In physics, the Faraday effect or Faraday rotation is a magneto-optical phenomenon—that is, an interaction between light and a magnetic field in a medium. The Faraday effect causes a rotation of the plane of polarization which is linearly proportional to the component of the magnetic field in the direction of propagation. Formally, it is a special case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal.
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 and 1870s. This effect occurs in most optically transparent dielectric materials (including liquids) under the influence of magnetic fields.
The Faraday effect is caused by left and right circularly polarized waves propagating at slightly different speeds, a property known as 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 and for remote sensing of magnetic fields (such as fiber optic current sensors). The Faraday effect is used in spintronics research to study the polarization of electron spins in semiconductors. 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.
By 1845, it was known through the work of Fresnel, 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. However, his experimental methods were not sensitive enough, and the effect was only measured thirty years later by John Kerr.
Faraday then attempted to look for the effects of magnetic forces on light passing through various substances. After several unsuccessful trials, he happened to test a piece of "heavy" glass, containing traces of lead, that he had made during his earlier work on glass manufacturing. Faraday observed that when a beam of polarized light passed through the glass in the direction of an applied magnetic force, the polarization of light rotated by an angle that was proportional to the strength of the force. He was later able to reproduce the effect in several other solids, liquids, and gases by procuring stronger electromagnets.
The discovery is well documented in Faraday's daily notebook, which has since been published. On 13 Sept. 1845, in paragraph #7504, under the rubric Heavy Glass, he wrote:
… BUT, when the contrary magnetic poles were on the same side, there was an effect produced on the polarized ray, and thus magnetic force and light were proved to have relation to each other. …— Faraday, Paragraph #7504, Daily notebook
He summarized the results of his experiments on 30 Sept. 1845, in paragraph #7718, famously writing:
… Still, I have at last succeeded in illuminating a magnetic curve or line of force, and in magnetizing a ray of light. …— Faraday, Paragraph #7718, Daily notebook
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 comprising the material (because of their low mass, 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 down 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 in the polarization direction.
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 down more.
The relation between the angle of rotation of the polarization and the magnetic field in a transparent material is:
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 (≈ −134 rad/(T·m) 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 (≈ −20 rad/(T·m) 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.
The effect is imposed on light over the course of its propagation from its origin to the Earth, through the interstellar medium. Here, the effect is caused by free electrons and can be characterized as a difference in the refractive index seen by the two circularly polarized propagation modes. Hence, in contrast to the Faraday effect in solids or liquids, interstellar Faraday rotation (β) has a simple dependence on the wavelength of light (λ), namely:
where the overall strength of the effect is characterized by RM, the rotation measure. This in turn depends on the axial component of the interstellar magnetic field B||, and the number density of electrons ne, both of which vary along the propagation path. In Gaussian cgs units the rotation measure is given by:
or in SI units:
The integral is taken over the entire path from the source to the observer.
Faraday rotation is an important tool in astronomy for the measurement of magnetic fields, which can be estimated from rotation measures given a knowledge of the electron number density. In the case of radio pulsars, the dispersion caused by these electrons results in a time delay between pulses received at different wavelengths, which can be measured in terms of the electron column density, or dispersion measure. A measurement of both the dispersion measure and the rotation measure therefore yields the weighted mean of the magnetic field along the line of sight. The same information can be obtained from objects other than pulsars, if the dispersion measure can be estimated based on reasonable guesses about the propagation path length and typical electron densities. In particular, Faraday rotation measurements of polarized radio signals from extragalactic radio sources occulted by the solar corona can be used to estimate both the electron density distribution and the direction and strength of the magnetic field in the coronal plasma.
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.
