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Ambiguities in the scattering tomography for central potentials.

Awatif Hendi1, Julian Henn, Ulf Leonhardt

  • 1Science and Medical Studies, Female Section, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia.

Physical Review Letters
|October 10, 2006
PubMed
Summary

Scientists uncovered scattering ambiguities in central potentials, revealing that scattering acts as a tomographic projection. This finding could enable invisibility devices without requiring infinite phase velocity.

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Area of Science:

  • Physics
  • Optics
  • Materials Science

Background:

  • Invisibility devices leverage ambiguities in the inverse scattering problem.
  • Scattering is crucial for understanding material structures.
  • Central potentials are fundamental in physics and describe interactions.

Purpose of the Study:

  • To elucidate the nature of scattering ambiguities in central potentials.
  • To explore the relationship between scattering data and potential functions.
  • To investigate the theoretical possibility of creating invisibility devices.

Main Methods:

  • Mathematical analysis of the inverse scattering problem.
  • Characterization of scattering as a tomographic projection.
  • Investigation of multivalued scattering functions and angles.
  • Application of scattering theory to invisibility device design.

Main Results:

  • Scattering is shown to be a tomographic projection of a scattering function onto the impact parameter.
  • Multivalued scattering functions can lead to ambiguities, where different potentials yield identical scattering data.
  • Multivalued scattering angles also contribute to these ambiguities.
  • The theory demonstrates the potential for constructing invisibility devices without infinite phase velocity.

Conclusions:

  • Scattering ambiguities in central potentials are well-defined and linked to tomographic projections.
  • Understanding these ambiguities is key to advancing invisibility technology.
  • It is theoretically possible to achieve invisibility without violating fundamental physics principles like finite phase velocity.