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\begin{document}

\title{A Scattering Problem for a Local Perturbation of an Open Periodic
Waveguide}



\author[1]{Andreas Kirsch}%
\affil[1]{KIT}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
In this paper we consider the propagation of waves in an open waveguide
in \textbf{R}\^{}2 where the index of refraction is a local perturbation
of a function which is periodic along the axis of the waveguide and
equal to one outside a strip of finite width. Motivated by the limiting
absorption principle (proven in an ealier paper by the author for the
case of an open waveguide in the half space) we formulate a radiation
condition which allows the existence of propagating modes and prove
uniqueness, existence, and stability of a solution. In the last part we
investigate the decay properties of the radiating part in the direction
of periodicity and orthogonal to it.%
\end{abstract}%



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