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Optical Thomas-Reiche-Kuhn sum rules.

Stephen M Barnett1, Rodney Loudon

  • 1Department of Physics, Unniversity of Strathclyde, Glasgow G4 0NG, United Kingdom.

Physical Review Letters
|February 7, 2012
PubMed
Summary
This summary is machine-generated.

The Thomas-Reiche-Kuhn sum rule for atomic electrons has an analogy in magnetodielectric media. Four new sum rules constrain polariton velocities, showing negative refractive index metamaterials cannot confine all modes to the negative-index region.

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Area of Science:

  • Physics
  • Electromagnetism
  • Materials Science

Background:

  • The Thomas-Reiche-Kuhn sum rule, derived from quantum mechanics, constrains atomic electron transitions.
  • Electromagnetic field operators in magnetodielectric media are subject to commutation relations.

Purpose of the Study:

  • To establish analogous sum rules for electromagnetic fields in magnetodielectric media.
  • To investigate the implications of these sum rules for polariton dispersion relations and metamaterials.

Main Methods:

  • Extension of the Thomas-Reiche-Kuhn sum rule concept to electromagnetic field operators.
  • Derivation of four sum rules governing phase and group velocities of polaritons.
  • Analysis of these sum rules in the context of bulk media and negative refractive index metamaterials.

Main Results:

  • Four sum rules were derived for polariton phase and group velocities in magnetodielectric media.
  • These sum rules are applicable to all bulk media, including metamaterials.
  • It is impossible to create a medium where all polariton modes for a given wavelength exhibit a negative refractive index.

Conclusions:

  • The derived sum rules provide fundamental constraints on electromagnetic wave propagation in magnetodielectric media.
  • These findings have significant implications for the design and limitations of metamaterials.
  • The inherent constraints prevent the realization of materials with universally negative refractive indices for all polariton modes at a given wavelength.