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

Demésy, Guillaume; Nicolet, André; Gralak, Boris; Geuzaine, Christophe; Campos, Carmen; Román, José E.

doi:10.1016/j.cpc.2020.107509

Cited by 19 publications

(12 citation statements)

References 42 publications

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“…To obtain the fields everywhere, ( 18) is inserted into the original Lippmann-Schwinger equation (12)…”

Section: Generalized Normal Mode Expansion For Spatially Varying Resonatorsmentioning

confidence: 99%

“…They can be difficult to discern from true modes, yet still need to be identified and discarded, a process that often requires manual inspection and experienced judgment. 12 These problems are particularly pronounced when searching for plasmonic modes. When high accuracy is desired, the algorithm often fails to converge altogether, precluding use of the modal approach.…”

Section: Introductionmentioning

confidence: 99%

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An efficient solver for the generalized normal modes of non-uniform open optical resonators

Chen

Sivan

Muljarov

2020

Journal of Computational Physics

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Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost instantaneously. Traditionally applied to closed systems, a simple and rigorous generalization of modal expansion to open systems using eigenpermittivity states is also available. These open modes are suitable for typical nanophotonic systems, for example. However, the numerical generation of modes is usually the most difficult and timeconsuming step of modal expansion techniques. Here, we demonstrate efficient and reliable mode generation, expanding the target modes into the modes of a simpler open system that are known. Such a re-expansion technique is implemented for resonators with non-uniform permittivity profiles, demonstrating its rapid convergence. Key to the method's success is the inclusion of a set of longitudinal basis modes.

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“…To obtain the fields everywhere, ( 18) is inserted into the original Lippmann-Schwinger equation (12)…”

Section: Generalized Normal Mode Expansion For Spatially Varying Resonatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient solver for the generalized normal modes of non-uniform open optical resonators

Chen

Sivan

Muljarov

2020

Journal of Computational Physics

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show abstract

“…To obtain the fields everywhere, ( 18) is inserted into the original Lippmann-Schwinger equation (12), this time operating Γ Ĉ on |E m , via…”

Section: Generalized Normal Mode Expansion For Spatially Varying Reso...mentioning

confidence: 99%

An efficient solver for the generalized normal modes of non-uniform open optical resonators

Chen,

Sivan,

Muljarov

2020

Preprint

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“…Our goal in SLEPc is to provide well-tested robust solvers with high performance for parallel computers that can be used from C/C++, Fortran and Python. We started the development of the NEP module in 2013, and since then it has been used in several scientific computing projects, e.g., in the simulation of photonic crystals [Demésy et al, 2020, Zolla et al, 2018, or the analysis of scattering resonances in metal-dielectric nano-structures [Araujo et al, 2020].…”

Section: Introductionmentioning

confidence: 99%

Nep

Campos

Román

2021

ACM Trans. Math. Softw.

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SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. Over the past few years, we have been developing a module within SLEPc, called NEP, that is intended for solving nonlinear eigenvalue problems. These problems can be defined by means of a matrix-valued function that depends nonlinearly on a single scalar parameter. We do not consider the particular case of polynomial eigenvalue problems (which are implemented in a different module in SLEPc) and focus here on rational eigenvalue problems and other general nonlinear eigenproblems involving square roots or any other nonlinear function. The article 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. Several test problems coming from real applications are used to evaluate the performance and reliability of the solvers.

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

Cited by 19 publications

References 42 publications

An efficient solver for the generalized normal modes of non-uniform open optical resonators

An efficient solver for the generalized normal modes of non-uniform open optical resonators

An efficient solver for the generalized normal modes of non-uniform open optical resonators

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