Due to spin-orbit coupling, undoped GaAs single crystal exhibits much larger Faraday rotation than glass (SiO2). Considering the atomic arrangement is different along the (100) and (110) plane, one might think the Faraday rotation is polarization dependent. However, experimental work revealed an immeasurable anisotropy in the wavelength range from 880–1,600 nm. Based on the large Faraday rotation, one might be able to use GaAs to calibrate the B field of the terahertz electromagnetic wave which requires very fast response time. Around the band gap, the Faraday effect shows resonance behavior.
More generally, (ferromagnetic) semiconductors return both electro-gyration and a Faraday response in the high frequency domain. The combination of the two is described by gyroelectromagnetic media, for which gyroelectricity and gyromagnetism (Faraday effect) may occur at the same time.
In organic materials, Faraday rotation is typically small, with a Verdet constant in the visible wavelength region on the order of a few hundred degrees per Tesla per meter, decreasing proportional to in this region. While the Verdet constant of organic materials does increase around electronic transitions in the molecule, the associated light absorption makes most organic materials bad candidates for applications. There are however also isolated reports of large Faraday rotation in organic liquid crystals without associated absorption.
In 2009  γ-Fe2O3-Au core-shell nanostructures were synthesized to integrate magnetic (γ-Fe2O3) and plasmonic (Au) properties into one composite. Faraday rotation with and without the plasmonic materials was tested and rotation enhancement under 530 nm light irradiation was observed. Researchers claim that the magnitude of the magneto-optical enhancement is governed primarily by the spectral overlap of the magneto-optical transition and the plasmon resonance.
The reported composite magnetic/plasmonic nanostructure can be visualized to be a magnetic particle embedded in a resonant optical cavity. Because of the large density of photon states in the cavity, the interaction between the electromagnetic field of the light and the electronic transitions of the magnetic material is enhanced, resulting in a larger difference between the velocities of the right- and left-hand circularized polarization, therefore enhancing Faraday rotation.
A Treatise on Electricity and Magnetism is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873. Maxwell was revising the Treatise for a second edition when he died in 1879. The revision was completed by William Davidson Niven for publication in 1881. A third edition was prepared by J. J. Thomson for publication in 1892.
According to one historian,
The Treatise was notoriously hard to read; it teemed with ideas but lacked the clear focus and orderly presentation that might have enabled it to win converts more readily. Rather than simply expounding his own system, Maxwell had set out to write a comprehensive treatise on electrical science, and so he had allowed his own new distinctive ideas, notably that of the displacement current, to be almost buried under long accounts of miscellaneous phenomena discussed from several points of view. Except for a fuller treatment of the Faraday effect (in which he again invoked the molecular vortices), Maxwell added little to his earlier work on the electromagnetic theory of light; he said nothing, for example, about how electromagnetic waves might be generated, nor did he attempt to derive laws governing reflection and refraction.Maxwell introduced the use of vector fields, and his labels have been perpetuated:
A (vector potential), B (magnetic induction), C (electric current), D (displacement), E (electric field – Maxwell's electromotive intensity), F (mechanical force), H (magnetic field – Maxwell's magnetic force).Maxwell's work is considered an exemplar of rhetoric of science:
Lagrange's equations appear in the Treatise as the culmination of a long series of rhetorical moves, including (among others) Green's theorem, Gauss's potential theory and Faraday's lines of force – all of which have prepared the reader for the Lagrangian vision of a natural world that is whole and connected: a veritable sea change from Newton's vision.Circulator
A circulator is a passive non-reciprocal three- or four-port device, in which a microwave or radio frequency signal entering any port is transmitted to the next port in rotation (only). A port in this context is a point where an external waveguide or transmission line (such as a microstrip line or a coaxial cable), connects to the device. For a three-port circulator, a signal applied to port 1 only comes out of port 2; a signal applied to port 2 only comes out of port 3; a signal applied to port 3 only comes out of port 1, so to up to a phase-factor, the scattering matrix for an ideal three-port circulator is
Optical circulators have similar behaviour.Duality (electricity and magnetism)
In physics, the electromagnetic dual concept is based on the idea that, in the static case, electromagnetism has two separate facets: electric fields and magnetic fields. Expressions in one of these will have a directly analogous, or dual, expression in the other. The reason for this can ultimately be traced to special relativity where applying the Lorentz transformation to the electric field will transform it into a magnetic field.
