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Trace formula for dielectric cavities. III. TE modes.

E Bogomolny1, R Dubertrand

  • 1Université Paris Sud, CNRS, LPTMS, UMR 8656, Orsay F-91405, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

This study details a semiclassical trace formula for transverse electric resonances in 2D dielectric cavities. The derived formulas accurately predict the average number of resonances, matching numerical results across various cavity shapes.

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Area of Science:

  • Physics
  • Optics
  • Mathematical Physics

Background:

  • Dielectric cavities are crucial in photonic devices.
  • Understanding resonance properties is key for device design.
  • Semiclassical methods offer approximations for complex systems.

Purpose of the Study:

  • To construct a semiclassical trace formula for transverse electric resonances in 2D dielectric cavities.
  • To derive the leading terms of Weyl's series for the average number of resonances.
  • To validate the derived formulas against numerical simulations.

Main Methods:

  • Development of a semiclassical trace formula.
  • Derivation of the first two terms of Weyl's series expansion.
  • Numerical calculations for dielectric cavities of varying geometries.

Main Results:

  • A novel semiclassical trace formula for transverse electric polarization was established.
  • The first two terms of Weyl's series for average resonance number were successfully derived.
  • The theoretical formulas demonstrated excellent agreement with numerical computations.

Conclusions:

  • The developed semiclassical trace formula provides an accurate method for analyzing resonances in 2D dielectric cavities.
  • The derived Weyl's series terms are reliable predictors of resonance density.
  • This work validates the utility of semiclassical approaches in understanding dielectric cavity behavior.