense of polarization o the light is at an angle to the fast an slow axes of the material. The polariza tion of the incident light has two compo nents of interest, one component paral lel to the fast axis and one parallel to th slow axis. Initially these two parts are i phase, that is, the oscillations in the electric field along the two axes are exactly in step. When the light passes through the birefringent material, however, the difference in the propagation speed of the two components causes one component to differ in phase from the other.

For example, suppose the width of the material is such that the light emerging along the slow axis lags behind the light emerging along the fast axis by a quarter of a wavelength, or 90 degrees (since a full wavelength along a wave is represented by 360 degrees). Then the phase difference between the two emerging components is said to be a quarter of a wavelength, or 90 degrees. In this case the material would be called either a quarter-wave plate or a 90-degree retarding plate, because it took two incident components of light that were in phase and left them 90 degrees out of phase. The emerging light is no longer linearly polarized because of this phase difference.

The combination of the two emerging components differing in phase by 90 degrees is elliptically polarized light in which the sense of polarization (the axis along which the net electric field oscillates) constantly rotates around the axis along which the light propagates. You can imagine that the tip of the arrow representing the sense of polarization maps out an ellipse around the propagation axis. If the two emerging components are of equal amplitude (if the maximum electric-field strength is the same along the fast axis and the slow one), the tip maps out a circle and the emerging light is circularly polarized. This result is obtained if the sense of polarization of the incident light lies at an angle of 45 degrees to the fast and slow axes of the birefringent material.

The material could also be of a thickness that would cause the emerging light components to be 180 degrees out of phase with each other, which is a shift of half a wavelength between the two. Then the material would be called a half-wave plate or a 1 80-degree retarding plate. The net electric field of the emerging components would oscillate along a single axis, and thus the light would again be linearly polarized. Now, however, the axis of polarization is not the same as it is for the incident light. The new axis of polarization will be flipped around either the slow axis or the fast one.

In his book Waves Frank S. Crawford, Jr., of the University of California at Berkeley describes several experiments you can do with common birefringent materials. He also provides information on how you can make your own quarterand half-wave plates. My topic this month involves making these optical devices, investigating their effects on polarized light and using the plates to demonstrate the birefringence in the cornea of your eye. Next month I shall describe how to employ the devices to make circularly polarized light.

Between two polarizing filters crossed to eliminate any transmitted light place a piece of clear plastic wrapping from a candy bar or a package of cigarettes. (The filters are available from the Edmund Scientific Company, 7778 Edscorp Building, Barrington, N.J. 08007, for $2.50 for a package of 20, or you can dismantle a pair of polarized sunglasses.) Then look at an incandescent lamp that has a clear glass bulb and a straight filament. With the plastic in place some light is transmitted through the system of filters because the plastic reorients the polarization of light incident on it and thereby provides the second polarizing filter with a component of light polarized in the same sense as the second filter. By rotating the plastic you can maximize the transmitted light.

A length of food wrapping (available in the U.S. under such names as HandiWrap and Saran Wrap) initially does not act in the same way. By stretching the wrapping, however, you can orient its long molecules as the molecules are oriented in the making of polarizing filters: you can thereby instill fast and slow axes in the material. Between two crossed polarizing filters place a stretched length of food wrapping so that the stretch direction is at 45 degrees to the polarization senses of the filters. You will then get a lot of transmitted light through the filter system.

From several layers of stretched food wrapping you can make your own quarter- or half-wave plate. Over a hole in a sturdy piece of metal, wood or cardboard tape from 10 to 14 layers of food wrapping, with each layer stretched in the same direction. Tape to one side of the hole a polarizing filter with its sense of polarization at an angle of 45 degrees to the stretch direction of the wrapping. The filter provides linearly polarized light to the layers, with equal components along the stretch axis and perpendicular to it.

With the proper number of layers taped in place the wrapping acts as a half-wave plate for a particular wavelength in the incident white light. For that wavelength the two components of the emerging light differ in phase by 180 degrees, or half a wavelength. You can detect this phase shift by placing another polarizing filter in the path of the emerging light and testing for its sense of polarization.

