  This study proposes a novel coupled-mode theory for two-dimensional exterior
Helmholtz problems. The proposed approach is based on the separation of the
entire space R2 into a fictitious disk and its exterior. The disk is allocated
in such a way that it comprises all the inhomogeneity; therefore, the exterior
supports cylindrical waves with a continuous spectrum. For the interior, we
expand an unknown wave field using normal modes that satisfy some auxiliary
boundary conditions on the surface of the disk. For the interior expansion, we
propose combining the Neumann and Dirichlet normal modes. We show that the
proposed expansion sacrifices L2 orthogonality but significantly improve the
convergence. Finally, we present some numerical verifications of the proposed
coupled-mode theory.