The electric field (E) is the dual of the magnetic field (H).
The electric displacement field (D) is the dual of the magnetic flux density (B).
Faraday's law of induction is the dual of Ampère's circuital law.
Gauss's law for electric field is the dual of Gauss's law for magnetism.
The electric potential is the dual of the magnetic potential.
Permittivity is the dual of permeability.
Electrostriction is the dual of magnetostriction.
Piezoelectricity is the dual of piezomagnetism.
Ferroelectricity is the dual of ferromagnetism.
An electrostatic motor is the dual of a magnetic motor;
Electrets are the dual of permanent magnets;
The Faraday effect is the dual of the Kerr effect;
The Aharonov–Casher effect is the dual to the Aharonov–Bohm effect;
The hypothetical magnetic monopole is the dual of electric charge.Electro-gyration
The electrogyration effect is the spatial dispersion phenomenon, that consists in the change of optical activity (gyration) of crystals by a constant or time-varying electric field. Being a spatial dispersion effect, the induced optical activity exhibit different behavior under the operation of wave vector reversal, when compared with the Faraday effect: the optical activity increment associated with the electrogyration effect changes its sign under that operation, contrary to the Faraday effect. Formally, it is a special case of gyroelectromagnetism obtained when the magnetic permeability tensor is diagonal.
The electrogyration effect linear in the electric field occurs in crystals of all point groups of symmetry except for the three cubic – m3m, 432 and . The effect proportional to the square of the electric field can exist only in crystals belonging to acentric point groups of symmetry.Faraday rotator
A Faraday rotator is a polarization rotator based on the Faraday effect, which in turn is based on a magneto-optic effect. It works because one polarization of the input light is in ferromagnetic resonance with the material which causes its phase velocity to be higher than the other.
The plane of linearly polarized light is rotated when a magnetic field is applied parallel to the propagation direction. The empirical angle of rotation is given by:
Where is the angle of rotation (in radians).
is the magnetic flux density in the direction of propagation (in teslas).
is the length of the path (in metres) where the light and magnetic field interact.
Then is the Verdet constant for the material. This empirical proportionality constant (in units of radians per tesla per metre, rad/(T·m)) varies with wavelength and temperature and is tabulated for various materials.
Faraday rotation is an example of non-reciprocal optical propagation. Unlike what happens in an optically active medium such as a sugar solution, reflecting a polarized beam back through the same Faraday medium does not undo the polarization change the beam underwent in its forward pass through the medium. This allows Faraday rotators to be used to construct devices such as optical isolators to prevent undesired back propagation of light from disrupting or damaging an optical system.
The geometry of nonreciprocal propagation may at first appear paradoxical. In an optically active medium, the polarization direction twists in the same sense (e.g. like a right-handed screw) during the forward and backward passes, whereas in a Faraday medium, because the light reverses its propagation direction with respect to the magnetic field, the helicity of the propagation also reverses. But because the propagation axis has also reversed, this reversal of helicity is just what is needed to cause the back-reflected light to have different polarization from the incident light. If the Faraday medium is of such thickness as to cause a 45 degree rotation on the way in, the back-reflected beam will have polarization perpendicular to the incident beam, allowing it to be cleanly blocked by the light source's polarizer.
Faraday rotators may be enhanced by the Zeeman effect.Fiber optic current sensor
A fiber optic current sensor (FOCS) is a current sensor for measuring direct current. By using a single-ended optical fiber around the current conductor that utilizes the magneto-optic effect (Faraday effect), FOCS measures uni- or bidirectional DC currents of up to 600 kA within ±0.1% of the measured value.Because it does not need a magnetic yoke, an FOCS is smaller and lighter than Hall effect current sensors, and suffers no reduction in accuracy due to saturation effects. Because magnetic field sensing is distributed around circumference, it is unaffected by stray magnetic fields, and there is no need for magnetic centering. It also does not need recalibration after installation or during its service life. Because the optical fiber is inherently insulating, electrical isolation is easier to maintain.
