Engineers often think of finite element method (FEM) calculations as routine, as they indeed are for well-posed mathematical situations. But under certain interesting conditions, this is no longer true – one has to work hard to deal with the singularities. In her thesis work, Camille Carvalho developed a finite element method for computing the scattering of electromagnetic waves from sharp corners, as in nanophotonic waveguides. The method given applies to 2.5D (the third dimension being translationally trivial), like one would find in a waveguide with corners defined by crystal planes, for example.
It seems to me that this approach may find use not only in the case of plasmonic waveguides, but also for certain situations in EUV metrology wherein plasmons contribute to the observed scattering.
Furthermore, it would be interesting if a fully 3D method could be developed. It may enhance our insight for photon-assisted field emission, which we discussed in a previous post.
- Dr. Carvalho’s website, where one finds a convincing visual, and links, among which are:
- Dr. Carvalho’s thesis presentation (français)
- Bonnet-Ben Dhia, Carvalho, Chesnel, Ciarlet, “On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients”, arXiv:1511.01932