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Faraday Effect

Definition: the rotation of the linear polarization direction in a medium exposed to a magnetic field

Alternative term: Faraday rotation

German: Faraday-Effekt

Category: physical foundations

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When exposed to a magnetic field, most transparent media exhibit the so-called Faraday effect (named after Michael Faraday, who discovered the effect in 1845). For a linearly polarized light beam propagating through the medium, the polarization direction is rotated. The rotation angle per unit angle is the product of two factors:

  • the Verdet constant V of the material (in units of rad / (T m), named after the French physicist Émile Verdet), and
  • the magnetic flux density B in the propagation direction.

Therefore, the total rotation angle (in radians) within a length L of the material is:

Faraday rotation angle

In some cases, rotation angles are measured in degrees, and Verdet constants specified with units of ° / (T m). Also, the H field was considered instead of B in some publications.

Note that the Faraday rotation is non-reciprocal: its direction is determined by the magnetic field direction but not by the propagation direction of light. If a light beam travels through a Faraday medium and back again on the same path, the polarization direction is not restored to the original direction, but rather the rotation is doubled.

The Faraday effect may also be called Faraday rotation or magnetically induced optical rotation; see also the article on optical activity. It is one particular type of magneto-optic effect.

The Faraday effect can be observed in wide spectral regions from the ultraviolet to visible and infrared light, and even for terahertz radiation.

Note that the polarization evolution can become more complex if Faraday rotation occurs at the same time as linear birefringence. Therefore, the Faraday effect is mostly applied in cases with no linear birefringence.

Relation of Polarization Rotation to Circular Birefringence

The rotation of linear polarization direction can be interpreted as resulting from circular birefringence, i.e., a difference in refractive index between left and right circularly polarized light of magnitude (λ/π) V B. This is in contrast to linear birefringence, which is related to a refractive index difference between orthogonal linear polarization directions, and occurs in various media without an externally applied electric or magnetic field.

Verdet Constants of Materials

The Verdet constant of a material can be positive or negative. A positive value implies rotation of the polarization direction to the left when the light propagates in the direction of the magnetic field.

The magnitude of the Verdet constant is very different for different materials (higher for paramagnetic than for diamagnetic substances), and generally has a substantial wavelength dependence. For example, for the common material TGG (used in many Faraday isolators), it is as high as −134 rad / (T m) at 623.8 nm (HeNe laser), but falls to only −40 rad / (T m) at 1064 nm (Nd:YAG laser). Part of that wavelength dependence comes from the fact that for a given refractive index difference between circularly polarized components the resulting phase difference is proportional to the wavenumber, i.e., inversely proportional to the wavelength. However, one often observes even roughly a λ−2 dependence, which was also found with early quantum-mechanical considerations for the long-wavelength regime. In the ultraviolet spectral regions, even materials like fused silica, not showing a strong Faraday effect e.g. in the near infrared, can have pretty large Verdet constants [12]. Particularly strong wavelength dependencies arise in cases where a resonance effect enhances the Verdet constant by orders of magnitude, as occurs e.g. in certain atomic vapors [9].

Even for materials with a rather high Verdet constant such as terbium gallium garnet (TGG) crystals, one requires a quite strong magnetic field for realizing a useful polarization rotation by e.g. 45° (as required for a Faraday isolator) within a short length of material. At 1064 nm, even with a rather strong B field of 1 T, for example, one requires a length of π/4 / (40 rad / (T m) · 1 T) = 1.96 cm.

Materials for application in magneto-optic devices are sometimes called magneto-optic materials. They should usually have a large Verdet constant. Various inorganic and organic materials may be used, including optical crystals, optical glasses and liquids. Optical fibers also exhibit the effect – with a relatively small Verdet constant but possibly over a long length.

Application of the Faraday Effect

In photonics technology, the Faraday effect is mostly applied for constructing Faraday rotators and devices derived from those – Faraday isolators and Faraday circulators.

A small Faraday rotation is utilized in nonplanar ring oscillatorssolid-state lasers with a non-planar ring resonator which can be made to operate in a unidirectional fashion by applying a moderately strong magnetic field.

Although this is not common, one can construct magneto-optic modulators based on the Faraday effect.

The Faraday effect can also be used for evaluating the magnetic flux density B by measuring the polarization rotation of light. This can be used for compact and fast magnetic field sensors, which can also be part of fiber-optic current sensors, for example. Another application is for magnetic field measurements in astronomy, where free electrons may be used as the Faraday medium. In the latter case, one of course also needs to measure the density of free electrons.

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Bibliography

[1]P. S. Pershan, “Magneto-optical effects”, J. Appl. Phys. 38, 1482 (1967), doi:10.1063/1.1709678
[2]A. A. Jaecklin and M. Lietz, “Elimination of disturbing birefringence effects on Faraday rotation”, Appl. Opt. 11 (3), 617 (1972), doi:10.1364/AO.11.000617
[3]H. A. Bomke and M. Harmatz, “Enhanced Faraday effect and its application to optical communication”, Appl. Opt. 16 (3), 751 (1977), doi:10.1364/AO.16.000751
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[5]J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications”, Appl. Opt. 34 (30), 6848 (1995), doi:10.1364/AO.34.006848
[6]T. Yoshino, “Theory for the Faraday effect in optical fiber”, J. Opt. Soc. Am. B 22 (9), 1856 (2005), doi:10.1364/JOSAB.22.001856
[7]L. Sun et al., “Effective Verdet constant in a terbium-doped-core phosphate fiber”, Opt. Lett. 34 (11), 1699 (2009), doi:10.1364/OL.34.001699
[8]L. Sun et al., “Compact all-fiber optical Faraday components using 65-wt%-terbium-doped fiber with a record Verdet constant of −32 rad/(Tm)”, Opt. Express 18 (12), 12191 (2010), doi:10.1364/OE.18.012191
[9]L. Weller et al., “Optical isolator using an atomic vapor in the hyperfine Paschen–Back regime”, Opt. Lett. 37 (16), 3405 (2012), doi:10.1364/OL.37.003405
[10]J. Q. Liu et al., “Giant Faraday rotation in graphene metamolecules due to plasmonic coupling”, J. Lightwave Technol. 36 (13), 2606 (2018)
[11]D. Vojna et al., “Verdet constant of magneto-active materials developed for high-power Faraday devices”, Appl. Sci. 9 (15), 3160 (2019), doi:10.3390/app9153160
[12]Y. Tamaru et al., “Wavelength dependence of the Verdet constant in synthetic quartz glass for deep-ultraviolet light sources”, Opt. Mater. Express 11 (3), 814 (2021), doi:10.1364/OME.412395
[13]E. A. Mironov, O. V. Palshov and S. S. Balabanov, “High-purity CVD-ZnSe polycrystal as a magneto-active medium for a multikilowatt Faraday isolator”, Opt. Lett. 46 (9), 2119 (2021), doi:10.1364/OL.423632
[14]S. V. Tomilin et al., “Giant enhancement of the Faraday effect in a magnetoplasmonic nanocomposite”, Opt. Mater. Express 12 (4), 1522 (2022), doi:10.1364/OME.446392
[15]K. J. Carothers, R. a. Norwood and J. Pyun, “High Verdet constant materials for magneto-optical Faraday rotation: a review”, Chem. Mater. 34 (6), 2531 (2022), doi:10.1021/acs.chemmater.2c00158

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See also: Faraday rotators, Faraday isolators, birefringence
and other articles in the category physical foundations

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