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Faraday Rotation

Faraday Rotation. Theory, Application, and Issues With a neat Tangent Zachary Marshall. 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

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Faraday Rotation

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  1. Faraday Rotation Theory, Application, and Issues With a neat Tangent Zachary Marshall

  2. 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"

  3. 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

  4. 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

  5. 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.

  6. 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. Ti:Saph) through the center of a cell

  7. 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.

  8. How else could we find [Rb]? Here comes the thermo…

  9. Killian Equations • First developed in the 1920’s, 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

  10. So What are A and B for Rb?

  11. And what did they get?

  12. Faraday to the Rescue? • Claimed to be the “only safe method.” • But why do we care so much?

  13. 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

  14. He-3 Lung Image

  15. And Some Secret Projects…

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

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