Numerical contributions in nanophotonics
Properties of nanostructured materials are the sources of a lot of positive emulation in physics. The way they react to their illumination by a light source is especially appealing since it may lead to huge light amplification (or absorption) and astonishing focusing ability. By exploiting these nice features, a lot of applications have emerged during the last decades. It ranges from nanolasers, nanoantennas to potential cancer therapy. A special branch of physics, nanophotonics, is dedicated to the development of the applications and the understanding of the various phenomena that come into play. In this talk, we will concentrate on how applied mathematicians are able to contribute to the progress of this field of physics. Indeed physicists are not only relying on experiments but are also eager on inputs on their feasibility, potential success and the optimization of their efficiency. Applied mathematicians have at hand theoretical and numerical tools that could partly address these questions and complement the work of the physicist. To illustrate this, we will identify several steps and their relative bottle-necks in this interdisciplinary work. From modelling issues (using PDE’s such as Maxwell’s equations) to the numerical simulation of real experiments through the decisive use of theoretical numerical analysis tools (such as a special class of Finite Element methods). The small scales, the geometry and the physical characteristics of the media are in particular challenging as well as the crucial need of high accuracy to deal
with the huge fields enhancements. We will exemplify each stages until the assessment of the numerical approach via actual numerical simulations.