The optical phase detection circuit, light source and digital signal processor are contained within the sensor electronics; this technology has been proven in highly demanding applications such as navigation systems in the air, on land and at sea.Inverse Faraday effect
The inverse Faraday effect is the effect opposite to the Faraday effect. A static magnetization is induced by an external oscillating electrical field with the frequency , which can be achieved with a high intensity laser pulse for example. The induced magnetization is proportional to the vector product of and :
From this equation we see that the circularly polarized light with the frequency should induce a magnetization along the wave vector . Because is in the vector product, left- and right-handed polarization waves should induce magnetization of opposite signs.
The induced magnetization is comparable to the saturated magnetization of the media.Magnetization reversal by circularly polarized light
Discovered only as recently as 2006 by C.D. Stanciu and F. Hansteen and published in Physical Review Letters, this effect is generally called all-optical magnetization reversal. This magnetization reversal technique refers to a method of reversing magnetization in a magnet simply by circularly polarized light and where the magnetization direction is controlled by the light helicity. In particular, the direction of the angular momentum of the photons would set the magnetization direction without the need of an external magnetic field. In fact, this process could be seen as similar to magnetization reversal by spin injection (see also spintronics). The only difference is that now, the angular momentum is supplied by the circularly polarized photons instead of the polarized electrons.
Although experimentally demonstrated, the mechanism responsible for this all-optical magnetization reversal is not clear yet and remains a subject of debate. Thus, it is not yet clear whether an Inverse Einstein–de Haas effect is responsible for this switching or a stimulated Raman-like coherent optical scattering process. However, because phenomenologically is the inverse effect of the magneto-optical Faraday effect, magnetization reversal by circularly polarized light is referred to as the inverse Faraday effect.
Early studies in plasmas, paramagnetic solids, dielectric magnetic materials and ferromagnetic semiconductors demonstrated that excitation of a medium with a circularly polarized laser pulse corresponds to the action of an effective magnetic field. Yet, before the experiments of Stanciu and Hansteen, all-optical controllable magnetization reversal in a stable magnetic state was considered impossible.In quantum field theory and quantum chemistry the effect where the angular momentum associated to the circular motion of the photons induces an angular momentum in the electrons is called photomagneton. This axial magnetic field with the origins in the angular momentum of the photons has been sometimes referred in the literature as the field B.Magnetization reversal by circularly polarized light is the fastest known way to reverse magnetization, and therefore to store data: magnetization reversal is induced on the femtosecond time scale - that translates to a potential of about 100 TBit/s data storage speeds.Magneto-optic Kerr effect
In physics the magneto-optic Kerr effect (MOKE) or the surface magneto-optic Kerr effect (SMOKE) is one of the magneto-optic effects. It describes the changes to light reflected from a magnetized surface. It is used in materials science research in devices such as the Kerr microscope, to investigate the magnetization structure of materials.Magneto-optic effect
A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a material, which is also called gyrotropic or gyromagnetic, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect).
In general, magneto-optic effects break time reversal symmetry locally (i.e. when only the propagation of light, and not the source of the magnetic field, is considered) as well as Lorentz reciprocity, which is a necessary condition to construct devices such as optical isolators (through which light passes in one direction but not the other).
Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called optical isomers.Optical isolator
An optical isolator, or optical diode, is an optical component which allows the transmission of light in only one direction. It is typically used to prevent unwanted feedback into an optical oscillator, such as a laser cavity.
