A scattering problem for a local perturbation of an open periodic waveguide

In this paper, we consider the propagation of waves in an open waveguide in Double-struck capital R2 where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the x(1) axis) and equal to one for |x(2)| > h(0) for some h(0) > 0. Motivated by the limiting absorption principle (proven in an earlier paper by the author), we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution under the assumption that no bound states exist. In the second part, we determine the order of decay of the radiating part of the solution in the direction of the layer and in the direction orthogonal to it. Finally, we show that it satisfies the classical Sommerfeld radiation condition and allows the definition of a far field pattern.

Automated summary

This paper investigates the propagation of waves in a two-dimensional open waveguide. By considering local perturbations of the index of refraction and applying a radiation condition, the uniqueness, existence, and stability of the solution are proven, and the decay order of the radiating part of the solution is determined.