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Rotation of the plane of polarization of a beam of linearly polarized light when the light passes through matter in the direction of the lines of force of an applied magnetic field. Discovered by M. Faraday in 1846, the effect is often called magnetic rotation. See Magnetooptics
The Faraday effect is particularly simple in substances having sharp absorption lines, that is, in gases and in certain crystals, particularly at low temperatures. Here the effect can be fully explained from the fundamental properties of the atoms and molecules involved. In other substances the situation may be more complex, but the same principles furnish the explanation.
Rotation of the plane of polarization occurs when there is a difference between the indices of refraction n+ for right-handed polarized light and n- for left-handed polarized light. Most substances do not show such a difference without a magnetic field, except optically active substances such as crystalline quartz or a sugar solution. It should be noted that the index of refraction in the vicinity of an absorption line changes with the frequency. See Polarized light
a magneto-optical effect that consists in the rotation of the plane of polarization of electromagnetic radiation, such as light, propagating in a substance parallel to the lines of force of a constant magnetic field that pass through the substance. The Faraday effect, discovered by M. Faraday in 1845, was the first proof of a direct connection between magnetism and light.
A phenomenological explanation of the Faraday effect follows. In the general case, a magnetized substance cannot be characterized by a single refractive index n. The refractive indexes n+ and n- for right- and left-handed circularly polarized radiation become different (seeMAGNETO-OPTICS). Linearly polarized radiation that passes through an isotropic medium can always be formally represented as a superposition of two waves that are right-and left-handed circularly polarized and rotated in opposite directions. The difference between n+ and n_ leads to a situation in which the right- and left-handed circularly polarized radiation components propagate in the medium with different phase velocities, acquiring a path difference that is linearly dependent on the optical path. As a result, after a path l is traversed in the medium, the plane of polarization of monochromatic light with a wavelength λ is rotated through an angle θ = π/(n+ – n_)/λ. The difference (n+ – n_) is linearly dependent on the magnetic field strength H in the region where the fields are not very strong. In this region, the following relation is valid in the general case:
θ = VHI
where the constant of proportionality V, called Verdet’s constant, depends on the properties of the substance, the wavelength of the radiation, and the temperature.
The Faraday effect is closely related to the Zeeman effect, which was discovered in 1896 and is due to the splitting of the energy levels of atoms and molecules by a magnetic field. The frequencies corresponding to the levels that are split are shifted symmetrically relative to the fundamental frequency. In particular, this symmetry is illustrated by the fact that quantum transitions between the levels that are split entail the emission and absorption of right- and left-handed circularly polarized photons when light propagates longitudinally with respect to the magnetic field; in the case of longitudinal propagation, the original level may be regarded as being split into just two sublevels. As a result of such symmetry, the refractive indexes and absorption coefficients, which are weakly dependent on the wavelength or frequency of the light, become different for the right- and left-handed circularly polarized components of monochromatic radiation. A rough description would be that the difference in the phase velocities is due to the difference in the wavelengths or frequencies of the light that is absorbed and reemitted by the particles of the substance. A rigorous description of the Faraday effect is possible only within the framework of quantum theory.
The specific nature of the magnetic field strength vector H, which is a pseudovector, is clearly manifested in the Faraday effect. In contrast to the situation in natural optical activity, the direction in which the plane of polarization is rotated as a result of H in the Faraday effect is independent of the direction in which the radiation propagates. Therefore, the repeated transmission of light through a medium situated in a magnetic field leads to an increase by the corresponding number of times in the angle through which the plane of polarization is rotated. This feature of the Faraday effect has found application in the design of, for example, nonreciprocal optical and microwave devices, as well as circulators, gyrators, and microwave phase shifters. The Faraday effect is widely used in scientific research.
REFERENCESLandsberg, G. S. Optika, 4th ed. Moscow, 1957. (Obshchii kurs fiziki, vol. 3.)
Vol’kenshtein, M. V. Molekuliarnaia optika. Moscow-Leningrad, 1951.
Frish, S. E. Opticheskiespektry atomov. Moscow-Leningrad, 1963.
V. S. ZAPASSKII