8/19/2019 Zach Marshall Faraday Rotation

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Faraday RotationFaraday Rotation

Theory, Application, and IssuesTheory, Application, and Issues

With a neat TangentWith a neat Tangent

Zachary MarshallZachary Marshall

8/19/2019 Zach Marshall Faraday Rotation

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Faraday RotationFaraday Rotation

First noticed in 1845 by Michael FaradayFirst noticed in 1845 by Michael Faraday

inearly polari!ed light near resonanceinearly polari!ed light near resonance

tra"els through a #aterial $esp% al&alitra"els through a #aterial $esp% al&ali

#etal gas' in a ()Field#etal gas' in a ()Field

The ()Field #ust ha"e a co#ponent inThe ()Field #ust ha"e a co#ponent in

the direction o* propagation%the direction o* propagation%

+olari!ation rotates+olari!ation rotates

e -rote in his noteboo&, .I ha"e at laste -rote in his noteboo&, .I ha"e at lastsucceeded insucceeded in illuminating a magneticilluminating a magnetic

curvecurve oror line of forceline of force and inand in magnetisingmagnetising

a ray of light a ray of light ..

8/19/2019 Zach Marshall Faraday Rotation

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/o#e and Wa"ing/o#e and Wa"ing

Applied magnetic field creates ZeemanApplied magnetic field creates Zeeman

splitting of energy levelssplitting of energy levels

LHC and RHC polarized light see differentLHC and RHC polarized light see differentscattering cross-sections, so different refractivescattering cross-sections, so different refractive

indices, and so have different phase velocitiesindices, and so have different phase velocities

Their different propagation means the linearTheir different propagation means the linear

 polarization of light rotates polarization of light rotates

8/19/2019 Zach Marshall Faraday Rotation

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 Again, -ith Math Again, -ith Math

Zeeman shift changes resonance by gZeeman shift changes resonance by gFFµµ!!zz∆θ =∆θ = " ! L" ! L

∆θ = π (∆θ = π (nn-- - n- n##$ L %$ L % λλ∆θ∆θ 0 0 RbRb  2al&ali3 ( 2al&ali3 ( ∆λ∆λ55

n 0n 0 ΣΣ ppii cc55 nnii

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Faraday Rotator Isolator Faraday Rotator Isolator 

&ptical element rotating the polarization of&ptical element rotating the polarization oflightlight

'olarizer - Faraday Rotator ( 'olarizer 'olarizer - Faraday Rotator ( 'olarizer 

'revents contamination and )bac*splash+ of'revents contamination and )bac*splash+ ofelectromagnetic aveselectromagnetic aves

Common materials for se in .-// nmCommon materials for se in .-// nm

range0 terbim doped borosillicate glass andrange0 terbim doped borosillicate glass andterbim gallim garnet crystal 1T22$3terbim gallim garnet crystal 1T22$3

They can be magnetized before hand3They can be magnetized before hand3

8/19/2019 Zach Marshall Faraday Rotation

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For Measuring 6u#ber 7ensityFor Measuring 6u#ber 7ensity

ell *illed -ith a gas, at least so#e o* -hich isell *illed -ith a gas, at least so#e o* -hich is

an al&ali #etal $usually belo- its boiling point'an al&ali #etal $usually belo- its boiling point'

Tunable laser $e%g% Ti/aph' through the centerTunable laser $e%g% Ti/aph' through the center

o* a cello* a cell

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What could possibly go -rong9What could possibly go -rong9

:ptical pu#ping during #easure#ent:ptical pu#ping during #easure#ent

aser heats the cell interior aser heats the cell interior 

Ther#al *luctuations in a cellTher#al *luctuations in a cell

Re#e#ber What e"er can go -rong,Re#e#ber What e"er can go -rong, will will  go -rong% (ut there are -ays aroundgo -rong% (ut there are -ays around

each proble#%each proble#%

8/19/2019 Zach Marshall Faraday Rotation

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o- else could -e *indo- else could -e *ind

2Rb392Rb39ere co#es the ther#o;ere co#es the ther#o;

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uationsuations

First developed in the /456s, credit is sallyFirst developed in the /456s, credit is sally

given to 7illian 1/458$3given to 7illian 1/458$3

d1ln '$%dT 9d1ln '$%dT 9 ∆∆H%1R TH%1R T55

$ 1Clasis-Clapeyron$$ 1Clasis-Clapeyron$ :n a small range,:n a small range, ∆∆H is temp3 invar3H is temp3 invar3

Reslting e;ation is of the formReslting e;ation is of the form

log ' 9 A # !%Tlog ' 9 A # !%TAdditional terms li*e C log T, < % TAdditional terms li*e C log T, < % T55 areare

commoncommon

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/o What are A and ( *or Rb9/o What are A and ( *or Rb9

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 And -hat did they get9 And -hat did they get9

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Faraday to the Rescue9Faraday to the Rescue9

lai#ed to be the ?only sa*e #ethod%@lai#ed to be the ?only sa*e #ethod%@

(ut -hy do -e care so #uch9(ut -hy do -e care so #uch9

8/19/2019 Zach Marshall Faraday Rotation

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+u#ping 6obel asses+u#ping 6obel asses

Rubidiu# is polari!ed -ith circularly polari!edRubidiu# is polari!ed -ith circularly polari!ed

laser laser 

ollisions trans*er spin to Be eollisions trans*er spin to Be e

6itrogen pre"ents i##ediate spin loss6itrogen pre"ents i##ediate spin loss

7epolari!ation co#es *ro# collisions7epolari!ation co#es *ro# collisions Rb depolari!ation ter#Rb depolari!ation ter#

depends on Rb nu#berdepends on Rb nu#berdensitydensity

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e)C ung I#agee)C ung I#age

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 And /o#e /ecret +roDects; And /o#e /ecret +roDects;

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 And in /pace And in /pace

Faraday rotation occurs in the interstellarFaraday rotation occurs in the interstellar

#ediu# due to *ree electrons#ediu# due to *ree electrons

∆θ∆θ

 00

λλ55

E integral o* (En E integral o* (Enee

 dsds

I* -e &no- nI* -e &no- nee, -e can deter#ine ( along, -e can deter#ine ( along

the path to us%the path to us%

Radio -a"es going through theRadio -a"es going through the

ionosphere rotate as -ell%ionosphere rotate as -ell%