Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures

@article{Demesy2020NonlinearEP,
  title={Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures},
  author={Guillaume Dem'esy and A. Nicolet and Boris Gralak and Christophe Geuzaine and Carmen Campos and Jos{\'e} E. Rom{\'a}n},
  journal={Comput. Phys. Commun.},
  year={2020},
  volume={257},
  pages={107509}
}

Figures and Tables from this paper

Quasinormal mode solvers for resonators with dispersive materials.
  • P. Lalanne, W. Yan, T. Weiss
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2019
TLDR
This work benchmarks several methods for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials, and compares them to elaborate standards for the computation of resonance modes.
Theory and numerical modeling of photonic resonances: Quasinormal Modal Expansion -- Applications in Electromagnetics
The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the
Continuous family of exact Dispersive Quasi-Normal Modal (DQNM) expansions for dispersive photonic structures.
TLDR
The non-uniqueness of the expansions related to the over-completeness of the set of modes is emphasized and a family of DQNM expansions depending on continuous parameters that can be freely chosen are discussed.
NEP: a module for the parallel solution of nonlinear eigenvalue problems in SLEPc
TLDR
The paper discusses how the NEP module has been designed to fit the needs of applications and provides a description of the available solvers, including some implementation details such as parallelization.
Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited].
The scattering of electromagnetic waves by resonant systems is determined by the excitation of the quasinormal modes (QNMs), i.e. the eigenmodes, of the system. This Review addresses three
Generalised normal mode expansion method for 1 open and lossy periodic structures 2
We describe and demonstrate the extension of permittivity mode expansion (aka 9 generalized normal mode expansion, GENOME) to open and lossy periodic structures. The 10 resulting expansion gives a
Negative index materials: at the frontier of macroscopic electromagnetism
The notions of negative refraction and negative index, introduced by V. Veselago more than 50 years ago, have appeared beyond the frontiers of macroscopic electromagnetism and purely formal during 30
Photonics in highly dispersive media: the exact modal expansion.
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
...
...

References

SHOWING 1-10 OF 57 REFERENCES
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
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
Computational Electrodynamics the Finite-Difference Time-Domain Method
TLDR
This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
Quasinormal mode solvers for resonators with dispersive materials.
  • P. Lalanne, W. Yan, T. Weiss
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2019
TLDR
This work benchmarks several methods for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials, and compares them to elaborate standards for the computation of resonance modes.
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has
Resonant dynamics of arbitrarily shaped meta-atoms
Meta-atoms, nano-antennas, plasmonic particles and other small scatterers are commonly modeled in terms of their modes. However these modal solutions are seldom determined explicitly, due to the
NEP: a module for the parallel solution of nonlinear eigenvalue problems in SLEPc
TLDR
The paper discusses how the NEP module has been designed to fit the needs of applications and provides a description of the available solvers, including some implementation details such as parallelization.
Some mathematical properties of Maxwell's equations for macroscopic dielectrics
  • A. Tip
  • Physics, Mathematics
  • 2006
We consider a number of mathematical properties of Maxwell’s equations for linear dispersive and absorptive dielectric media using the auxiliary field method developed earlier by the author [A. Tip,
Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc
TLDR
This work focuses on Krylov methods that operate on the companion linearization of the polynomial but exploit the block structure with the aim of being memory-efficient in the representation of the Krylov subspace basis.
...
...