Narrow-band optical filtering is required in many spectroscopy applications to suppress unwanted background light. One example is quantum communication where the fidelity is often limited by the performance of the optical filters. This limitation can be circumvented by utilizing the GHz-wide features of a Doppler broadened atomic gas. The anomalous dispersion of atomic vapours enables spectral filtering. These, so-called, Faraday anomalous dispersion optical filters (FADOFs) can be by far better than any commercial filter in terms of bandwidth, transition edge and peak transmission. We present a theoretical and experimental study on the transmission properties of a sodium vapour based FADOF with the aim to find the best combination of optical rotation and intrinsic loss. The relevant parameters, such as magnetic field, temperature, the related optical depth, and polarization state are discussed. The non-trivial interplay of these quantities defines the net performance of the filter. We determine analytically the optimal working conditions, such as transmission and the signal to background ratio and validate the results experimentally. We find a single global optimum for one specific optical path length of the filter. This can now be applied to spectroscopy, guide star applications, or sensing.
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