DGTD method for a non-local Drude model
Results.DGTDNonlocDrude History
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Available as INRIA RR-8726 on Hyper Article Online
Available as INRIA RR-8726 on Hyper Article Online (2015)
Available as INRIA RR-7983 on Hyper Article Online
Available as INRIA RR-8726 on Hyper Article Online
N. Schmitt, C. Scheid, S. Lanteri, J. Viquerat and A. Moreau
A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects
Available as INRIA RR-7983 on Hyper Article Online
For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local Drude dispersion model.
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For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local Drude dispersion model. In a preliminary study, we restricted on a two-dimensional setting.
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Related publications
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For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local dispersion model relevant to plasmonics.
For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local Drude dispersion model.
For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-loca dispersion model relevant to plasmonics.
For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local dispersion model relevant to plasmonics.
For the numerical modeling of light/structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-loca dispersion model relevant to plasmonics.
For the numerical modeling of light/metallic structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-loca dispersion model relevant to plasmonics.
The interaction of light with metallic nanostructures is of increasing interest for various fields of research. When metallic structures have sub-wavelength sizes and the illuminating frequencies are in the regime of metal's plasma frequency, electron interaction with the exciting fields have to be taken into account. Due to these interactions, plasmonic surface waves can be excited and cause extreme local field enhancements (e.g. surface plasmon polariton electromagnetic waves). Exploiting such field enhancements in applications of interest requires a detailed knowledge about the occurring fields which can generally not be obtained analytically. For the latter mentioned reason, numerical tools as well as a deeper understanding of the underlying physics, are absolutely necessary. For the numerical modeling of light/structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-loca dispersion model relevant to plasmonics.
For the numerical modeling of light/structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-loca dispersion model relevant to plasmonics.
Field solution computed with the DGTD-P2 method for a anodisk dimmer computed (radius of a disk is 2 nm)
Field solution computed with the DGTD-P2 method for a nanodisk dimer (radius of a disk is 2 nm)
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(:table border='0' width='100%' align='center' cellspacing='1px':) (:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/2RectClEx.png (:cell align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/2RectClEx.png (:cellnr align='center':) Ex component (:cell align='center':) Ey component (:tableend:)
Field solution computed with the DGTD-P2 method for a square dimer (edge length is 4 nm)
(:table border='0' width='100%' align='center' cellspacing='1px':) (:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/2DiscClEx.png (:cell align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/2DiscClEx.png (:cellnr align='center':) Ex component (:cell align='center':) Ey component (:tableend:)
Field solution computed with the DGTD-P2 method for a anodisk dimmer computed (radius of a disk is 2 nm)
(:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png (:cell align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/nonlocP2Exh.png
(:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png (:cell align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/nonlocP2Exh.png
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(:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png
(:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png
Module of the Fourier transformed field plot of Ex computed with
the DGTD-P2 method
Module of the Fourier transformed field plot of Ex computed with the DGTD-P2 method
(:table border='0' width='100%' align='center' cellspacing='1px':) (:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png (:cell align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/nonlocP2Exh.png (:cellnr align='center':) Local Drude model (:cell align='center':) Non-local Drude model (:tableend:)
Module of the Fourier transformed field plot of Ex computed with
the DGTD-P2 method
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The interaction of light with metallic nanostructures is of increasing interest for various fields of research. When metallic structures have sub-wavelength sizes and the illuminating frequencies are in the regime of metal's plasma frequency, electron interaction with the exciting fields have to be taken into account. Due to these interactions, plasmonic surface waves can be excited and cause extreme local field enhancements (e.g. surface plasmon polariton electromagnetic waves). Exploiting such field enhancements in applications of interest requires a detailed knowledge about the occurring fields which can generally not be obtained analytically. For the latter mentioned reason, numerical tools as well as a deeper understanding of the underlying physics, are absolutely necessary. For the numerical modeling of light/structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2 nm to 25 nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this context, we study a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-loca dispersion model relevant to plasmonics.
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