The operation of [some of] the devices depends on the Faraday effect (which in turn is produced by magneto-optic effect), which is used in the main component, the Faraday rotator.Optical rotation
Optical rotation or optical activity (sometimes referred to as rotary polarization) is the rotation of the plane of polarization of linearly polarized light as it travels through certain materials. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins, and also chiral liquid crystals. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes (such as quartz) or metamaterials. Rotation of light's plane of polarization may also occur through the Faraday effect which involves a static magnetic field, however this is a distinct phenomenon that is not usually classified under "optical activity."
The rotation of the plane of polarization may be either clockwise, to the right (dextrorotary — d-rotary), or to the left (levorotary — l-rotary) depending on which stereoisomer is present (or dominant). For instance, sucrose and camphor are d-rotary whereas cholesterol is l-rotary. For a given substance, the angle by which the polarization of light of a specified wavelength is rotated is proportional to the path length through the material and (for a solution) proportional to its concentration. The rotation is not dependent on the direction of propagation, unlike the Faraday effect where the rotation is dependent on the relative direction of the applied magnetic field.
Optical activity is measured using a polarized source and polarimeter. This is a tool particularly used in the sugar industry to measure the sugar concentration of syrup, and generally in chemistry to measure the concentration or enantiomeric ratio of chiral molecules in solution. Modulation of a liquid crystal's optical activity, viewed between two sheet polarizers, is the principle of operation of liquid-crystal displays (used in most modern televisions and computer monitors).Photomagneton
The photomagneton is a theoretical treatment of the unitary group in quantum field theory and quantum chemistry that effectively describes the experimentally observed inverse Faraday effect. When circularly polarized light travels through a plasma, the angular momentum associated to the circular motion of the photons induces an angular momentum in the electrons of the plasma. This angular momentum induces an associated magnetic field.
Exactly how this happens remains a subject of debate. For instance, if the so-called ghost field does not contribute to the free electromagnetic energy density in the plasma, then the electron must couple to something like a complex electric field. However, if the field induces a finite magnetic field in the absence of matter, then the implication may be a finite photon rest mass.Polarization rotator
A polarization rotator is an optical device that rotates the polarization axis of a linearly polarized light beam by an angle of choice. Such devices can be based on the Faraday effect, on birefringence, or on total internal reflection. Rotators of linearly polarized light have found widespread applications in modern optics since laser beams tend to be linearly polarized and it is often necessary to rotate the original polarization to its orthogonal alternative.QMR effect
Quadratic magnetic rotation (also known as QMR or QMR effect) is a type of magneto-optic effect, discovered in the mid 1980s by a team of Ukrainian physicists. QMR, like the Faraday effect, establishes a relationship between the magnetic field and rotation of polarization of the plane of linearly polarized light. In contrast to the Faraday effect, QMR originates from the quadratic proportionality between the angle of the rotation of the plane of polarization and the strength of the magnetic field. Mostly QMR can be observed in the transverse geometry when the vector of the magnetic field strength is perpendicular to the direction of light propagation.
The first evidence of QMR effect was obtained in the antiferromagnetic crystal of cobalt fluoride in 1985.Considerations of the symmetry of the media, light and axial vector of the magnetic field forbid QMR in non-magnetic or magnetically disordered media. Onsager's reciprocal relations generalized for magnetically ordered media eliminate symmetry restrictions for QMR in the media which have lost the center of anti-inversion as an operation of symmetry at an ordering of its magnetic subsystem. Despite the fact that some crystal groups of symmetry are devoid of the center of anti-inversion, they also don’t have QMR because of action of other operators of symmetry. They are eleven groups without the center of anti-inversion 432, 43'm, m3m, 422, 4mm, 4'2m, 4/mmm, 622, 6mm, 6'm2 and 6/mmm. Accordingly, the rest of groups of crystal symmetry where QMR can be observed constitutes 27 antiferromagnetic and 31 pyromagnetic crystal classes.
