Thin Film Polarizers and Polarizing Beam Splitters Angus Macleod Thin Film Center, Inc, Tucson, AZ Contributed Original Article Introduction normal to the plane of incidence, known as s-polarization. The proper- Optical coatings are stratified media. Thus, although individual films ties of the layers appear different to each eigenmode of polarization, may be isotropic, an optical coating as a whole is anisotropic, and this and so the properties of the coating also vary. This implies a different appears in the performance at oblique incidence as a sensitivity to performance for each eigenmode, which is called polarization splitting. polarization. This sensitivity can be a problem when insensitivity is a For a high-performance polarizer or analyzer it is desirable that one requirement, but, of great benefit, when the objective is the manipula- eigenmode should be completely reflected, while the other is completely tion of polarized light. Typical components are polarizers and polariz- transmitted. This is possible under certain circumstances, leading to a ing beam splitters. Most polarizers and analyzers are based on anisotro- coating that can perform the function of a polarizer or analyzer, and, pic materials, the traditional ones being birefringent crystals. A limita- because the two modes are physically separated, a polarizing beam tion common to most of them is size. Also many of the high-perfor- splitter. mance devices are not useful as polarizing beam splitters. At first sight, There are enormous advantages in thin-film devices. Their charac- the usual thin-film calculations tend to show that polarizers and polar- teristics can be placed at virtually any wavelength in the wide region of izing beam splitters can have performance almost without limit, the transparency of their materials simply by altering the thicknesses of their only restriction being the total number of layers in the coating. layers, and, once a design has been established, the time to production is However, there are important limitations that should be understood if exceptionally short. the devices are to be correctly deployed. The range of different types and designs of polarization-sensitive The Thin-Film Polarizer coatings is enormous and well beyond the capacity of this article. We There are two effects of oblique incidence on thin film coatings. The limit ourselves to one or two well-known types. first effect is that the layers appear thinner to the light. This is a strange effect, but completely understandable in terms of the change in phase Polarizers, Analyzers and Polarizing Beam Splitters induced in the light by the traversal of the film. It is explained in an Polarizers and analyzers are identical devices but used in slightly differ- earlier Bulletin [1]. It causes the characteristic of the coating to shift ent ways. They both pass linearly polarized light of a definite orienta- towards shorter wavelengths when tilted to oblique incidence. The sec- tion and block orthogonally polarized light. We call the device a polar- ond effect is a shift in the optical admittances of the layers. The admit- izer when it is used to produce polarized light from unpolarized, and tances for s-polarization fall, and those for p-polarization rise. However, an analyzer when it is used to detect the orientation of polarized light. the high-index layers are less affected than low-index, and this implies A polarizing beam splitter divides incident unpolarized light into two that the ratio of the admittance of a high-index layer to that of a low- orthogonally polarized beams. index layer in a coating becomes smaller for p-polarization but larger for Most high-performance polarizers are based on birefringent crys- s-polarization. This, in turn, implies a weakening of the characteristic for tals. Unpolarized light is incident internally on a tilted surface. The p-polarization and a strengthening of that for s-polarization. In crystal presents a refractive index that depends on the orientation of fact, under certain conditions the high and low-index admittances for the polarization, and the surface tilt is arranged so that, for the greater p-polarization can actually coincide, so that the reflectance characteris- of the two refractive indices, the surface is slightly beyond critical tic of the coating collapses completely. The name Brewster, after David angle, and, for the lower index, slightly below critical. Then that por- Brewster the original discoverer, is given to this condition. If the two tion of the incident light with appropriate orientation of polarization indices of refraction of the materials on either side of the interface are is totally internally reflected, while the other portion is largely trans- n1 and n2, then the angle of propagation, , in material n1 that corre- mitted. The total internal reflection removes its component essentially sponds to the Brewster condition is given by: completely and, although there may be a residual loss in transmission (1) through the surface, the transmitted light is polarized to a very high The common thin-film reflecting coating is based on a series of degree. Usually a second component that is the reverse of the first is quarterwave optical thicknesses of dielectric materials of alternate high added beyond the surface to return the orientation of the transmitted and low refractive index. This structure is known as a quarterwave beam to that of the input. The reflected beam contains also the residu- stack. The characteristic performance of a quarterwave stack is a band ally reflected orthogonally polarized light and the device is, therefore, of high reflectance, the width of which depends on the ratio of the high unsuitable as a polarizing beam splitter. The rejected light is usually to low admittances of the layers. Outside this band, the reflectance falls trapped by a blackened surface so that it does not emerge. rapidly to a low value with a superimposed ripple that can be reduced by The thin-film polarizer, or beam splitter, makes use of the phe- suitable outer matching layers. When tilted, the high-reflectance band nomenon known as polarization splitting [1]. The plane of incidence is moves towards shorter wavelengths and its width changes because the defined as that plane containing the normal to the coated surface and ratios of the admittances have changed. The weakening and strength- the incident ray direction. The reflected and transmitted ray directions ening effects just mentioned imply that for p-polarization, the width are also in this plane. In general, the polarization of the incident ray is reduced, but for s-polarization it is increased. There is, therefore, a is altered by either a reflection or transmission, except in the cases of band of wavelengths at the edge of the high-reflectance zone where two special modes of polarization, called the eigenmodes, that are not the system reflects strongly for s-polarization but transmits strongly perturbed. These eigenmodes are linearly polarized with electric vector for p-polarization. In transmission in that region the light is, therefore, oriented either in the plane of incidence, known as p-polarization, or 24 2009 Summer Bulletin strongly p-polarized. The result in Figure 1 is typical. The angle of tilt is chosen to be the Brewster angle for a glass-air interface. This implies no reflection loss at the uncoated rear surface of the component, avoiding an antireflection coating. (2) so that (3) Typical values of n1 and n2 require values of n0 rather greater than ϑ unity to yield real values of 0. This implies that a polarizer based on this principle must be immersed in a medium of elevated index. In the most usual arrangement the device is made up of two isosceles right- angle prisms, at least one having a coated hypotenuse, cemented into a cube. An early polarizer of this type was patented by MacNeille [3] and is Figure 1. The transmittance of the plate polarizer including the rear surface of usually known by his name. Its construction was described by Banning the substrate. The coating is deposited on glass and the angle of incidence is [4]. Banning used zinc sulfide (n = 2.30) and cryolite (n = 1.25) as the 56.43° so that the rear glass surface is at the Brewster angle in the useful materials, and to obtain an angle of incidence of 45° and, hence, a cube zone. prism, used glass of index 1.55. Banning correctly pointed out that the dispersion of the film materials would imply a variation in the value of n0 The Extinction Ratio is sometimes quoted as a guide to performance from equation (3). In order to preserve the angle of incidence, and hence of a polarizer. It is the ratio of the irradiance of the undesired mode the optimum polarization, the glass of the prism should have the correct of polarization to that of the desired. The polarizer in Figure 1 has an dispersion. The Abbe Number (or sometimes the V-Number) is defined extinction ratio of 6.6×10-5 at 1.06μm. This can be improved simply by as: adding more layers. Extinction ratio takes no account of the level of (4) throughput of the device. It has virtually the same value in the center of the high-reflectance zone (because of the difference between p- and where the symbols D, F and C indicate that the indices are measured at s-performance) and so we must supplement it by some measure of effi- the corresponding Fraunhofer lines at 589.2 nm, 486.1 nm and ciency, usually the transmittance, or the reflectance if appropriate. 656.3 nm respectively. Note that the Abbe Number is inversely pro- There is virtually no absorption in the device of Figure 1, and so the portional to the degree of dispersion.