Dichroic and Diffraction-Type Polarizers

This is a continuation from the previous tutorial - multidimensional optimized optical modulation formats.

Some of the most useful polarizers available employ either dichroism or diffraction effects. These polarizers come in sheet form, sometimes in large sizes, are easily rotated, and produce negligible beam deviation.

Also, they are thin, lightweight, and rugged, and most can be made in any desired shape. The cost is generally much less than that of a prism-type polarizer. Furthermore, both types are insensitive to the degree of collimation of the beam, so that dichroic or diffraction-type polarizers can be used in strongly convergent or divergent light.

A dichroic material is one which absorbs light polarized in one direction more strongly than light polarized at right angles to that direction. Dichroic materials are to be distinguished from birefringent materials, which may have different refractive indexes for the two electric vectors vibrating at right angles to each other but similar (usually negligible) absorption coefficients.

Various materials are dichroic, either in their natural state or in a stretched condition. The most common materials used as dichroic polarizers are stretched polyvinyl alcohol sheets treated with absorbing dyes or polymeric iodine, commonly marketed under the trade name Polaroid.

Another type of dichroic polarizer is prepared by rubbing a glass or plastic surface in a single direction and then treating it with an appropriate dye. Polarizers of this type are sold under the trade name Polacoat.

In certain portions of the infrared spectral region, calcite is strongly dichroic and makes an excellent high-extinction polarizer. Pyrolytic graphite is electrically and optically anisotropic and has been successfully used as an infrared polarizer.

Other materials which exhibit dichroism in the infrared include single-crystal tellurium, ammonium nitrate, mica, rubber under tension, polyvinyl alcohol, and polyethylene.

In the visible region, gold, silver, and mercury in the form of microcrystals, needles of tellurium, graphite particles, and glasses containing small elongated silver particles are all dichroic.

A sodium nitrate polarizer described by Yamaguti is not dichroic in the strict sense of the word but acts like a dichroic polarizer. Roughened plates of SK5 glass are bonded together by a single crystal of sodium nitrate, which has a refractive index for the ordinary ray nearly equal to that of the glass. The extraordinary ray has a much lower index, so that it is scattered out of the beam by the rough surfaces, leaving the ordinary ray to be transmitted nearly undiminished.

Diffraction-type polarizers include diffraction gratings, echelettes, and wire grids. These are all planar structures that have properties similar to those of dichroic polarizers except that they transmit one component of polarization and reflect the other when the wavelength of the radiation is much longer than the grating or grid spacing. 

None of these polarizers has as high a degree of polarization as the prism polarizers. Thus it is frequently necessary to measure the polarizing properties of the particular polarizer used.

A source of plane-polarized light is desirable for such a measurement. Lacking that, one of the procedures can be followed if there are two identical imperfect polarizers. Alternate methods are also described which are applicable to two nonidentical imperfect polarizers.

Sheet Polarizers

Various types of sheet polarizers have been developed by Edwin H . Land and coworkers at the Polaroid Corporation, Cambridge, Mass. Sheet polarizers are also available from several European companies.

The J sheet polarizer, the first type available in America (around 1930), consisted of submicroscopic needles of herapathite oriented parallel to one another in a sheet of cellulose acetate.

Since this type of polarizer, being microcrystalline, had some tendency to scatter light, it was superseded by H and K sheet molecular polarizers, which exhibit virtually no scattering.

The most widely used sheet polarizer is the H type, which consists of a sheet of polyvinyl alcohol that has been unidirectionally stretched and stained with iodine in a polymeric form.

The K type is made by heating a sheet of polyvinyl alcohol in the presence of a catalyst to remove some of the water molecules and produce the dichromophore polyvinylene. It was developed primarily for applications where resistance to high temperature and high humidity are necessary.

Another type of polarizing sheet, made from a combination of the H and K types, has an absorption maximum at about 1.5 μm in the infrared and is designated as HR Polaroid.

The history of the development of the various kinds of sheet polarizers has been given by Land, their chemical composition by Land and West, and their optical performance by Shurcliff, Baumeister and Evans, Land and West, and Land.

