polarization of light

a fundamental property of optical radiation, or light. It consists in the nonequivalence of different directions in the plane perpendicular to a light ray, or to the direction of propagation of a light wave. The geometric characteristics reflecting the properties of this nonequivalence are also referred to as polarization.

The concept of polarization of light was introduced into optics between 1704 and 1706 by I. Newton. Phenomena caused by polarization, however, had been studied previously. For example, double refraction in crystals had been discovered by E. Bartholin in 1669 and had received a theoretical explanation by C. Huygens between 1678 and 1690. The term “polarization of light” was proposed in 1808 by E. Malus. The beginning of the extensive investigation of effects based on polarization was associated with such scientists as Malus, J. Biot, A. Fresnel, D. Arago, and D. Brewster.

The connection between polarization and interference effects was of great importance for the understanding of polarization. It can be shown by a simple experiment that two light rays linearly polarized at a right angle to each other do not interfere. This fact provided decisive proof of the transverse nature of light waves, which was established by Fresnel, Arago, and T. Young in work between 1816 and 1819. Polarization found a natural explanation in J. C. Maxwell’s electromagnetic theory of light, which was formulated between 1865 and 1873.

The transverse nature of a light wave—indeed, of any electromagnetic wave—means that the electric field strength vector E and magnetic field strength vector H vibrating in the wave are perpendicular to the direction of propagation of the wave. E and H single out certain directions in the space occupied by the wave —hence the nonequivalence pointed out above. Moreover, E and H are almost always mutually perpendicular; for this reason, the behavior of just one of them needs to be known in order to describe completely the state of polarization. The electric vector is usually selected for this purpose.

A light pulse emitted by any individual elementary radiator (an atom or molecule) in a single radiative event is always completely polarized. Macroscopic light sources, however, consist of a great number of such particle radiators. In most cases, the spatial orientations of the electric vectors of the light pulses of the individual radiators are randomly distributed, as are the times of occurrence of the radiative events; laser light is an example of a nonrandom distribution of orientations. In addition, the polarization is changed as a result of the processes of interaction between the particle radiators. In the radiation from the overwhelming majority of sources, therefore, the direction of the electric vector is in general not defined but changes continuously and randomly over extremely short time intervals. Such radiation is called unpolarized, or natural, light. Like any vector, the electric vector can always be represented as the sum of its components in two mutually perpendicular directions chosen in a plane perpendicular to the direction of propagation of the light. In natural light the phase difference between such components changes continuously and randomly. In completely polarized light this phase difference is strictly constant—that is, the mutually perpendicular components of the electric vector are coherent. By imposing certain conditions on the path of propagation of natural light, it is possible to isolate from it a completely or partially polarized component. Moreover, complete or partial polarization arises in a number of natural processes of light emission and the interaction of light with matter.

Figure 1. Oscillations of the projections of the electric vector E of a light wave on the mutually perpendicular x- and y-axes; the direction z of propagation of the wave is perpendicular to both the x- and the y-axis. (b), (c) Instantaneous representations of the oscillations and the corresponding envelope of the ends of the total electric vector E at’ different points of the wave for the case where the vertical oscillations (along the x-axis) are a quarter period (90°) ahead of the horizontal oscillations (along the y-axis). At each single point, in this case, the end of the electric vector E describes a circle. The arrows in (c) are included only in order to indicate more clearly the form of the right-handed helix. The helical surface does not rotate around the z-axis during passage of the wave. On the contrary, the helical surface should be viewed as moving as a whole, without rotating, along the z-axis with the velocity of the wave.

