Nanophotonics

Nanophotonics is one great path into our future since it renders
possible to build e.g. absorber, emitter or amplifier on a scale of
a few dozen nanometers. To use this effectively we will have to
understand firstly the resonances of plasmons and secondly the
interaction of electromagnetic waves with complex media. Here on
the one hand we can model light as waves and describe what is
happening for the different frequencies of monochromatic light
waves. We have to model the evolution in air or in more complex
media.

On the other hand - taking the more particle centered point of
view - we can try to model the reaction of the photons to certain
stimuli.


The modelling is still in progress and explored in many different
ways.


The main focus of our guest Claire Scheid who is working on
nanophotonics is to solve the corresponding partial differential
equations numerically. It is challenging that the
nanoscale-photons have to be visible in a discretization for a
makro domain. So one needs special ideas to have a geometrical
description for changing properties of the material. Even on the
fastest available computers it is still the bottleneck to make
these computations fast and precise enough.


A special property which has to be reflected in the model is the
delay in response of a photon to incoming light waves - also
depending on the frequency of the light (which is connected to
its velocity- also known as dispersion). So an equation for the
the evolution of the electron polarization must be added to the
standard model (which is the Maxwell system).


One can say that the model for the permeability has to take into
account the whole history of the process. Mathematically this is
done through a convolution operator in the equation. There is
also the possibility to explain the same phenomenon in the
frequency space as well.


In general the work in this field is possible only in good
cooperation and interdisciplinary interaction with physicists -
which also makes it especially interesting.


Since 2009 Claire Scheid works at INRIA méditerranée in
Sophia-Antipolis as part of the Nachos-Team and is teaching at
the university of Nice as a member of the Laboratoire Dieudonné.


She did her studies at the Ecole Normale Superieure in Lyon and
later in Paris VI (Université Pierre et Marie Curie). For her PhD
she changed to Grenoble and spent two years as Postdoc at the
university in Oslo (Norway).
Literature and additional material

R. Léger, J. Viquerat, C. Durochat, C. Scheid and S. Lanteri:
A parallel non-confoming multi-element DGTD method for the
simulation of electromagnetic wave interaction with metallic
nanoparticles, J. Comput. Appl. Math. Vol 270, p. 330-342, 2014.

S. Descombes, C. Durochat, S. Lanteri, L. Moya, C. Scheid, J.
Viquerat: Recent advances on a DGTD method for time-domain
electromagnetism, Photonics and Nanostructures, Volume 11, issue
4, 291-302, 2013.

K. Busch, M. König, J. Niegemann: Discontinuous Galerkin
methods in nanophotonics, Laser and Photonics Reviews, 5, pp.
1–37, 2011.