Helmholtz equation in periodic structures

Zakaria Kassali

Recent research has shown that the use of periodically nanostructured materials can improve the efficiency of solar cells. Indeed, periodic nanostructures allow to tailor light-matter interactions and they can support optical resonances which increase the absorption of light. This motivates the numerical study of light propagation in these solar cells, which can be modeled by the Helmholtz equation with a quasi-periodic boundary condition. Due to this quasi-periodic condition quasi-resonant frequencies appear, and affect the problem stability. In turn, this lack of stability affects the use of a perfectly matched layer (PML) to truncate the infinite domain, and the accuracy of numerical discretizations. This work is dedicated to showing frequency-explicit stability results that help to clearly reveal the effect of the resonance frequencies on PMLs and numerical discretizations.