Editing Verdet constant (section)

{{Short description|Optical property}}
{{More citations needed|date=December 2014}}
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.<ref>{{cite journal |last1=Vojna |first1=David |last2=Slezák |first2=Ondřej |last3=Lucianetti |first3=Antonio |last4=Mocek |first4=Tomáš |title=Verdet Constant of Magneto-Active Materials Developed for High-Power Faraday Devices |journal=Applied Sciences |date=2019 |volume=9 |issue=15 |page=3160 |doi=10.3390/app9153160 |doi-access=free }}</ref> For a constant magnetic field parallel to the path of the light, it can be calculated as<ref>{{cite journal | last1=Kruk | first1=Andrzej | last2=Mrózek | first2=Mariusz | title=The measurement of Faraday effect of translucent material in the entire visible spectrum | journal=Measurement | publisher=Elsevier BV | volume=162 | year=2020 | issn=0263-2241 | doi=10.1016/j.measurement.2020.107912 | page=107912| bibcode=2020Meas..16207912K | s2cid=219429531 }}</ref>

: <math>\theta = V B L,</math>

where <math>\theta</math> is the angle between the starting and ending polarizations, <math>V</math> is the Verdet constant, <math>B</math> is the strength of the magnetic flux density, and <math>L</math> 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]] [[ion]]s such as [[terbium]]. The highest Verdet constants in bulk media are found in terbium-[[doping (semiconductor)|doped]] dense flint glasses or in [[crystal]]s of [[terbium gallium garnet]] (TGG). These materials have excellent [[transparency (optics)|transparency]] properties and high damage thresholds for [[laser]] radiation. Atomic vapours, however, can have Verdet constants which are orders of magnitude larger than TGG,<ref>{{Cite journal |doi=10.1038/nphoton.2009.27 |title=A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect |journal=Nature Photonics |volume=3 |issue=4 |pages=225 |year=2009 |last1=Siddons |first1=Paul |last2=Bell |first2=Nia C. |last3=Cai |first3=Yifei |last4=Adams |first4=Charles S. |last5=Hughes |first5=Ifan G. |bibcode=2009NaPho...3..225S |arxiv=0811.2316}}</ref> but only over a very narrow wavelength range. Alkali vapours can therefore be used as an [[optical isolator]]<ref>{{cite journal |doi=10.1364/OL.37.003405 |pmid=23381272 |title=Optical isolator using an atomic vapor in the hyperfine Paschen–Back regime |journal=Optics Letters |volume=37 |issue=16 |pages=3405–3407 |year=2012 |last1=Weller |first1=L. |last2=Kleinbach |first2=K. S. |last3=Zentile |first3=M. A. |last4=Knappe |first4=S. |last5=Hughes |first5=I. G. |last6=Adams |first6=C. S. |bibcode=2012OptL...37.3405W |arxiv=1206.0214 |s2cid=39307069}}</ref> 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.<ref>{{cite journal |last1=Vojna |first1=David |last2=Slezák |first2=Ondřej |last3=Yasuhara |first3=Ryo |last4=Furuse |first4=Hiroaki |last5=Lucianetti |first5=Antonio |last6=Mocek |first6=Tomáš |title=Faraday Rotation of Dy2O3, CeF3 and Y3Fe5O12 at the Mid-Infrared Wavelengths |journal=Materials |date=2020 |volume=13 |issue=23 |page=5324 |doi=10.3390/ma13235324 |pmid=33255447 |pmc=7727863 |bibcode=2020Mate...13.5324V |doi-access=free }}</ref><ref>{{cite journal |last1=Vojna |first1=David |last2=Duda |first2=Martin |last3=Yasuhara |first3=Ryo |last4=Slezák |first4=Ondřej |last5=Schlichting |first5=Wolfgang |last6=Stevens |first6=Kevin |last7=Chen |first7=Hengjun |last8=Lucianetti |first8=Antonio |last9=Mocek |first9=Tomáš |title=Verdet constant of potassium terbium fluoride crystal as a function of wavelength and temperature |journal=Opt. Lett. |date=2020 |volume=45 |issue=7 |pages=1683–1686 |doi=10.1364/ol.387911 |pmid=32235973 |bibcode=2020OptL...45.1683V |s2cid=213599420 |url=https://www.osapublishing.org/ol/fulltext.cfm?uri=ol-45-7-1683&id=429076|url-access=subscription }}</ref> At 632.8&nbsp;[[nanometre|nm]], the Verdet constant for TGG is reported to be {{val|-134|u=[[radian|rad]]/([[tesla (unit)|T]]·m)}}, whereas at 1064&nbsp;nm it falls to {{val|-40|u=rad/(T·m)}}.<ref>{{Cite web |url=http://www.northropgrumman.com/BusinessVentures/SYNOPTICS/Products/SpecialtyCrystals/Documents/pageDocs/TGG.pdf |title=Terbium Gallium Garnet – TGG |publisher=Northrop Grumman Synoptics |date=2011 |access-date=2015-02-11 |archive-date=2016-04-18 |archive-url=https://web.archive.org/web/20160418061032/http://www.northropgrumman.com/BusinessVentures/SYNOPTICS/Products/SpecialtyCrystals/Documents/pageDocs/TGG.pdf |url-status=dead }}</ref> 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 rotator]]s and [[Faraday isolator|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 laser]]s and the tunable [[vibronic laser]]s) will not see the same rotation across the whole wavelength band.