Analysis and optimization of transmission resonances through periodic plasmonic structures

This dissertation is focused on electromagnetic wave propagation through periodic structures. The work consists of two main parts. In the rst part we deal with electromagnetic radiation through periodic aperture arrays in an \in nitesimally thin perfect electric conductor". Electromagnetic radiation through a bounded medium with two-dimensional geometry and nite width is considered as the second model. First of all, we formulate a mathematical model for electromagnetic transmission through periodic hole arrays in a thin perfect electric conductor, where we can obtain an explicit linear operator equation for the tangential components of the electric and magnetic elds inside the apertures. The linear operator is regularized to ensure a stable numerical solution. We then analyze the solvability of the linear operator equation with a truncated, regularized and mollifi ed operator. The extension of our model to the case of an arbitrary incoming wave by adding a Bloch condition is included. We establish the conservation of energy, stating that the total energy of the reflected and transmitted waves is equal to the energy of the incident wave. We then introduce some numerical experiments and show numerically that energy dissipation occurs with the regularization.