The complete polarization of monochromatic light is characterized by the projection of the path of the end of the electric vector (Figure 1) at each point of the ray onto a plane perpendicular to the ray. In the most general case of elliptical polarization, the projection is an ellipse. This fact can be easily understood by taking into consideration the constancy of the phase difference between the mutually perpendicular components of the electric vector and the components’ identical vibration frequencies in a monochromatic wave. In order to give a complete description of elliptical polarization, we must know the direction of rotation of the electric vector about the ellipse (right or left), the orientation of the ellipse’s axes, and the eccentricity of the ellipse (see, for example, Figure 2, b, d, and f) · The two limiting cases of elliptical light polarization are of the greatest interest. One such case is linear polarization, where the ellipse degenerates into a line segment; the phase difference here is 0 or kπ, where k is an integer (Figure 2, a and e). The other limiting case is circular polarization, where the phase difference is ± (2k+ 1) π/2 and the ellipse becomes a circle. In defining the state of linearly polarized, or plane-polarized, light, it is sufficient to indicate the position of the plane of polarization; for circularly polarized light, the direction of rotation—right (Figure 2,c) or left—must be indicated. In complex inhomogeneous light waves —for example, in metals or after total internal reflection—the instantaneous directions of the electric and magnetic vectors are not mutually perpendicular; in order to describe completely the polarization in such waves, the separate behavior of each of the vectors must be known.

If the phase relation between the components (projections) of the electric vector varies over time intervals much shorter than the time required to measure the polarization, we cannot speak of complete polarization. In the monochromatic waves making up a light beam, however, it may happen that the variation in the electric vector is not entirely random, and a preferential phase shift (phase correlation) that is preserved for a rather long

Figure 2. Examples of different polarizations of a light ray (paths of the end of the electric vector E at some single point of the ray) for various phase differences between the mutually perpendicular components E_x and E_y; the plane of the figure is perpendicular to the direction of light propagation: (a) and (e) linear polarizations; (c) right-handed circular polarization; (b), (d), and (f) elliptical polarizations with different orientations; (λ) wavelength of the light. Each division of the figure — (a) through (f) — corresponds to a positive phase difference δ of the vertical oscillations with respect to the horizontal oscillations.

time may exist between the mutually perpendicular components of the electric vector. In physical terms this means that in the field of a light wave the amplitude of the projection of the electric vector in one of the mutually perpendicular directions is always greater than in the other direction. The degree of this phase correlation in such partially polarized light is described by a parameter p, which is called the degree of polarization. Thus, if the preferential phase shift is equal to zero, the light is partially linearly polarized; if it is ± π/2, the light is partially circularly polarized. Partially polarized light can be considered a mixture of the two extreme types of completely polarized light and natural light. The ratio of these two types is also given by the parameter p, which often, but not always, is defined as ǀI₁—I₂ǀ/(I₁ + I₂). The subscripts 1 and 2 here refer to the intensities I of light having two orthogonal polarizations—for example, linear polarizations in mutually perpendicular planes or polarizations corresponding to right-handed and left-handed circular polarizations; p can range from 0 to 100 percent and thus reflects all the quantitative gradations of the state of polarization. It should be noted that light that appears unpolarized in some experiments may be completely polarized in other experiments —the polarization varying with time across a section of the beam or over the spectrum.

In quantum optics, electromagnetic radiation is regarded as a flux of photons. From the quantum point of view, the states of polarization of light are defined by the angular momentum possessed by the photons in the flux. Thus, photons with right-handed or left-handed circular polarization have an angular momentum equal to ± ℏ, where ℏ is Planck’s constant. Any state of light polarization can be expressed in terms of just two basis states. When the polarization is described, the selection of the pair of initial basis states is not unique. For example, the states may be any two mutually orthogonal linear polarizations, or they may be right-handed and left-handed circular polarizations. In each case, it is possible to move from one pair of basis states to another by using certain rules.

