A Lanczos model-order reduction technique to efficiently simulate electromagnetic wave propagation in dispersive media

Zimmerling, Jörn; Wei, Lei; Urbach, Paul; Remis, Rob

doi:10.1016/j.jcp.2016.03.057

Cited by 21 publications

(26 citation statements)

References 23 publications

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“…A general approach consists in transforming the nonlinear eigenvalue problem into a linear one by introducing auxiliary fields to account for material dispersion. Several variants exist and, for the sake of simplicity, we limit ourselves to a generic presentation of auxiliary‐field techniques . The latter have been initially used in the time‐domain for modeling wave propagation in dispersive media and then in the frequency domain for computing band diagrams of dispersive photonic crystals …”

Section: Overview Of Qnm Solversmentioning

confidence: 99%

“…Note that the Drude model, a particular case for which

ω_{0} = 0

, requires a single auxiliary‐field,

{bold-italic \overset{J}{true}}_{m}

. QNM eigensolvers based on auxiliary‐field method have been initially implemented with finite‐difference methods . The latter may introduce inaccuracies for complex geometries, which may lead to the prediction of spurious modes when discretizing curved metallic surfaces on a rectangular grid for instance.…”

Section: Overview Of Qnm Solversmentioning

confidence: 99%

“…QNMs of PML‐truncated spaces have been first computed with the pole‐search approach. Virtually any frequency‐domain method may be used, such as the finite‐element method (FEM), the finite‐difference method, the Fourier modal method …”

Section: Overview Of Qnm Solversmentioning

confidence: 99%

See 2 more Smart Citations

Light Interaction with Photonic and Plasmonic Resonances

Lalanne

Yan

Vynck

et al. 2018

Laser & Photonics Reviews

489

585

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In this Review, the theory and applications of optical micro-and nano-resonators are presented from the underlying concept of their natural resonances, the so-called quasi-normal modes (QNMs). QNMs are the basic constituents governing the response of resonators. Characterized by complex frequencies, QNMs are initially loaded by a driving field and then decay exponentially in time due to power leakage or absorption. Here, the use of QNM-expansion formalisms to model these basic effects is explored. Such modal expansions that operate at complex frequencies distinguish from the current user habits in electromagnetic modeling, which rely on classical Maxwell's equation solvers operating at real frequencies or in the time domain; they also bring much deeper physical insight into the analysis. An extensive overview of the historical background on QNMs in electromagnetism and a detailed discussion of recent relevant theoretical and numerical advances are therefore presented. Additionally, a concise description of the role of QNMs on a number of examples involving electromagnetic resonant fields and matter, including the interaction between quantum emitters and resonators (Purcell effect, weak and strong coupling, superradiance, . . . ), Fano interferences, the perturbation of resonance modes, and light transport and localization in disordered media is provided. (3 of 38)www.advancedsciencenews.com www.lpr-journal.org Figure 2. Examples of applications whose analysis benefit from QNM-expansion approaches. a) Nonlocal plasmonics. QNMs can be used to predict the nonlocal response of free electron gas on the Purcell factor of an emitter placed in the near-field of a gold nanorod. Predictions from two different nonlocal models-the hydrodynamic Drude model (HDM) and the generalized nonlocal optical response (GNOR) Model-are shown and compared to classical predictions obtained with a Drude model. The inset shows the electric field intensity of the nonlocal GNOR QNM. Adapted with permission. [53] Copyright 2017, Optical Society of America. b) QNM expansion of the scattering matrix. (Upper panel) Absorption cross section of a multi-layered metallic-dielectric sphere in air, demonstrating the good agreement between the results obtained with Mie's scattering theory (dashed black curve) and a QNM-expansion formalism for the scattering matrix (solid red curve) computed with the QNM eigenfrequencies shown in the Lower panel. Reproduced with permission. [40] Copyright 2017, American Physical Society. c) Quantum hybrids. Supperradiant and subradiant decay rates m and energies m of a quantum hybrid formed by 100 molecules that are randomly distributed and oriented around a silver nanorod (diameter 30 nm, length 100 nm), predicted with the QNM formalism. γ 0 denotes the decay rate of every individual molecule in the vacuum. The left inset shows the superradiant state of the hybrid, with a large cooperativity involving more than one half of the molecules. Reproduced with permission. [28] Copyright 2017, American Physical Society. d) Quant...

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Section: Overview Of Qnm Solversmentioning

confidence: 99%

“…Note that the Drude model, a particular case for which

ω_{0} = 0

, requires a single auxiliary‐field,

{bold-italic \overset{J}{true}}_{m}

Section: Overview Of Qnm Solversmentioning

confidence: 99%

See 1 more Smart Citation

Light Interaction with Photonic and Plasmonic Resonances

Lalanne

Yan

Vynck

et al. 2018

Laser & Photonics Reviews

489

585

View full text Add to dashboard Cite

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“…(8) is not feasible, however, since the order of the system matrix A is simply too large. Fortunately, it can be shown that the system matrix satisfies the symmetry relation hAx; yi ¼ hx; Ayi for all x; y 2 C n ; ð11Þ where hÁ; Ái is a bilinear form given by hx; yi ¼ y T WMx with WM complex-symmetric and W a step size matrix containing the step sizes of the computational grid (see [7]). This property allows us to carry out a Lanczos-type reduction algorithm [7,8] …”

Section: Krylov Model-order Reductionmentioning

confidence: 99%

Efficient computation of the spontaneous decay rate of arbitrarily shaped 3D nanosized resonators: a Krylov model-order reduction approach

et al. 2016

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We present a Krylov model-order reduction approach to efficiently compute the spontaneous decay (SD) rate of arbitrarily shaped 3D nanosized resonators. We exploit the symmetry of Maxwell's equations to efficiently construct so-called reduced-order models that approximate the SD rate of a quantum emitter embedded in a resonating nanostructure. The models allow for frequency sweeps, meaning that a single model provides SD rate approximations over an entire spectral interval of interest. Field approximations and dominant quasinormal modes can be determined at low cost as well.

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“…MOR method is useful for accelerating simulations in many fields of science and engineering [16,17,18,19,20,21,22]. In particular, MOR method is also widely used in the context of electromagnetics [19,23,24,25,26,27,28,29,30,31,32]. The overall goal of MOR can be stated as to reduce the computational requirements while maintaining an acceptable level of accuracy.…”

Section: Introductionmentioning

confidence: 99%

POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations

Huang

et al. 2019

Journal of Computational Physics

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A Lanczos model-order reduction technique to efficiently simulate electromagnetic wave propagation in dispersive media

Cited by 21 publications

References 23 publications

Light Interaction with Photonic and Plasmonic Resonances

Light Interaction with Photonic and Plasmonic Resonances

Efficient computation of the spontaneous decay rate of arbitrarily shaped 3D nanosized resonators: a Krylov model-order reduction approach

POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations

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