Aperiodic Fourier modal method in contrast-field formulation for simulation of scattering from finite structures

Pisarenco, Maxim; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.

doi:10.1364/josaa.27.002423

Cited by 32 publications

(44 citation statements)

References 28 publications

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“…To explore the convergence we increase the number of harmonics N g (see Ref. [8], where N g = 2N + 1) and simultaneously increase the thickness h PML /2 of the PML and h air according to h PML = h air = a 2 log N g .…”

Section: Discussionmentioning

confidence: 99%

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Resonant-state expansion of light propagation in nonuniform waveguides

et al. 2017

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A new rigorous approach for precise and efficient calculation of light propagation along nonuniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoingwave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

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Section: Discussionmentioning

confidence: 99%

“…One popular approach is the aperiodic Fourier modal method (a-FMM) [5][6][7][8], a generalization of the standard FMM [9][10][11], which allows to treat an open WG by introducing an artificial periodicity and a perfectly matched layer (PML) [6,12].…”

Section: Introductionmentioning

confidence: 99%

Resonant-state expansion of light propagation in nonuniform waveguides

et al. 2017

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“…As explained in (Pisarenco et al, 2010), the compact support condition is required in order to avoid non-zero source terms in the PML. Typically ϵ b represents the permittivity of the background multilayer which supports the scatterer.…”

Section: Perfectly Matched Layers and The Maxwell Equations For The Cmentioning

confidence: 99%

“…The AFMM-CFF (Pisarenco et al, 2010(Pisarenco et al, , 2011) is a recent extension of the FMM to aperiodic structures. It builds upon the aperiodic Fourier modal method developed and refined by Lalanne and co-workers (Lalanne and Silberstein, 2000;Silberstein et al, 2001;Cao et al, 2002;Hugonin and Lalanne, 2005;Lecamp et al, 2007) with the key difference that the AFMM-CFF solves Maxwell's equations formulated in terms of a contrast (scattered) field instead of a total field.…”

Section: Introductionmentioning

confidence: 99%

“…It builds upon the aperiodic Fourier modal method developed and refined by Lalanne and co-workers (Lalanne and Silberstein, 2000;Silberstein et al, 2001;Cao et al, 2002;Hugonin and Lalanne, 2005;Lecamp et al, 2007) with the key difference that the AFMM-CFF solves Maxwell's equations formulated in terms of a contrast (scattered) field instead of a total field. This reformulation allows prescription of arbitrary incoming fields onto the structure of interest (Pisarenco et al, 2010). Aperiodicity is achieved by using perfectly matched layers (PMLs) (Berenger, 1994) on the vertical boundaries in order to annihilate the periodic boundary condition.…”

Section: Introductionmentioning

confidence: 99%

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Efficient solution of Maxwell’s equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method

Pisarenco

Maubach

Setija

et al. 2012

Journal of Computational Physics

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Physics‐Informed Machine Learning for Optical Modes in Composites

Ghosh

Elhamod

et al. 2022

Advanced Photonics Research

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Herein, example of study of optical modes propagating through spatially periodic composites is used to demonstrate that embedding physics‐driven constraints into machine‐learning process can dramatically improve accuracy and generalizability of resulting models. Comprehensive analysis of common compromises between direct physics‐based solutions, machine‐learning training and deployment times, as well as accuracies of the resulting models is presented. The approach to physics‐informed machine learning, presented in this work, can be readily utilized in other situations mapped onto an eigenvalue problem, a known bottleneck of computational electrodynamics. Crucially, the technique provides a way to train the model on configurations with no known solutions. The approach presented in this work can be utilized for machine‐learning‐driven design, optimization, and characterization of composites with 1D and 2D structure. Physics‐informed design of machine learning can be further used to produce high‐quality models, in particular, in situations where exact solutions are scarce or are slow to come up with.

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Aperiodic Fourier modal method in contrast-field formulation for simulation of scattering from finite structures

Cited by 32 publications

References 28 publications

Resonant-state expansion of light propagation in nonuniform waveguides

Resonant-state expansion of light propagation in nonuniform waveguides

Efficient solution of Maxwell’s equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method

Physics‐Informed Machine Learning for Optical Modes in Composites

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