A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects
Résumé
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 work, we present 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. While the method is
presented in the general 3d case, numerical results are given for 2d
simulation settings only.
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