This ambiguity is fundamental to the quantum approach. The arbitrariness, however, is usually limited by the specific physical conditions. Thus, it is most convenient to select as the basis pair the states of polarization that predominate in events of photon emission by the elementary radiators or that determine the process of the light-matter interaction under consideration. The state of polarization in an experiment is determined by means of such an interaction. According to the general rules of quantum mechanics, such an experiment always alters—sometimes negligibly, sometimes considerably—the initial polarization. Basis states and states describable by any linear combination of basis states—that is, by superposition—are called pure states. They correspond to complete polarization of the light, where the degree of polarization is 100 percent. Photons may be found not only in pure states but also in mixed states, in which the degree of polarization is less than 100 percent and may reach zero, as in natural light. Mixed states can also be expressed in terms of basis states, but in a more complicated manner than linear superposition; they are referred to as an incoherent mixture of pure states. Under certain conditions, the interaction of light with matter can lead to complete or partial separation of pure states from mixed states because of the already mentioned change in polarization during such an interaction.

Many polarization devices make use of this phenomenon to obtain completely polarized light or to increase the degree of polarization. If right-handed and left-handed circular polarizations are selected as the basis states of polarization, linear polarization is observed when they are superposed (coherent superposition) in equal proportions. Superpositions in other ratios yield elliptical polarization with various characteristics. Any mixed states can be expressed in terms of these basis states. Thus, the proper choice of just two basis states permits the description of any state of polarization.

Experiment has confirmed the theoretical conclusion that every circularly polarized photon has an angular momentum ℏ = ℏ /2π. The character of the polarization of photons is determined by the law of conservation of angular momentum in the system consisting of an elementary radiator and the emitted photon, provided that the interaction of the individual radiators with each other may be ignored.

In addition to the characteristics of elementary radiative events, a number of physical processes result in partial, and sometimes complete, polarization. Examples are the reflection and refraction of light, in which polarization is caused by the difference in the optical characteristics of the interface of two media for the components of a light beam that are polarized parallel and perpendicular to the plane of incidence. Light may be polarized during passage through a medium that has natural or externally induced optical anisotropy. Such anisotropy can consist in different absorption factors for light in different states of polarization; for example, for right-handed and left-handed circular polarization there is the phenomenon of circular dichro-ism, which is a special case of pleochroism. Another instance of anisotropy is double refraction, wherein a medium has different refractive indexes for rays of different linear polarizations. Laser radiation is often completely polarized. The specific nature of stimulated emission, in which the polarization of the emitted photon and the photon inducing the emission event are absolutely identical, is one of the main causes—but not the only cause —of the polarization of laser light. Thus, when avalanche-type multiplication of the number of emitted photons in a laser pulse occurs, the polarization of the photons may also be identical. Resonance radiation from vapors, liquids, and solids, can be polarized. Polarization resulting from the scattering of light is so

Figure 3. Schematic diagram of the observation of the chromatic polarization effect due to the interference of two polarized beams in a parallel beam of light. The polarizer N₁, transmits only one linearly polarized (in the direction N₁ N₁,) component of the original beam. In the plate K, which is cut from a doubly refracting uniaxial crystal parallel to the crystal’s optic axis OO and is mounted perpendicular to the beam, the plane-polarized beam is divided into two components A_o, and A_o, which are called the extraordinary ray and the ordinary ray, respectively. The vibrations of the electric vector of A_o are parallel to OO, and the vibrations of the electric vector of A_o are perpendicular to OO. The refractive indexes of the material of K are different for the two rays (n_e, and n_o, and consequently the rays’ rates of propagation in K differ. For this reason, the rays acquire a path difference when they propagate in the same direction. The phase difference of their vibrations on emerging from K is equal to δ = (1/λ)2π/(n_o – n_e), where / is the thickness of K and λ is the wavelength of the incident light. The analyzer N₂ transmits from each ray only the component with vibrations lying in the plane of its principal section N₂ N₂, If N₁ N₂ (the optic axes of the analyzer and polarizer are crossed), then the amplitudes of the components A₁ and A₂ are equal, and the phase difference of A₁ and A₂ is Δ = δ + π. The components are coherent and interfere with each other. Depending on the magnitude of Δ for a certain region of K, the observer sees this region as dark [Δ = (2k + 1)π, where k is an integer] or as light (Δ = 2kπ) in monochromatic light and as colored in white light.

characteristic that its investigation is one of the basic methods of studying the nature and conditions of light scattering itself and also the properties of the scattering centers, particularly the structure and interaction of the centers. It may be noted that when polarized light is scattered, depolarization occurs—that is, the degree of polarization decreases. Under certain conditions, luminescence is strongly polarized, particularly when it is excited by polarized light. Polarization is extremely sensitive to the strength and orientation of electric and magnetic fields; in strong fields, the components into which the spectral emission, absorption, and luminescence lines of gaseous and condensed systems are split turn out to be polarized.

