Faraday RotationFaraday Rotation

Theory, Application, and IssuesTheory, Application, and IssuesWith a neat TangentWith a neat Tangent

Zachary MarshallZachary Marshall

Faraday RotationFaraday Rotation

First noticed in 1845 by Michael FaradayFirst noticed in 1845 by Michael Faraday Linearly polarized light near resonance Linearly polarized light near resonance

travels through a material (esp. alkali travels through a material (esp. alkali metal gas) in a B-Field metal gas) in a B-Field

The B-Field must have a component in The B-Field must have a component in the direction of propagation.the direction of propagation.

Polarization rotatesPolarization rotates He wrote in his notebook, "I have at last He wrote in his notebook, "I have at last

succeeded in succeeded in illuminating a magnetic illuminating a magnetic curvecurve or or line of forceline of force and in and in magnetising magnetising a ray of lighta ray of light" "

Some Hand WavingSome Hand Waving

Applied magnetic field creates Zeeman Applied magnetic field creates Zeeman splitting of energy levelssplitting of energy levels

LHC and RHC polarized light see different LHC and RHC polarized light see different scattering cross-sections, so different scattering cross-sections, so different refractive indices, and so have different phase refractive indices, and so have different phase velocitiesvelocities

Their different propagation means the linear Their different propagation means the linear polarization of light rotatespolarization of light rotates

Again, with MathAgain, with Math

Zeeman shift changes resonance by gZeeman shift changes resonance by gFF00BBzz

V B LV B Lnn-- - n - n++) L / ) L / = C= CRbRb L [alkali] B / L [alkali] B / 22

n = n = p pii c c22 n nii

Faraday Rotator / IsolatorFaraday Rotator / Isolator

Optical element rotating the polarization of Optical element rotating the polarization of lightlight

Polarizer - Faraday Rotator – PolarizerPolarizer - Faraday Rotator – Polarizer Prevents contamination and “backsplash” of Prevents contamination and “backsplash” of

electromagnetic waveselectromagnetic waves Common materials for use in 700-1100 nm Common materials for use in 700-1100 nm

range: terbium doped borosillicate glass and range: terbium doped borosillicate glass and terbium gallium garnet crystal (TGG). terbium gallium garnet crystal (TGG).

They can be magnetized before hand.They can be magnetized before hand.

For Measuring Number DensityFor Measuring Number Density

Cell filled with a gas, at least some of which is Cell filled with a gas, at least some of which is an alkali metal (usually below its boiling point)an alkali metal (usually below its boiling point)

Tunable laser (e.g. Ti:Saph) through the center Tunable laser (e.g. Ti:Saph) through the center of a cellof a cell

What could possibly go wrong?What could possibly go wrong?

Optical pumping during measurementOptical pumping during measurementLaser heats the cell interiorLaser heats the cell interior

Thermal fluctuations in a cellThermal fluctuations in a cell

Remember: What ever can go wrong, Remember: What ever can go wrong, willwill go wrong. But there are ways around go wrong. But there are ways around each problem.each problem.

How else could we find How else could we find [Rb]?[Rb]?

Here comes the thermo…Here comes the thermo…

Killian EquationsKillian Equations

First developed in the 1920’s, credit is usually First developed in the 1920’s, credit is usually given to Killian (1926). given to Killian (1926).

d(ln P)/dT = d(ln P)/dT = H/(R TH/(R T22) (Clausius-Clapeyron)) (Clausius-Clapeyron) In a small range, In a small range, H is temp. invar.H is temp. invar. Resulting equation is of the form Resulting equation is of the form

log P = A + B/Tlog P = A + B/T Additional terms like C log T, D / TAdditional terms like C log T, D / T22 are are

commoncommon

So What are A and B for Rb?So What are A and B for Rb?

And what did they get?And what did they get?

Faraday to the Rescue?Faraday to the Rescue?

Claimed to be the “only safe method.”Claimed to be the “only safe method.”

But why do we care so much?But why do we care so much?

Pumping Nobel GassesPumping Nobel Gasses

Rubidium is polarized with circularly polarized Rubidium is polarized with circularly polarized laserlaser

Collisions transfer spin to Xe / HeCollisions transfer spin to Xe / He Nitrogen prevents immediate spin lossNitrogen prevents immediate spin loss Depolarization comes from collisionsDepolarization comes from collisions Rb depolarization term Rb depolarization term depends on Rb number depends on Rb number densitydensity

He-3 Lung ImageHe-3 Lung Image

And Some Secret Projects…And Some Secret Projects…

And in SpaceAnd in Space

Faraday rotation occurs in the interstellar Faraday rotation occurs in the interstellar medium due to free electronsmedium due to free electrons

= = 2 2 C * integral of B*nC * integral of B*nee ds ds

If we know nIf we know nee, we can determine B along , we can determine B along

the path to us.the path to us.

Radio waves going through the Radio waves going through the ionosphere rotate as well.ionosphere rotate as well.