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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.[1] For a constant magnetic field parallel to the path of the light, it can be calculated by:[2]
Where is the angle between the starting and ending polarizations, is the Verdet constant, is the strength of the magnetic flux density, and is the path length in the material.
The Verdet constant of a material is wavelength dependent and for most materials is extremely small. 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,[3] but only over a very narrow wavelength range. Alkali vapours can therefore be used as an optical isolator[4] or as an extremely sensitive magnetometer.
The Faraday effect is chromatic (i.e. it depends on wavelength) and therefore the Verdet constant is quite a strong function of wavelength.[5][6] 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).[7] 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.
^Vojna, David; Slezák, Ondřej; Lucianetti, Antonio; Mocek, Tomáš (2019). "Verdet Constant of Magneto-Active Materials Developed for High-Power Faraday Devices". Applied Sciences. 9 (15): 3160. doi:10.3390/app9153160.
^Kruk, Andrzej; Mrózek, Mariusz (2020). "The measurement of Faraday effect of translucent material in the entire visible spectrum". Measurement. 162. Elsevier BV: 107912. Bibcode:2020Meas..16207912K. doi:10.1016/j.measurement.2020.107912. ISSN 0263-2241. S2CID 219429531.
^Siddons, Paul; Bell, Nia C.; Cai, Yifei; Adams, Charles S.; Hughes, Ifan G. (2009). "A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect". Nature Photonics. 3 (4): 225. arXiv:0811.2316. Bibcode:2009NaPho...3..225S. doi:10.1038/nphoton.2009.27.
^Weller, L.; Kleinbach, K. S.; Zentile, M. A.; Knappe, S.; Hughes, I. G.; Adams, C. S. (2012). "Optical isolator using an atomic vapor in the hyperfine Paschen–Back regime". Optics Letters. 37 (16): 3405–3407. arXiv:1206.0214. Bibcode:2012OptL...37.3405W. doi:10.1364/OL.37.003405. PMID 23381272. S2CID 39307069.
^Vojna, David; Slezák, Ondřej; Yasuhara, Ryo; Furuse, Hiroaki; Lucianetti, Antonio; Mocek, Tomáš (2020). "Faraday Rotation of Dy2O3, CeF3 and Y3Fe5O12 at the Mid-Infrared Wavelengths". Materials. 13 (23): 5324. Bibcode:2020Mate...13.5324V. doi:10.3390/ma13235324. PMC 7727863. PMID 33255447.
^Vojna, David; Duda, Martin; Yasuhara, Ryo; Slezák, Ondřej; Schlichting, Wolfgang; Stevens, Kevin; Chen, Hengjun; Lucianetti, Antonio; Mocek, Tomáš (2020). "Verdet constant of potassium terbium fluoride crystal as a function of wavelength and temperature". Opt. Lett. 45 (7): 1683–1686. Bibcode:2020OptL...45.1683V. doi:10.1364/ol.387911. PMID 32235973. S2CID 213599420.
^"Archived copy" (PDF). Archived from the original (PDF) on 2016-04-18. Retrieved 2015-02-11.{{cite web}}: CS1 maint: archived copy as title (link)
The Verdetconstant is an optical property named after the French physicist Émile Verdet. It describes the strength of the Faraday effect for a particular...
{\displaystyle \scriptstyle {\mathcal {V}}} is the Verdetconstant for the material. This empirical proportionality constant (in units of radians per tesla per meter)...
{\displaystyle \beta =\nu Bd\,} , where, ν {\displaystyle \nu } is the Verdetconstant of the material (amorphous or crystalline solid, or liquid, or crystalline...
magnetic field sensors. TGG has a high Verdetconstant which results in the Faraday effect. The Verdetconstant increases substantially as the mineral...
interact, and V {\displaystyle V} is the Verdetconstant for the material. This empirical proportionality constant (in units of radians per tesla per metre...
Terbium gallium garnet, a chemical compound whose crystals have a high Verdetconstant TGG Group, an American management consulting holding company The Golden...
example, interesting magnetic properties can be obtained. YIG has a high Verdetconstant which results in the Faraday effect, high Q factor in microwave frequencies...
elements as an inexpensive anti-reflective coating.[citation needed] Its Verdetconstant is 0.00810 arcmin⋅G−1⋅cm−1 at 632.8 nm. Chronic exposure to magnesium...
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D.; Adamietz, F.; Kalafatis, A. "All-Optical Measurements of the VerdetConstant in Achiral and Chiral Liquids: Toward All-Optical Magnetic Spectroscopies"...
polytechnique and the École des mines. Upon the death of Émile Verdet in 1866, Cornu became, in 1867, Verdet's successor as professor of experimental physics at the...
strength of the magnetic field, the width of the vapor cell and the Verdetconstant (which is dependent on the temperature of the cell, wavelength of the...
good mechanical properties with a high degree of transparency, high Verdetconstant and superparamagnetism in order to avoid remnant magnetism and facilitate...
parallèles à l'axe", read 9 December 1822; printed in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), Oeuvres complètes d'Augustin Fresnel, vol. 1 (1866)...
eq. (4.42). Fresnel, 1866, p. 757. Hecht, 2002, p. 115, eq. (4.43). E. Verdet, in Fresnel, 1866, p. 789n. Born & Wolf, 1970, p. 40, eqs. (21a). Jenkins...
former Assembly members were recovered in post-1989 politics, including Ilie Verdeț, who established a Socialist Party of Labour (PSM). The election took place...
9: 57–66 (Sep. 1818), 286–7 (Nov. 1818); reprinted in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), Oeuvres complètes d'Augustin Fresnel, vol. 2 (1868)...
9: 57–66 (Sep. 1818), 286–7 (Nov. 1818); reprinted in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), Oeuvres complètes d'Augustin Fresnel, vol. 2 (1868)...
numbers are from the translation.) A. Fresnel (ed. H. de Sénarmont, E. Verdet, and L. Fresnel), 1866–70, Oeuvres complètes d'Augustin Fresnel (3 volumes)...
Austin, accessed 14 March 2018. A. Fresnel, 1866 (ed. H. de Senarmont, E. Verdet, and L. Fresnel), Oeuvres complètes d'Augustin Fresnel, Paris: Imprimerie...
corrections, 2002), ISBN 978-0-521-64222-4. A. Fresnel (ed. H. de Senarmont, E. Verdet, and L. Fresnel), 1868, Oeuvres complètes d'Augustin Fresnel, Paris: Imprimerie...
(replaced Étienne Eusèbe Joseph Huard after the latter's death (1789)). Louis Verdet (1744–1819), deputy of the clergy of the bailiwick of Sarreguemines. Théodore...
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