This works deals with one dimensional infinite perturbation - namely line
defects - in periodic media. In optics, such defects are created to construct
an (open) waveguide that concentrates light. The existence and the computation
of the eigenmodes is a crucial issue. This is related to a self-adjoint
eigenvalue problem associated to a PDE in an unbounded domain (in the
directions orthogonal to the line defect), which makes both the analysis and
the computations more complex. Using a Dirichlet-to-Neumann (DtN) approach, we
show that this problem is equivalent to one set on a small neighborhood of the
defect. On contrary to existing methods, this one is exact but there is a price
to be paid : the reduction of the problem leads to a nonlinear eigenvalue
problem of a fixed point nature
