A novel full-wave method to perform modal analysis on waveguides based on an Interior Penalty Discontinuous Galerkin (IPDG) discretization of the vector wave equation. From an appropriate penalty function, a spurious-free and high accuracy method are achieved for a large class of waveguides, including intricate optical waveguides with leaky modes and plasmonic waveguides. This subject is part of a master thesis supervised by Dr. Hugo E. H. Figueroa.