QMR is described by fourth-order c-tensor which is antisymmetrical as to the first two indices.Terbium gallium garnet
Terbium gallium garnet (TGG) is a kind of synthetic garnet, with the chemical composition Tb3Ga5O12. This is a Faraday rotator material with excellent transparency properties and is very resistant to laser damage. TGG can be used in optical isolators for laser systems, in optical circulators for fiber optic systems, in optical modulators, and in current and magnetic field sensors.
TGG has a high Verdet constant which results in the Faraday effect. The Verdet constant increases substantially as the mineral approaches cryogenic temperatures. The highest Verdet constants are found in terbium doped dense flint glasses or in crystals of TGG. The Faraday effect is chromatic (i.e. it depends on wavelength) and therefore the Verdet constant is quite a strong function of wavelength. At 632 nm, the Verdet constant for TGG is reported to be −134 rad/(T·m), whereas at 1064 nm it falls to −40 rad/(T·m). This behavior means that the devices manufactured with a certain degree of rotation at one wavelength, will produce much less rotation at longer wavelengths. Many Faraday rotators and isolators are adjustable by varying the degree to which the amount of the Faraday rotator material is inserted into the magnetic field of the device. In this way, the device can be tuned for use with a range of lasers within the design range of the device.Verdet constant
The Verdet constant is an optical property named after the French physicist Émile Verdet. It describes the strength of the Faraday effect for a particular material.
The Verdet constant for most materials is extremely small and is wavelength dependent. It is strongest in substances containing paramagnetic ions such as terbium. The highest Verdet constants in bulk media are found in terbium doped dense flint glasses or in crystals of terbium gallium garnet (TGG). These materials have excellent transparency properties and high damage thresholds for laser radiation. Atomic vapours, however, can have Verdet constants which are orders of magnitude larger than TGG, but only over a very narrow wavelength range. Alkali vapours can therefore be used as an optical isolator, as demonstrated in Durham University's Atomic and Molecular Physics research group.The Faraday effect is chromatic (i.e. it depends on wavelength) and therefore the Verdet constant is quite a strong function of wavelength. At 632.8 nm, the Verdet constant for TGG is reported to be −134 rad/(T·m), whereas at 1064 nm it falls to −40 rad/(T·m). This behavior means that the devices manufactured with a certain degree of rotation at one wavelength, will produce much less rotation at longer wavelengths. Many Faraday rotators and isolators are adjustable by varying the degree to which the active TGG rod is inserted into the magnetic field of the device. In this way, the device can be tuned for use with a range of lasers within the design range of the device. Truly broadband sources (such as ultrashort-pulse lasers and the tunable vibronic lasers) will not see the same rotation across the whole wavelength band.Yttrium iron garnet
Yttrium iron garnet (YIG) is a kind of synthetic garnet, with chemical composition Y3Fe2(FeO4)3, or Y3Fe5O12. It is a ferrimagnetic material with a Curie temperature of 560 K. YIG may also be known as yttrium ferrite garnet, or as iron yttrium oxide or yttrium iron oxide, the latter two names usually associated with powdered forms.In YIG, the five iron(III) ions occupy two octahedral and three tetrahedral sites, with the yttrium(III) ions coordinated by eight oxygen ions in an irregular cube. The iron ions in the two coordination sites exhibit different spins, resulting in magnetic behavior. By substituting specific sites with rare earth elements, for example, interesting magnetic properties can be obtained.YIG has a high Verdet constant which results in the Faraday effect, high Q factor in microwave frequencies, low absorption of infrared wavelengths down to 1200 nm, and very small linewidth in electron spin resonance. These properties make it useful for MOI (magneto optical imaging) applications in superconductors.YIG is used in microwave, acoustic, optical, and magneto-optical applications, e.g. microwave YIG filters, or acoustic transmitters and transducers. It is transparent for light wavelengths over 600 nm. It also finds use in solid-state lasers in Faraday rotators, in data storage, and in various nonlinear optics applications.