Quantitative optical spectroscopy of ${}^{87}$Rb vapour in the Voigt geometry in DC magnetic fields up to 0.4T

We present a detailed spectroscopic investigation of a thermal ${}^{87}$Rb atomic vapour in magnetic fields up to 0.4T in the Voigt geometry. We fit experimental spectra with our theoretical model $\mathit{\text{ElecSus}}$ and find excellent quantitative agreement, with RMS errors of $\sim 0.3$%. We extract the magnetic field strength and the angle between the polarisation of the light and the magnetic field from the atomic signal and find excellent agreement to within $\sim 1$% with a commercial Hall probe. Finally, we present an investigation of the relative sensitivity of this technique to variations in the field strength and angle with a view to enabling atom-based high-field vector magnetometry.