Chromatic polarization effects occur in the interference of polarized rays of white light.

All interference phenomena are dependent on the wavelength (“color”) of the radiation. In chromatic polarization effects, this dependence results in the coloring of the interference pattern if the initial flux is of white light. The usual scheme for obtaining a chromatic polarization pattern in parallel rays is illustrated in Figure 3. Depending on the path difference between the ordinary and extraordinary rays that is acquired in a doubly refracting plate, the observer sees this plate in the light emerging from the analyzer as dark or light if the light is monochromatic or as colored if the light is white. If the plate is nonuniform in thickness or refractive index, the regions in which these parameters are the same will appear to be identically dark or light or to be identically colored. Lines of the same chromaticity are called isochromates. A scheme for the observation of this chromatic polarization effect in converging light rays is illustrated in Figure 4.

Figure 4. Schematic diagram for the observation of chromatic polarization effects in converging rays: (N₁) polarizer. (N₂) analyzer, (K) plate of thickness I cut from a doubly refracting uniaxial crystal parallel to the crystal’s optic axis, (L₁) and (L₂) lenses. Rays of different inclination travel by different paths in K and acquire path differences, which are different for the ordinary and extraordinary rays. On emerging from the analyzer the rays interfere and produce characteristic interference patterns.

Many of the above phenomena underlie the operating principles of various polarization devices that are used not only to analyze the state of polarization of light emitted by external sources but also to obtain a required polarization and to convert some types of polarization into others.

The characteristics of the interaction of polarized light with matter account for the exceptionally wide use made of such light not only in the investigation of the crystal chemistry and the magnetic structure of solids, the structure of biological objects (as in studies with the polarizing microscope), and the states of elementary radiators and the individual centers responsible for quantum transitions but also in the obtaining of information on extremely remote objects, particularly astrophysical objects. In general, the polarization of light, as an essentially anisotropic property of radiation, makes possible the study of all types of anisotropy in matter. Thus, it permits investigation of the behavior of gases, liquids, and solids in fields of anisotropic disturbances (mechanical, acoustical, electric, magnetic, and light disturbances). In crystal optics, it permits study of the structure of crystals, which in the overwhelming majority of cases are optically anisotropic. In engineering—for example, in machine building—it is made use of for such purposes as the investigation of elastic stresses in structures. The study of the polarization of light emitted or scattered by a plasma has an important role in plasma diagnostics. The interaction of polarized light with matter can result, for example, in the optical orientation or alignment of atoms or in the generation of powerful polarized radiation in lasers.

On the other hand, the investigation of the depolarization of light during photoluminescence gives information on the interaction of the absorbing and radiating centers in particles of matter.

The study of depolarization during light scattering provides valuable information on the structure and properties of the scattering molecules or other particles. In other cases, information on the course of such phenomena as phase transitions can be obtained.

Extensive use is made of the polarization of light in technology. For example, polarization is used when smooth regulation of the intensity of a light beam is necessary. It is used in order to heighten contrast and eliminate hot spots in photography. It finds application in the design of light filters and of radiation modulators, which are an important element in optical detection and ranging systems and in optical communication systems. Polarization is also made use of to study the course of chemical reactions and the structure of molecules and to determine concentrations of solutions.

Polarization plays an important role in living nature. Many living creatures can sense the polarization of light. Bees and ants orient themselves in space by the light of the blue sky; such light is polarized by scattering in the atmosphere. Under certain conditions the human eye also becomes sensitive to polarization, as is evidenced by Haidinger brushes.