Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates

Teppo Häyrynen, Andreas Dyhl Østerkryger, Jakob Rosenkrantz de Lasson, Niels Gregersen

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand the wholespace. The strength of the method lies in discretizing the Fourier integralsusing a non-uniform circular "dartboard" sampling of the Fourier $k$ space. Weshow that our sampling technique leads to a more accurate description of thecontinuum of the radiation modes that leak out from the structure. We alsocompare our approach to conventional discretization with direct and inversefactorization rules commonly used in established Fourier modal methods. Weapply our method to a variety of optical waveguide structures and demonstratethat the method leads to a significantly improved convergence enabling moreaccurate and efficient modeling of open 3D nanophotonic structures.
Original languageEnglish
JournalJournal of the Optical Society of America A
Volume34
Issue number9
Pages (from-to)1632-1641
ISSN0740-3232
DOIs
Publication statusPublished - 2017

Keywords

  • Fourier modal method
  • Computational electromagnetic methods
  • Micro-optics
  • Waveguides
  • Mathematical methods in physics
  • Numerical approximation and analysis

Cite this

Häyrynen, Teppo ; Østerkryger, Andreas Dyhl ; de Lasson, Jakob Rosenkrantz ; Gregersen, Niels. / Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates. In: Journal of the Optical Society of America A. 2017 ; Vol. 34, No. 9. pp. 1632-1641.
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abstract = "Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand the wholespace. The strength of the method lies in discretizing the Fourier integralsusing a non-uniform circular {"}dartboard{"} sampling of the Fourier $k$ space. Weshow that our sampling technique leads to a more accurate description of thecontinuum of the radiation modes that leak out from the structure. We alsocompare our approach to conventional discretization with direct and inversefactorization rules commonly used in established Fourier modal methods. Weapply our method to a variety of optical waveguide structures and demonstratethat the method leads to a significantly improved convergence enabling moreaccurate and efficient modeling of open 3D nanophotonic structures.",
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Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates. / Häyrynen, Teppo; Østerkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels.

In: Journal of the Optical Society of America A, Vol. 34, No. 9, 2017, p. 1632-1641.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates

AU - Häyrynen, Teppo

AU - Østerkryger, Andreas Dyhl

AU - de Lasson, Jakob Rosenkrantz

AU - Gregersen, Niels

PY - 2017

Y1 - 2017

N2 - Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand the wholespace. The strength of the method lies in discretizing the Fourier integralsusing a non-uniform circular "dartboard" sampling of the Fourier $k$ space. Weshow that our sampling technique leads to a more accurate description of thecontinuum of the radiation modes that leak out from the structure. We alsocompare our approach to conventional discretization with direct and inversefactorization rules commonly used in established Fourier modal methods. Weapply our method to a variety of optical waveguide structures and demonstratethat the method leads to a significantly improved convergence enabling moreaccurate and efficient modeling of open 3D nanophotonic structures.

AB - Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand the wholespace. The strength of the method lies in discretizing the Fourier integralsusing a non-uniform circular "dartboard" sampling of the Fourier $k$ space. Weshow that our sampling technique leads to a more accurate description of thecontinuum of the radiation modes that leak out from the structure. We alsocompare our approach to conventional discretization with direct and inversefactorization rules commonly used in established Fourier modal methods. Weapply our method to a variety of optical waveguide structures and demonstratethat the method leads to a significantly improved convergence enabling moreaccurate and efficient modeling of open 3D nanophotonic structures.

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KW - Numerical approximation and analysis

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