Faraday effect

The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the magnetic field along the direction of the light propagation. Formally, it is a special case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal. This effect occurs in most optically transparent dielectric materials (including liquids) under the influence of magnetic fields. Discovered by Michael Faraday in 1845, the Faraday effect was the first experimental evidence that light and electromagnetism are related. The theoretical basis of electromagnetic radiation (which includes visible light) was completed by James Clerk Maxwell in the 1860s. The Faraday effect is caused by left and right circularly polarized waves propagating at slightly different speeds, a property known as optical rotation (or circular birefringence). Since a linear polarization can be decomposed into the superposition of two equal-amplitude circularly polarized components of opposite handedness and different phase, the effect of a relative phase shift, induced by the Faraday effect, is to rotate the orientation of a wave's linear polarization. The Faraday effect has applications in measuring instruments.…

The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the magnetic field along the direction of the light propagation. Formally, it is a special case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal. This effect occurs in most optically transparent dielectric materials (including liquids) under the influence of magnetic fields. Discovered by Michael Faraday in 1845, the Faraday effect was the first experimental evidence that light and electromagnetism are related. The theoretical basis of electromagnetic radiation (which includes visible light) was completed by James Clerk Maxwell in the 1860s. The Faraday effect is caused by left and right circularly polarized waves propagating at slightly different speeds, a property known as optical rotation (or circular birefringence). Since a linear polarization can be decomposed into the superposition of two equal-amplitude circularly polarized components of opposite handedness and different phase, the effect of a relative phase shift, induced by the Faraday effect, is to rotate the orientation of a wave's linear polarization. The Faraday effect has applications in measuring instruments. For instance, the Faraday effect has been used to measure optical rotatory power, for remote sensing of magnetic fields (such as fiber optic current sensors) and for magneto-optical imaging. The Faraday effect is used in spintronics research to study the polarization of electron spins in semiconductors. In the superconducting field, it is used to study the dynamic of fluxons in thin films. Faraday rotators can be used for amplitude modulation of light, and are the basis of optical isolators and optical circulators; such components are required in optical telecommunications and other laser applications. ==History== holding a piece of glass of the type he used to demonstrate the effect of magnetism on polarization of light, c. 1857. By 1845, it was known through the work of Augustin-Jean Fresnel, Étienne-Louis Malus, and others, that different materials are able to modify the direction of polarization of light when appropriately oriented, making polarized light a very powerful tool to investigate the properties of transparent materials. Faraday firmly believed that light was an electromagnetic phenomenon, and as such should be affected by electromagnetic forces. He spent considerable effort looking for evidence of electric forces affecting the polarization of light through what are now known as electro-optic effects, starting with decomposing electrolytes. ==Physical interpretation== The linear polarized light that is seen to rotate in the Faraday effect can be seen as consisting of the superposition of a right- and a left- circularly polarized beam (this superposition principle is fundamental in many branches of physics). We can look at the effects of each component (right- or left-polarized) separately, and see what effect this has on the result. In circularly polarized light the direction of the electric field rotates at the frequency of the light, either clockwise or counter-clockwise. In a material, this electric field causes a force on the charged particles that compose the material (because of their large charge to mass ratio, the electrons are most heavily affected). The motion thus effected will be circular, and circularly moving charges will create their own (magnetic) field in addition to the external magnetic field. There will thus be two different cases: the created field will be parallel to the external field for one (circular) polarization, and in the opposing direction for the other polarization direction – thus the net B field is enhanced in one direction and diminished in the opposite direction. This changes the dynamics of the interaction for each beam and one of the beams will be slowed more than the other, causing a phase difference between the left- and right-polarized beam. When the two beams are added after this phase shift, the result is again a linearly polarized beam, but with a rotation of the polarization vector. The direction of polarization rotation depends on the properties of the