In addition, Blake et al. mention the HR infrared polarizer, and Makas describes the modified H-film polarizer for use in the near ultraviolet. Baxter et al . describe a technique for measuring the optical density of high-extinction polarizers in the presence of instrumental polarization.

Figure 13 shows the principal transmittance \(T_1\) and extinction ratio \(T_2/T_1\) of various types of H and K sheet polarizers used in the visible and near ultraviolet.

In addition, curves for two sheet polarizers manufactured by Zeiss and two types of polarizing filters from Polacoat are shown. The letter N in the designation of the Polaroid sheets stands for neutral (to distinguish them from sheet polarizers prepared from colored dyes), and the number 22, 32, etc., indicates the approximate transmittance of unpolarized visible light.

Figure 14 gives the principal transmittance and extinction ratio of a typical plastic laminated HR infrared polarizer. Sometimes the optical density \(D\) of a polarizer is plotted instead of its transmittance. The relation between these two quantities is

\[\tag{8}D=\log\frac{1}{T}\]

The extinction ratio of the HN-22 Polaroid compares favorably with that of Glan- Thompson prisms throughout the visible region, but the transmission of the Glan- Thompson is superior.

In the ultraviolet, the new HNP'B material has a reasonably good extinction ratio (about \(10^{-3}\) or better) for wavelengths longer than 3200 Å. It is a specially purified form of HN-32, and its properties match those of the standard HNT-32 Polaroid at wavelengths longer than 4500 Å.

Optical properties of various types of Polaroid dichroic polarizers have been described by Trapani. According to West and Jones, the extinction ratio for a dichroic polarizer of the Polaroid type has a practical limit of about \(10^{-5}\) because, as the concentration of dichromophore is increased beyond a certain value, the optical density no longer increases proportionately.

Gunning and Foschaar have described a method for the controlled bleaching of the iodine dichromophore in iodine-polyvinyl alcohol polarizers to achieve an increased internal transmission of up to 95 percent for the principal transmittance of linearly polarized light in the 5000- to 6000- Å wavelength region.

This is achieved at the expense of degrading the extinction ratio and drastically affecting the short wavelength performance of the polarizer. Baum describes the application of sheet polarizers to liquid crystal displays and problems encountered in this application.

If Polaroids are used in applications where beam deviation is important, they should be checked for possible deviation. Most Polaroids, which are laminated in plastic sheets, do produce a slight beam deviation that can be observed through a telescope as a shift in the image position when the Polaroid is rotated.

The amount of the deviation varies from point to point on the Polaroid and can be much worse if the material is mounted between glass plates . It is possible to order specially selected sheet Polaroid laminated between polished glass plates that deviates the beam by only about 5 seconds of arc.

Sheet polarizers made of stretched polyvinyl alcohol that has been stained with iodine or various dyes are also made in countries outside the United States.

King and Talim have measured the axis wander and ellipticity of beams transmitted by various types of sheet polarizers in the same way as for Glan-Thompson prisms. They found considerable variations from one type of sheet polarizer to another and also over a single sheet.

Dichroic Polarizing Coatings

Beilby-layer polarizers are dichroic coatings that can be applied to the surface of glass or plastic. The process was developed by Dreyer, who founded the company which manufactures Polacoat polarizing filters.

There are three main steps in the production of these polarizers.

First, the substrate (quartz, glass, plastic, etc.) is rubbed along parallel lines with filter paper, cotton, or rouge to produce a preferred surface orientation. (The affected region of minute scratches extends to a depth of less than 1 μm.)

Then the sheet is rinsed and treated with a solution of dichroic molecules, e. g., a 0.5 percent solution of methylene blue in ethanol or one or more azo dyes, and then dried in a controlled fashion. Presumably the molecules line up preferentially along the rubbing direction, resulting in a greater absorption for light, polarized in that direction.

As a final step, the surface is treated with an acidic solution, often that of a metallic salt such as stannous chloride, which can increase the dichroism and produce a more neutral color. A protective coating over the polarized surface provides mechanical protection for the fragile layer with no loss in transmission.

McDermott and Novick give a somewhat more complete description of the Polacoat process, and Anderson has investigated the absorption of methylene blue molecules on a unidirectionally polished surface.