For example, suppose you have taped down enough layers to make a halfwave plate at a wavelength of 500 nanometers, which is green light. Then the green in the incident light undergoes a 1 80-degree phase shift between the two components in the emerging light. The emerging components add to give a net sense of polarization that is linear and perpendicular to the initial polarization. If the second polarizing filter is oriented to pass this polarization, you will see mostly green light. If the second filter is oriented parallel to the polarization sense of the first filter, the green light is blocked by the second filter and you see instead the visible spectrum with green absent.

For any orientation of the second filter you see colors (perhaps dimly) for which the food wrapping is not a halfwave plate, so that the colors emerge elliptically polarized. You can "tune" the half-wave plate by adding or subtracting layers of food wrapping and then testing for the color transmitted when the second filter is placed perpendicular to the first one. If you halve the number of layers, you will have a quarter-wave plate.

You can also make a half-wave plate out of a single layer of clear plastic tape (not "magic transparent tape," which is only semitransparent). Stick the layer on a piece of glass (for support) and then place it between two polarizing filters with their senses of polarization crossed. A particular range of colors will be transmitted; they are the colors for which the thickness of the tape is approximately a half-wave plate. My cellophane tape was approximately a halfwave plate for much of the visible spectrum except at the blue end. With crossed filters the transmitted light appeared to be white: with parallel filters the transmitted light was blue.

With a half-wave plate made out of either plastic wrapping or cellophane tape, examine the emerging light with a diffraction grating. (Such a grating, which is available from Edmund Scientific for about 50 cents. spreads the light out into a spectrum.) If the second polarizing filter is oriented to transmit the wavelength for which the device is a half-wave plate, you will find that color in the spectrum from the grating. Rotating the second filter to the perpendicular orientation blocks that color and eliminates it from the spectrum seen in the grating.

With several layers of transparent tape you can make a filter that passes light only in certain narrow ranges of wavelength. Make a stack of 16 layers of clear plastic tape on a piece of glass. To improve the transmission through the layers place a small drop of machine oil between each successive layer and between the first layer and the glass. Then orient the stack between two polarizing filters as you did with the single layer of tape.

Again examine the emerging light with the diffraction grating. The transmitted spectrum has several dark lines between colored images of the lamp's filament, indicating that the second polarizing filter is blocking several different wavelengths in the light emerging from the layers. As you rotate the second filter the dark lines are replaced by bright lines and vice versa. When the second filter is turned perpendicular to its first orientation, it passes the wavelengths it formerly blocked and blocks the ones it formerly passed.

For some wavelengths in the incident white light the stacked layers effectively constitute a half-wave plate, and their emerging polarizations are linear and flipped around either the slow axis or the fast one. For some of the other wavelengths the stacked layers are effectively a full-wave plate; their polarization is maintained. (A phase shift of any integral number of wavelengths merely causes the emerging components of the light-the ones along the slow and fast axes-to come back in phase. so that they have the same polarization as the incident light does.) Hence one orientation of the second polarizing filter selects one of these results to transmit. Another orientation of the polarizing filter selects the other result. In either case the spectrum is incomplete; only certain wavelengths are allowed to pass.

A single layer of tape gives a phase shift of about half a wavelength in the visible spectrum. To obtain a shift of a full wavelength for some colors you need a thicker stack of tape. Four layers Of tape will work, but the dark lines are more apparent with 16 layers. To see this effect make two rnore stacks of cellophane tape, one with four layers and one with eight. For a particular orientation of the second polarizing filter the 16-layer stack passes light in fairly narrow ranges of wavelengths. The smaller stacks also pass light only in certain ranges of wavelengths, but the ranges are wider the smaller the stack is.

