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},
  year={2015},
  volume={48},
  pages={195202}
}
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 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 derivatives for the… 
View via Publisher
fis.unam.mx
1 Citations

Figures from this paper

One Citation

Citation Type

Citation Type

$SU(2)$ -particle sigma model: momentum-space quantization of a particle on the sphere S 3
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based…

References

SHOWING 1-10 OF 38 REFERENCES
Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space.
  • M. Alonso
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2004
TLDR
For partially coherent fields, the ray-based approach provided by the new representations can reduce dramatically the computation times for the physical properties mentioned earlier.
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…
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…
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…
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 III: partial coherence.
  • M. Alonso
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2001
TLDR
The analogs of the generalized radiances introduced in two previous manuscripts for fully coherent fields in two- and three-dimensional free space are given here for the case of partial coherence, suitable for the description of fields with components propagating in any direction.
Measurement of Helmholtz wave fields
  • Alonso
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2000
TLDR
A simple formalism is found for the measurement of wave fields that satisfy the Helmholtz equation in free space and corresponds to the squared magnitude of the inner product of the wave field and a field that is associated with the detector.
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…
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…
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…
...
...