Derivation of the Resonant Faraday Effect

The phenomenon of Faraday rotations is when the polarization of linearly polarized light rotates as it passes through a circularly birefringent medium, often an alkali vapor. Precision data were recently taken at the University of Kentucky, and it is essential to be able to describe these data with a theoretical prediction. The purpose of this project is to derive an equation for the Faraday rotation angle that holds near the resonance frequencies of the potassium D1 and D2 transitions. The calculation was performed semi-classically, using tools from Quantum Mechanics to derive quantities that were then substituted into classical expressions such as those describing optical rotation. This project resulted in both a cataloged derivation and an expression for the Faraday rotation angle in terms of relevant parameters with a functional form that can fit the data. It makes no assumptions about proximity to resonance and accounts for the Zeeman effect, hyperfine effect, and Doppler broadening. In conclusion, this project provides a model to interpret the uniquely precise near-Resonance Faraday rotation angle data.