  In this paper, a general methodology to study rigorously discontinuities in
open waveguides is presented. It relies on a full vector description given by
Maxwell's equations in the framework of the finite element method. The
discontinuities are not necessarily small perturbations of the initial
waveguide and can be very general, such as plasmonic inclusions of arbitrary
shapes. The leaky modes of the invariant structure are first computed and then
injected as incident fields in the full structure with obstacles using a
scattered field approach. The resulting scattered field is finally projected on
the modes of the invariant structure making use of their bi-orthogonality. The
energy balance is discussed. Finally, the modes of open waveguides periodically
structured along the propagation direction are computed. The relevant complex
propagation constants are compared to the transmission obtained for a finite
number of identical cells. The relevance and complementarity of the two
approaches are highlighted on a numerical example encountered in infrared
sensing. Open source models allowing to retrieve most of the results of this
paper are provided.
