DGTD method for a non-local Drude model

Available as %newwin% [[https://hal.inria.fr/hal-01150076 | INRIA RR-8726 on Hyper Article Online]]

Available as %newwin% [[https://hal.inria.fr/hal-01150076 | 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 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. 

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. 

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. 

%center% Field solution computed with the DGTD-P'_2_' method for a anodisk dimmer computed (radius of a disk is 2 nm)

(:cellnr align='center':) %width=345px% http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png
(:cell  align='center':) %width=345px% http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/nonlocP2Exh.png

(:cellnr align='center':) %width=350px% http://www-sop.inria.fr/nachos/pics/results/nano_nonloc_drude/locP2Exh.png

%center% Module of the Fourier transformed field plot of E'_x_' computed with
the DGTD-P'_2_' method