  This thesis explores the application of Plane Wave Discontinuous Galerkin
(PWDG) methods for the numerical simulation of electromagnetic scattering by
periodic structures. Periodic structures play a pivotal role in various
engineering and scientific applications, including antenna design, metamaterial
characterization, and photonic crystal analysis. Understanding and accurately
predicting the scattering behavior of electromagnetic waves from such
structures is crucial in optimizing their performance and advancing
technological advancements.
  The thesis commences with an overview of the theoretical foundations of
electromagnetic scattering by periodic structures. This theoretical
dissertation serves as the basis for formulating the PWDG method within the
context of wave equation. The DtN operator is presented and it is used to
derive a suitable boundary condition.
  The numerical implementation of PWDG methods is discussed in detail,
emphasizing key aspects such as basis function selection and boundary
conditions. The algorithm's efficiency is assessed through numerical
experiments.
  We then present the DtN-PWDG method, which is discussed in detail and is used
to derive numerical solutions of the scattering problem. A comparison with the
finite element method (FEM) is presented.
  In conclusion, this thesis demonstrates that PWDG methods are a powerful tool
for simulating electromagnetic scattering by periodic structures.
