Position and momentum bases for the monochromatic Maxwell fish-eye and the sphere

@article{SaltoAlegre2015PositionAM,
  title={Position and momentum bases for the monochromatic Maxwell fish-eye and the sphere},
  author={Cristina Salto-Alegre and Kurt Bernardo Wolf},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2015},
  volume={48}
}
In geometric optics the Maxwell fish-eye is a medium where light rays follow circles, while in scalar wave optics this medium can only ‘trap’ fields of certain discrete frequencies. In the monochromatic case characterized by a positive integer ℓ, there are 2 ℓ + 1 ?> independent fields. We identify two bases of functions: one, known as the Sherman–Volobuyev functions, is characterized as of ‘most definite’ momenta; the other is new and composed of ‘most definite’ positions and normal… 
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