Azimuthal number $m$ of radiation

I am reading a paper (and a review) on superradiance phenomena, and in particular on rotational superradiance. In this review, they consider incident radiation and classify the radiation modes by frequency $omega $ and by what they call the Azimuthal number $m$. In another source they refer to these as the $m$ pole waves. However, I do not know what this means, about the wave. My understanding of the azimuthal number is from quantum mechanics and atomic orbitals and the like. That seems unrelated to this.

Does this azimuthal number $m$ have anything to do with mathematically expanding the incident wave into partial waves or something? If so, how is this done?

EDIT: For context, just thought I’d link the paper (https://arxiv.org/abs/gr-qc/9803033) and the review (https://arxiv.org/abs/1501.06570). The things I said are first mentioned in the beginning of the paper and under the sections on rotational superradiance in both the paper and the review.