This type of band-pass filter was developed by the French astronomer B. F. Lyot in 1932 for photographing the sun. The bandwidth (the width of the wavelength range transmitted by the filter) was as small as .1 nanometer in the Lyot filters, which were made out of quartz. With the Lyot filter tuned to pass, say, one of the hydrogen-emission wavelengths and to block all other visible wavelengths the sun could be photographed in its hydrogen emission, thereby displaying the behavior of hydrogen on the sun.

Most people are able to detect polarized light with the unaided eye. Look through a linearly polarizing filter at a blue portion of the sky or at some other blue and generally featureless background. In the center of your field of vision will lie a small, faint, yellow hourglass figure subtending an angle of about three degrees. Small blue areas may also be seen at the sides of the hourglass. (They are not visible to everyone.)

The hourglass is called Haidinger's brushes, after the Austrian mineralogist Wilhelm Karl von Haidinger, who discovered the effect in 1844. The fig~re quickly fades unless the sense of polar ization of the light incident on your eyes changes, so that you should rotate the polarizing filter slowly to keep the figure visible. The hourglass rotates in the same way.

If you cannot see the hourglass, you may be able to see it later in life. Several years ago I could see the figure in the polarized light from the sky without using any polarizing filter. Now I need the filter because the polarization of the sky is apparently not sufficient to produce the hourglass in my eye.

Although Haidinger's brushes have been discussed for a long time, their full explanation is still not available. They are probably caused by the selective absorption of light by the pigment in the macula lutea, the small region of the retina that is responsible for the greatest acuity in seeing. The pigment absorbs in the blue end of the visible spectrum, at wavelengths from 430 to 490 nanometers, but the absorption depends on the polarization sense of the incident light.

To schematize the absorption characteristics, one draws pigment elements laid out in radial lines from a center. The maximum absorption occurs along a diameter of such a pattern when the diameter is perpendicular to the sense of polarization of the light incident on the macula lutea. For example, suppose you hold the polarizing filter so that vertically polarized light enters the eye. Then the maximum absorption of the blue in the incident light takes place along a horizontal diameter. If you rotate the filter, maximum absorption occurs along other diameters, always perpendicular to whatever sense of polarization you happen to give your eye. As we have seen, material that absorbs different amounts of light along different axes is defined as being dichroic. The pigment in the macula lutea of your eye is said to be radially dichroic because of this dependence on the incident polarization.

For the sake of simplicity consider the incident light to be vertically polarized. The elimination of the blue along the horizontal by the pigment means that the retina reports to the brain the complementary color yellow as being along the horizontal. This yellow is the long axis of Haidinger's brushes. The blue clouds on each side of the hourglass have not been completely explained but are probably psychological in that the brain itself is responsible for the impression that blue is present. If you cannot find the hourglass while looking at the sky with a filter, you might try viewing a blue wall illuminated by sunlight. In any case the hourglass requires linearly polarized blue light incident on the eye in order to be seen.

Haidinger's brushes do more than indicate that part of your eye is sensitive to the polarization sense of light; they can also be employed to show that another part of your eye is birefringent. To demonstrate this effect you need a linear polarizing filter and a quarter-wave plate tuned to the green or yellow. Orient the linear filter to yield vertically polarized light. Insert between it and your eye a quarter-wave plate with its slow axis slanted upward and outward. (If you are using your right eye, the slow axis should run from the bottom left to the top right.) By inserting the quarterwave plate in this way you make the Haidinger's brushes from the linear filter suddenly change orientation by 90 degrees, from the horizontal to the vertical. If the plate's slow axis is instead slanted upward and inward (for the right eye running from the bottom right to the top left), the hourglass disappears. Using a half-wave plate (in the green or yellow) instead of a quarter-wave one gives opposite results.

Because the brushes may be difficult to see with your homemade quarterwave plate, you might want to replace it and the linear polarizer with a circular polarizer that the Polaroid Corporation will provide to readers of this department without charge (Polaroid Corporation, Polarizer Technical Products, 20 Ames Street, Cambridge, Mass. 02139). Ask for the card "Polaroid Circular Polarizers for Contrast Improvement," to which the polarizer is taped. Several of the uses to which a circular polarizer can be put will be discussed in this department next month.