The principal transmittance and extinction ratio of two standard Polacoat coatings, PL-40 and 105 UVR (32 percent transmission of unpolarized light at 5460 Å), are shown in Fig. 13.

These curves are taken from the data of McDermott and Novick. Polacoat 105 UVR coating comes in various densities; the data shown are for the highest-density material with the best extinction ratio. A major advantage of Polacoat over sheet Polaroid is that it does not bleach upon exposure to intense ultraviolet radiation.

Kyser tested a stock PL40 polarizing filter on fused quartz and found that it produced a large quantity of scattered light of the unwanted component. This light was dispersed spectrally and was scattered at angles up to about \(20^\circ\) as though the scratches on the rubbed surface were acting like rulings on a diffraction grating.

There was relatively little of the unwanted component on axis; most of it was scattered at larger angles. Despite these difficulties, Polacoat PL40 polarizers appear to be the best large-aperture transmission-type polarizers available for work in the 2000- to 3000- Å wavelength range in the ultraviolet.

Pyrolytic-Graphite Polarizers

Pyrolytic graphite has a large anisotropy in both the electric conductivity and in the optical properties.

If the \(E\) vector of an electromagnetic wave is pointing in the direction of the \(c\)-axis of the graphite, the absorption coefficient is a minimum, the reflectance is also a minimum, and hence the transmittance is a maximum.

If the \(E\) vector lies in the plane perpendicular to the \(c\) direction, the absorption is a maximum, reflectance is a maximum, and transmittance is a minimum.

Thus, pyrolytic graphite should be a good material from which to make a dichroic polarizer if a thin foil is cut and polished to contain the \(c\)-axis.

Several such polarizers have been made by Rupprecht et al.; two had thicknesses of 9.2 μm, and a third was 4.2 μm thick. The transmittances \(T_1\) of the thinner one and \(T_1\) and \(T_2\) of the two thicker ones were determined.

The principal transmittance and extinction ratio for one of the 9.2-μm-thick ones are shown in Fig. 15 for infrared wavelengths from 2 to 16 μm, along with curves for various wire-grid polarizers.

In the far infrared out to 600 μm, \(T_1\) gradually increases to 0.50, and \(T_2/T_1\) drops down to the \(10^{-3}\) range.

The transmittance of the thinner pyrographite polarizer was larger than the curve shown, but its extinction ratio, although not given, was probably poorer.

Pyrolytic-graphite polarizers have the advantages of being planar and thus easily rotatable, having large acceptance angles, and having reasonably high transmittances and good extinction ratios in the far infrared.

However, in the shorter-wavelength region shown in Fig. 15, they are inferior to all the wire-grid polarizers. In addition, they are fragile, and the largest clear aperture obtained by Rupprecht et al. was about 12 mm diameter.

Wire-Grid and Grating Polarizers

Wire grids have a long history of use as optical elements to disperse radiation and detect polarization in far-infrared radiation and radio waves.

They transmit radiation whose \(E\) vector is vibrating perpendicular to the grid wires and reflect radiation with the \(E\) vector vibrating parallel to the wires when the wavelength \(\lambda\) is much longer than the grid spacing \(d\). When \(\lambda\) is comparable to \(d\), both components are transmitted.

For grids made of good conductors, absorption is negligible. Casey and Lewis considered the effect of the finite conductivity of the wires on the transmission and reflection of wire-grid polarizers when the light was polarized parallel to the wires.

Mohebi, Liang, and Soileau extended the treatment to the case for which light was polarized both parallel and perpendicular to the wires; they also calculated the absorption of the wire grids as a function of \(d/\lambda\). In addition, they measured the absorption and surface damage of wire-grid polarizers consisting of aluminum strips (0.84 μm period) deposited on ZnSe substrates at 10.6 μm, 1.06 μm, and 0.533 μm.

Stobie and Dignam calculated the amplitude transmission coefficients for parallel and perpendicular components and relative phase retardation between them, both as a function of \(\lambda/d\). Burton proposed using wire-grid polarizers in the form of cylinders and paraboloids instead of planar structures in infrared interferometers, but did not show any experimental measurements.

