  The perfectly matched layers method is a well known truncation technique for
its efficiency and convenience in numerical implementations of wave scattering
problems in unbounded domains. In this paper, we study the convergence of the
perfectly matched layers (PML) for wave scattering from a local perturbation of
an open waveguide in the half space above the real line, where the refractive
index is a function which is periodic along the axis of the waveguide and
equals to one above a finite height. The problem is challenging due to the
existence of guided waves, and a typical way to deal with the difficulty is to
apply the limiting absorption principle. Based on the Floquet-Bloch transform
and a curve deformation theory, the solution from the limiting absorption
principle is rewritten as the integral of a coupled family of quasi-periodic
problems with respect to the quasi-periodicity parameter on a particularly
designed curve. By comparing the Dirichlet-to-Neumann maps on a straight line
above the locally perturbed periodic layer, we finally show that the PML method
converges exponentially with respect to the PML parameter. Finally, the
numerical examples are shown to illustrate the theoretical results.
