Faraday Rotation

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Faraday Rotation

• Theory, Application, and Issues
• With a neat Tangent
• Zachary Marshall

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Faraday Rotation

• First noticed in 1845 by Michael Faraday
• Linearly polarized light near resonance travels
  through a material (esp. alkali metal gas) in a
  B-Field
• The B-Field must have a component in the
  direction of propagation.
• Polarization rotates
• He wrote in his notebook, "I have at last
  succeeded in illuminating a magnetic curve or
  line of force and in magnetising a ray of light"

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Some Hand Waving

• Applied magnetic field creates Zeeman splitting
  of energy levels
• LHC and RHC polarized light see different
  scattering cross-sections, so different
  refractive indices, and so have different phase
  velocities
• Their different propagation means the linear
  polarization of light rotates

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Again, with Math

• Zeeman shift changes resonance by gFm0Bz
• Dq V B L
• Dq p (n- - n) L / l
• Dq CRb L alkali B / Dl2
• n S pi c2 ni

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Faraday Rotator / Isolator

• Optical element rotating the polarization of
  light
• Polarizer - Faraday Rotator Polarizer
• Prevents contamination and backsplash of
  electromagnetic waves
• Common materials for use in 700-1100 nm range
  terbium doped borosillicate glass and terbium
  gallium garnet crystal (TGG).
• They can be magnetized before hand.

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For Measuring Number Density

• Cell filled with a gas, at least some of which is
  an alkali metal (usually below its boiling point)
• Tunable laser (e.g. TiSaph) through the center
  of a cell

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What could possibly go wrong?

• Optical pumping during measurement
• Laser heats the cell interior
• Thermal fluctuations in a cell
• Remember What ever can go wrong, will go wrong.
  But there are ways around each problem.

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How else could we find Rb?

• Here comes the thermo

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Killian Equations

• First developed in the 1920s, credit is usually
  given to Killian (1926).
• d(ln P)/dT DH/(R T2) (Clausius-Clapeyron)
• In a small range, DH is temp. invar.
• Resulting equation is of the form
• log P A B/T
• Additional terms like C log T, D / T2 are common

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So What are A and B for Rb?
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And what did they get?
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Faraday to the Rescue?

• Claimed to be the only safe method.
• But why do we care so much?

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Pumping Nobel Gasses

• Rubidium is polarized with circularly polarized
  laser
• Collisions transfer spin to Xe / He
• Nitrogen prevents immediate spin loss
• Depolarization comes from collisions

• Rb depolarization term depends on Rb number
  density

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He-3 Lung Image
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And Some Secret Projects
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And in Space

• Faraday rotation occurs in the interstellar
  medium due to free electrons
• Dq l2 C integral of Bne ds
• If we know ne, we can determine B along the path
  to us.
• Radio waves going through the ionosphere rotate
  as well.