Photonics in highly dispersive media: the exact modal expansion.

@article{Zolla2018PhotonicsIH,
  title={Photonics in highly dispersive media: the exact modal expansion.},
  author={Fr{\'e}d{\'e}ric Zolla and A. Nicolet and Guillaume Dem{\'e}sy},
  journal={Optics letters},
  year={2018},
  volume={43 23},
  pages={
          5813-5816
        }
}
We present exact modal expansions for photonic systems including highly dispersive media. The formulas, based on a simple version of the Keldyš theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly nonreciprocal. A simple dispersive test case where both plasmonic and geometrical resonances strongly interact exemplifies the numerical efficiency of our approach. 

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References

SHOWING 1-10 OF 35 REFERENCES
Eigenmode computations of frequency-dispersive photonic open structures: A non-linear eigenvalue problem
TLDR
A classical finite element formulation is derived for each proposed solution, which leads to a non-linear eigenvalue problem solved using recent adapted algorithms.
Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure.
We present a semi-analytical formalism capable of handling the coupling of electromagnetic sources, such as point dipoles or free-propagating fields, with various kinds of dissipative resonances with
Calculation and analysis of the complex band structure of dispersive and dissipative two-dimensional photonic crystals
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell’s equations where
Resonant-state expansion of dispersive open optical systems: Creating gold from sand
A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the permittivity is presented. The RSE of dispersive systems converts Maxwell's wave equation into a
Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators.
TLDR
A self-consistent electromagnetic theory of the coupling between dipole emitters and dissipative nanoresonators that predicts that a spectral detuning between the emitter and the resonance does not necessarily result in a Lorentzian response in the presence of dissipation.
Quasimodal expansion of electromagnetic fields in open two-dimensional structures
A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which
Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line.
TLDR
This Letter describes a very general procedure to obtain a causal fit of the permittivity of materials from experimental data with very few parameters and its independence on the material or frequency range at stake.
...
...