The question of why the hourglass either disappears or is flipped by 90 degrees is not settled. Apparently the effect of the inserted plate is to add to the birefringence already present in the cornea to give a net birefringence of either a quarter- or half-wave plate for blue light. If the inserted plate and the cornea are effectively a quarter-wave plate for blue light, the brush disappears. If they are effectively a half-wave plate for blue light, the brush is flipped perpendicular to the orientation the linear filter alone would give.

The cornea contains fibrils of collagen that slant mainly upward and outward. They are birefringent, with the slow axis along the length of the fiber and the fast axis upward and inward. The phase shift between the fast and slow axes is normally not sufficient to be noticed, being only about a twelfth of a wavelength in green light. If the quarter- or half-wave plate is used properly, however, the total shift of the plate and the collagen can be sufficient to change the sense of polarization of the incident blue light that is necessary to create Haidinger's brushes.

Consider the quarter-wave plate as being oriented with its slow axis upward and outward, as the slow axis of the collagen fibrils is. In the green-yellow the quarter-wave plate produces a phase shift of about a quarter of a wavelength and the collagen produces an additional shift of about a twelfth, giving a total shift of approximately a third of a wavelength in that color region. Other colors are shifted proportionately to their wavelength, the blue being shifted less than the red.

Since Haidinger's brushes depend on blue light, the shift in the blue is the interesting one. The total shift in the blue is about two-fifths of a blue wavelength. Thus the quarter-wave plate and your cornea act in combination as approximately a half-wave plate in the blue. Vertically polarized light transmitted through a half-wave plate oriented with its slow axis perpendicular to the polarization changes the polarization by 90 degrees (from vertical to horizontal in this case). Correspondingly, the brushes flip from the horizontal when no plate is in place to the vertical when the plate is inserted, provided that the plate is positioned properly.

If the quarter-wave plate has its slow axis upward and inward, the brushes are eliminated. In the~yellow-green region the plate phase shifts the light by about a quarter of a wavelength in one direction and the collagen shifts it by about a twelfth of a wavelength in the opposite direction, giving a net phase shift of about a sixth of a wavelength in the green-yellow. In the blue this is a net phase shift of about a fifth of a wavelength. In other words, the combination of the collagen and the quarter-wave plate oriented in this way in effect creates a quarter-wave plate in the blue. The combination produces elliptically polarized light to illuminate the macula lutea, but light of that type does not produce Haidinger's brushes. With this sense of orientation for the inserted quarter-wave plate the brushes therefore disappear.

The effect of a half-wave plate inserted between a vertically oriented polarizing filter and your eye is similar. With the slow axis upward and outward the combined phase shift produced by the plate and your cornea is about threequarters of a wavelength in the blue. The plate and cornea hence act as a quarter-wave plate in the blue, producing elliptically polarized light for the retina. No brushes appear. With the slow axis upward and inward the net phase shift is about half a wavelength in the blue. This time the plate and the cornea together act as a half-wave plate in the blue; they flip the sense of the incident linearly polarized light by 90 degrees and thereby rotate the Haidinger's brushes from the horizontal to the vertical.

If you can successfully see the effects with the preceding arrangements, you might want to try other relative orientations of the linearly polarized filter, the quarter- or half-wave plate and the collagen fibrils. The principles are the same, but predicting the outcome in each case would be a good test of your understanding of how quarter- and halfwave plates work.

Bibliography

POLARIZED LIGHT. William A. Shurcliffe and Stanley S. Ballard. D. Van Nostrand Company, 1964.

WAVES. Frank S. Crawford. McGraw-Hill Book Company, 1968.

HAIDINGER'S BRUSHES AND PREDOMINANT ORIENTATION OF COLLAGEN IN CORNEAL STROMA. C.C.D. Shute in Nature, Vol. 250, No. 5462, pages 163-164; July 12, 1974.

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