Figure 16 shows values of the calculated principal transmittance and extinction ratio for various values of the refractive index \(n\) as a function of \(\lambda/d\). It is clear that the shortest wavelength for which a given grid will act as a useful polarizer is \(\lambda\approx2d\).

Also, the best performance is obtained with the lowest refractive index substrate. Since absorption in the substrate material has been neglected, principal transmittances measured for real materials will be lower than the calculated values, but the extinction ratios should be unaffected.

If one must use a high refractive index substrate such as silicon or germanium, the performance of the grid can be considerably improved by applying an antireflection coating to the substrate before depositing the conducting strips, since a perfectly antireflected substrate acts like an unsupported grid. However, if the antireflecting layer is laid down over the grid strips, the performance of the wire grid polarizer is degraded.

Many people have built and tested wire-grid polarizers. In addition, two types of wire grids are manufactured commercially by Buckbee Mears and Perkin-Elmer and a third type composed of 152-μm-diameter tungsten wires spaced 800 to the inch has been mentioned, but no performance characteristics have been given.

Hwang and Park measured the polarization characteristics of two-dimensional wire mesh (64 μm and 51 μm spacings) at a laser wavelength of 118.8 μm. The different wire-grid polarizers are listed in Table 2, and the principal transmittances and extinction ratios of several are shown in Figs 14 and 15.

The polarizers with grid spacings of 1.69 μm and less were all made by evaporating the grid material at a very oblique angle onto a grating surface which had been prepared either by replicating a diffraction grating with the appropriate substrate material (silver bromide, Kel-F, polymethyl methacrylate, etc.) or by ruling a series of lines directly onto the substrate (Irtran 2 and Irtran 4).

The oblique evaporation (\(8\) to \(12^\circ\) from the surface) produced metallic lines on the groove tips which acted like the conducting strips of the theory, while the rest of the surface was uncoated and became the transparent region between strips.

Larger grid spaces (4 to 25.4 μm) were produced by a photoetching process, and one 25.4-μm grid was made by an electroforming process. Still larger grid spacings were achieved by wrapping wires around suitable mandrels.

If a wire-grid polarizer is to be used in the near infrared, it is desirable to have the grid spacing as small as possible. Bird and Parrish succeeded in obtaining a very good extinction ratio in the 2- to 6-μm wavelength region with an aluminum-coated Kel-F substrate (Figs . 14 and 15).

Unfortunately, Kel-F (CF₂CFCl)_n, has absorption bands at 7.7 to 9.2 and 10.0 to 11.0 μm, making the polarizer useless in these regions, but it can be used at longer wavelengths out to 25 μm.

Polyethylene would be an excellent substrate material since it has fewer absorption bands than Kel-F, but its insolubility in common solvents makes it much more difficult to use for replicating gratings. It does, however, make an excellent substrate material for photoetched grids.

For infrared wavelengths longer than about 24 μm, a photoetched grid with 1-μm-wide lines (close to the present limit for the photoetching process) and a 2-μm spacing should have an extinction ratio of \(5\times10^{-3}\) or better if the refractive index of the substrate is about 1.5—for example, polyethylene.

The extinction ratio would continue to decrease; i. e., the polarization properties would improve as the wavelength increased. At very long wavelengths, grids with a larger spacing would have a high degree of polarization. The important factor is the ratio of wavelength to grid spacing, which should be kept as large as possible (Fig. 16b).

One definite advantage of the wire-grid polarizer is that it can be used in sharply converging beams, i. e., systems with high numerical apertures. Young et al. found no decrease in percent of polarization for an Irtran 2 polarizer at 12 μm used at angles of incidence from 0 to \(45^\circ\). They did find, however, that the transmittance decreased from 0.55 at normal incidence to less than 0.40 at \(45^\circ\) incidence.

If a grid were to be used at a single wavelength, one might possibly make use of interference effects in the substrate to increase the transmission. If the substrate has perfectly plane-parallel surfaces, it will act like a Fabry-Perot interferometer and transmit a maximum amount of light when twice the product of the thickness and refractive index is equal to an integral number of wavelengths. The 0.25-mm-thick pressed polyethylene substrates used by Auton were not uniform enough to show interference effects, but the Mylar film backing on the Buckbee Mears electroformed grid did show interference effects.