material through which the light is shone. A full treatment would have to take into account the effect of the external and radiation-induced fields on the wave function of the electrons, and then calculate the effect of this change on the refractive index of the material for each polarization, to see whether the right- or left-circular polarization is slowed more. ==Mathematical formulation== Formally, the magnetic permeability is treated as a non-diagonal tensor as expressed by the equation: \mathbf{B}(\omega) = \begin{bmatrix} \mu_{1} & -i \mu_{2} & 0 \\ i \mu_{2} & \mu_{1} & 0 \\ 0 & 0 & \mu_{z} \\ \end{bmatrix} \mathbf{H}(\omega) The relation between the angle of rotation of the polarization and the magnetic field in a transparent material is: \beta = \mathcal{V}Bd where β is the angle of rotation (in radians) B is the magnetic flux density in the direction of propagation (in teslas) d is the length of the path (in meters) where the light and magnetic field interact \scriptstyle \mathcal{V} is the Verdet constant for the material. This empirical proportionality constant (in units of radians per tesla per meter) varies with wavelength and temperature and is tabulated for various materials. A positive Verdet constant corresponds to L-rotation (anticlockwise) when the direction of propagation is parallel to the magnetic field and to R-rotation (clockwise) when the direction of propagation is anti-parallel. Thus, if a ray of light is passed through a material and reflected back through it, the rotation doubles. Some materials, such as terbium gallium garnet (TGG) have extremely high Verdet constants (≈ for 632 nm light). By placing a rod of this material in a strong magnetic field, Faraday rotation angles of over 0.78 rad (45°) can be achieved. This allows the construction of Faraday rotators, which are the principal component of Faraday isolators, devices which transmit light in only one direction. The Faraday effect can, however, be observed and measured in a Terbium-doped glass with Verdet constant as low as (≈ for 632 nm light). Similar isolators are constructed for microwave systems by using ferrite rods in a waveguide with a surrounding magnetic field. A thorough mathematical description can be found here. \beta = R_M \, \lambda^2 , where the overall strength of the effect is characterized by R_M , the rotation measure. This in turn depends on the projection of the magnetic field along the line of sight B_\parallel and the number density of electrons n e , both of which vary along the propagation path. In the ideal-plasma approximation, the rotation measure is given (in the Gaussian CGS units) by R_M = \frac{e^3}{2\pi m^2c^4}\int_0^d n_e(s) B_\parallel(s) \;\mathrm{d}s or, in the SI units, by R_M = \frac{e^3}{8\pi^2 \varepsilon_0 m^2 c^3} \int_0^d n_e(s) B_ (s) \;\mathrm{d}s \approx (2.62 \times 10^{-13}\, \mathrm T^{-1})\times\, \int_0^d n_e(s) B_\parallel(s)\; \mathrm{d}s where n e (s) is the density of free electrons at each point s along the path; B ‖ (s) is the component of the magnetic field in the direction of propagation at each point s along the path; e is the elementary charge; c is the speed of light in vacuum; m is the electron mass; \scriptstyle\epsilon_0 is the vacuum permittivity, and the integral is taken over the entire path from the source to the observer. Electron Coulomb collisions and plasma instabilities may significantly alter this simple expression, however. Radio waves passing through the Earth's ionosphere are likewise subject to the Faraday effect. The ionosphere consists of a plasma containing free electrons which contribute to Faraday rotation according to the above equation, whereas the positive ions are relatively massive and have little influence. In conjunction with the Earth's magnetic field, rotation of the polarization of radio waves thus occurs. Since the density of electrons in the ionosphere varies greatly on a daily basis, as well as over the sunspot cycle, the magnitude of the effect varies. However the effect is always proportional to the square of the wavelength, so even at the UHF television frequency of 500 MHz (λ = 60 cm), there can be more than a complete rotation of the axis of polarization. A consequence is that although most radio transmitting antennas are either vertically or horizontally polarized, the polarization of a medium or short wave signal after reflection by the ionosphere is rather unpredictable. However the Faraday effect due to free electrons diminishes rapidly at higher frequencies (shorter wavelengths) so that at microwave frequencies, used by satellite communications, the transmitted polarization is maintained between the satellite and the ground. ==See also== Electro-optic Kerr effect Faraday rotator Inverse Faraday effect Magnetic circular dichroism Magneto-optic Kerr effect Optical rotation Polarization spectroscopy QMR effect (quadratic rather than linear) Voigt effect (magnetic-linear birefringence) ==References== ==External links== Faraday Rotation (at Eric W. Weisstein's World of Physics) Electro-optical measurements (Kerr, Pockels, and Faraday) Faraday Rotation Effect in (radio)astronomy A simple

Text derived from https://en.wikipedia.org/w/index.php?oldid=1378603330 under CC BY-SA 4.0; modifications have been made.