Boundary element method for resonances in dielectric microcavities

@article{Wiersig2002BoundaryEM,
  title={Boundary element method for resonances in dielectric microcavities},
  author={Jan Wiersig},
  journal={Journal of Optics},
  year={2002},
  volume={5},
  pages={53-60}
}
  • J. Wiersig
  • Published 7 June 2002
  • Physics
  • Journal of Optics
A boundary element method based on a Green function technique is introduced to compute resonances with intermediate lifetimes in quasi-two-dimensional dielectric cavities. It can be applied to single or several optical resonators of arbitrary shape, including corners, for both TM and TE polarization. For cavities with symmetries a symmetry reduction is described. The existence of spurious solutions is discussed. The efficiency of the method is demonstrated by calculating resonances in two… 

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References

SHOWING 1-10 OF 45 REFERENCES

High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners

For part I see ibid., p. 1210, 2002. We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a

Resonance line shapes in quasi-one-dimensional scattering.

that cause this phenomenon are identified in this paper using first a coupled-channel theory that starts from the full scattering Hamiltonian, and secondly a more general S-matrix approach. The

Light Scattering by Particles: Computational Methods

This book presents the separation-of-variables and T-matrix methods of calculating the scattering of electromagnetic waves by particles, and the connection between the theory and the computer programs is reinforced by references in thecomputer programs to equations in the text.

The Rayleigh hypothesis in the theory of diffraction by a cylindrical obstacle

The Rayleigh hypothesis in the theory of scattering by a cylindrical obstacle of arbitrary cross section is investigated analytically. The hypothesis asserts that outside and on the obstacle the

Ray and wave chaos in asymmetric resonant optical cavities

OPTICAL resonators are essential components of lasers and other optical devices. A resonator is characterized by a set of modes, each with a resonant frequency ω and resonance width δω= 1/τ, where τ

Boundary element methods

This book has been written as a self-contained reference, combining both the mathematical rigor necessary for a full understanding of BEM, and extensive examples of applications and illustrations.

The application of integral equation methods to the numerical solution of some exterior boundary-value problems

  • A. J. BurtonG. F. Miller
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1971
The application of integral equation methods to exterior boundary-value problems for Laplace’s equation and for the Helmholtz (or reduced wave) equation is discussed. In the latter case the

Multimode resonances in square-shaped optical microcavities.

Square-shaped two-dimensional optical microc Cavities (micro-cavities) were investigated for possible applications as filters for dense wavelength-division multiplexing and accounted for the multimode spectrum by different normal modes with rays confined by total internal reflection.

Signature of dynamical localization in the resonance width distribution of wave-chaotic dielectric cavities

It is shown that dynamical localization leads to a log-normal distribution of the resonance widths which scales with the localization length in excellent agreement with the results of numerical calculations for open rough microcavities.

Boundary integral method for stationary states of two-dimensional quantum systems

The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method,