This thesis presents both a computational and experimental investigation into light propagation in hot alkali-metal vapours, with a particular focus on utilizing the Faraday effect for practical applications. A model to calculate various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field is presented. A computer program (ElecSus) was developed which implements this model efficiently. Using ElecSus we design optical devices such as Faraday filters and laser frequency stabilizing references. The design of Faraday filters utilizing compact vapour cells is shown, along with excellent agreement with experiment. The importance of including the effect of self broadening in the model is shown for these short path length vapour cells. Also, a Faraday filter is presented that can potentially be used for quantum optics experiments on the caesium D
1 line (894~nm). The filter displays the highest ratio of transmission to equivalent noise bandwidth to date for a linear Faraday filter, demonstrating the power of computerized optimization for this application. Furthermore, a Faraday filter is presented for use as an intra-cavity element in an external-cavity diode laser. A proof-of-principle experiment is demonstrated which shows that using a short external cavity with the Faraday filter eliminates mode-hops. Experimentally and theoretically the Faraday effect is investigated in large magnetic fields where alkali-metal atoms enter the hyperfine Paschen-Back regime. This hyperfine Paschen-Back Faraday effect is shown to allow a direct measure of the refractive indices for left and right circular polarized light. Furthermore, fitting the weak-probe spectra using ElecSus is found to give measures of the magnetic field with a fractional precision of the order of
10−4. In addition we study slow-light pulse propagation in a high density rubidium vapour, showing that our theoretical model for the electric susceptibility is valid for short pulses as well as continuous-wave light. This shows that the model is accurate for predicting weak-probe pulse propagation.
We propose a far off-resonance laser frequency stabilization method that can accurately adjust the frequency lock points based on the Faraday rotation spectroscopy. The atomic magnetometer based on the spin-exchange relaxation-free (SERF) theory needs to stabilize the frequency of the probe laser on the detuning of several gigahertz (GHz) away from the resonance of the alkali metal atom, to reduce the absorption of the probe light by the alkali metal vapor cell. We propose a laser frequency stabilization method that can accurately adjust the frequency lock points using an acousto-optic modulator based on Faraday rotation spectroscopy. We reveal the principles of the method and simulate the new Faraday rotation spectra. Besides, we study the effect of the amount of frequency shift of the acousto - optic modulator and the temperature of the alkali metal vapor cell on the frequency lock points of the spectra, and give the formula for calculating the frequency point. Our proposed laser frequency stabilization method can stabilize the laser frequency on the detuning of several gigahertz (GHz) away from the resonance of the alkali metal atom and can adjust the frequency lock points quickly and accurately. This method can be used in atomic magnetometer, degenerate Raman sideband cooling (DRSC) and two photon excitation of Rydberg states.