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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References

SHOWING 1-10 OF 41 REFERENCES
Hidden symmetry and potential group of the Maxwell fish-eye
The Maxwell fish‐eye is an exceptional optical system that shares with the Kepler problem and the point rotor (mass point on a sphere) a hidden, higher rotation symmetry. The Hamiltonian is
Wigner distribution function for Euclidean systems
Euclidean systems include poly- and monochromatic wide-angle optics, acoustics, and also infinite discrete data sets. We use a recently defined Wigner operator and (quasiprobability) distribution
Wigner functions for Helmholtz wave fields
We investigate a general form of the Wigner function for wave fields that satisfy the Helmholtz equation in two-dimensional free space. The momentum moment of this Wigner function is shown to
Radiometry and wide-angle wave fields. II. Coherent fields in three dimensions
The wave-based generalized radiance definitions presented in a previous manuscript [J. Opt. Soc. A18, 902 (2001)] for two-dimensional coherent monochromatic fields in free space are extended here to
Quantization of the Maxwell fish-eye problem and the quantum-classical correspondence
The so-called fish-eye model, originally investigated by Maxwell in geometrical optics, is studied both in the classical as well as in the quantum formulations. The best agreement between the two
Wigner functions for curved spaces. II. On spheres
The form of the Wigner distribution function for Hamiltonian systems in spaces of constant negative curvature (i.e., hyperboloids) proposed in M. A. Alonso, G. S. Pogosyan, and K. B. Wolf, “Wigner
The Coulomb problem and the Maxwell fish‐eye problem
The potential related to the Maxwell fish‐eye problem by optico‐mechanical analogy is derived from mechanical considerations. The dynamics of this potential is shown to be related to the dynamics of
On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator
The complete manifold of ground-state eigenfunctions for the purely magnetic two-dimensional Pauli operator is considered as a byproduct of a new reduction (found by the authors several years ago)
Supersymmetric features of the Maxwell fish-eye lens
We provide a supersymmetric analysis of the Maxwell fisheye (MF) wave problem at zero energy. Working in the so-called Ro equals 0 sector, we obtain the corresponding superpartner (fermionic) MF
Position-dependent mass oscillators and coherent states
The solution of the Schrödinger equation for a position-dependent mass quantum system is studied in two ways. First, the interaction is found which must be applied to a mass m(x) in order to supply
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