Self-similarity of optical rotation trajectories around the Poincare sphere with application to an ultra-narrow atomic bandpass filter

We present an investigation of magneto-optic rotation in both the Faraday and Voigt geometries. We show that more physical insight can be gained in a comparison of the Faraday and Voigt effects by visualising optical rotation trajectories on the Poincare sphere. This insight is applied to design and experimentally demonstrate an improved ultra-narrow optical bandpass filter based on combining optical rotation from two cascaded cells - one in the Faraday geometry and one in the Voigt geometry. Our optical filter has an equivalent noise bandwidth of 0.56 GHz, and a figure-of-merit value of 1.22(2) GHz${}^{-1}$ which is higher than any previously demonstrated filter on the Rb D2 line.