Lamellar eutectics of two phases consist of thin needles of a conducting material embedded in a transparent matrix. The material is made by a controlled cooling process in which there is a unidirectional temperature gradient. This method of cooling orients conducting needles parallel to the temperature gradient, and hence the material can act like a wire-grid polarizer.

Weiss and coworkers have grown eutectic alloys of InSb and NiSb in which the conducting needles of NiSb are approximately 1 μm in diameter and approximately 50 μm long. A degree of polarization of more than 99 percent has been reported.

Other eutectic alloys of InAs, GaSb, and InSb containing conducting needlelike crystals of Ni, Fe, Mn, Cr, and Co (or their compounds) have also been investigated. An advantage of this type of polarizer is that its performance can be optimized at a specific wavelength, e. g., that of a CO₂ laser line, by choosing the thickness of the crystalline film so that there will be an interference maximum at the desired wavelength.

Recently, Saito and Miyagi have proposed using a thin film of anodized aluminum with implanted metallic columns to make a high-performance polarizer. Their theoretical calculations suggest that this type of polarizer should have a large extinction ratio and low loss in the infrared.

In summary, wire grids are very useful infrared polarizers, particularly for wavelengths much greater than the grid spacing. They are compact and easily rotatable and can be used with sharply converging beams. A major advantage is the extreme breadth of the wavelength band over which they have good polarizing properties.

The long-wavelength limit is set by the transmission of the substrate material rather than by the loss of polarization of the grid. The short-wavelength limit is determined by the grid spacing; if gratings with smaller spacings could be successfully replicated and coated, the short-wavelength limit could be pushed closer to the visible region.

Another possible method of producing plane-polarized light is by using diffraction gratings or echelette gratings. Light reflected from diffraction gratings has long been known to be polarized, but the effect is generally small and extremely wavelength-dependent.

However, Roumiguieres predicted that under certain conditions (rectangular groove grating with equal groove and land spacings and small groove depth), a high polarizing efficiency could be obtained.

For wavelengths in the range \(1.1\lt\lambda/d\lt1.7\), over 80 percent of the light polarized parallel to the grooves should be reflected in the zero order at a \(50^\circ\) angle of incidence and less than 5 percent of the other polarization.

His predictions were verified by Knop who fabricated gold-coated photoresist gratings as well as an electroplated nickel master grating. Knop’s measured reflectances of the two polarized components were within \(\pm3\) percent of the predicted values.

In general, one tries to avoid polarization in the diffracted light to obtain high efficiencies in a blazed grating since polarization effects are frequently associated with grating anomalies.

In contrast to diffraction gratings, echelette gratings have been found to produce an appreciable amount of plane-polarized light. Experimental studies have been made. The theory of the polarization of light reflected by echelette gratings in the far-infrared and microwave regions has been given by Janot and Hadni and Rohrbaugh et al.

A general numerical technique published by Kalhor and Neureuther should be useful for calculating the polarization effects of echelette gratings of arbitrary groove shape used in the visible region.

Measuring Polarization of Imperfect Polarizers

In determining the principal transmittance, extinction ratio, and other properties of an imperfect polarizer, the effects of source polarization, instrumental polarization, and sensitivity of the detector to the plane of polarization must either be measured or eliminated from the calculations.

This is easy if an auxiliary polarizer is available that has a much higher degree of polarization than the one to be measured. In such a case, the ‘‘perfect’’ polarizer can be placed in the beam, and the transmittances \(T_1\) and \(T_2\) for the unknown polarizer can be measured directly.

Source polarization, instrumental polarization, and variation of detector response with plane of polarization can all be lumped together as a product. If this product is different in the horizontal and vertical planes, the ratio of the signals obtained when the ‘‘perfect’’ polarizer is oriented horizontally and vertically will not equal unity. One should always take more than the minimum number of measurements, i. e., introduce redundancy, to make sure that no systematic errors are present.

If a high-quality polarizer is not available, two polarizers having unknown properties may be used instead.

The next tutorial introduces non-normal-incidence reflection and transmission polarizers.