  In this paper, we consider the problem of the scattering of in-plane waves at
an interface between a homogeneous medium and a metamaterial. The relevant
eigenmodes in the two regions are calculated by solving a recently described
non self-adjoint eigenvalue problem particularly suited to scattering studies.
The method efficiently produces all propagating and evanescent modes consistent
with the application of Snell's law and is applicable to very general
scattering problems. In a model composite, we elucidate the emergence of a rich
spectrum of eigenvalue degeneracies. These degeneracies appear in both the
complex and real domains of the wave-vector. However, since this problem is non
self-adjoint, these degeneracies generally represent a coalescing of both the
eigenvalues and eigenvectors (exceptional points). Through explicit
calculations of Poynting vector, we point out an intriguing phenomenon: there
always appears to be an abrupt change in the sign of the refraction angle of
the wave on two sides of an exceptional point. Furthermore, the presence of
these degeneracies, in some cases, hints at fast changes in the scattered field
as the incident angle is changed by small amounts. We calculate these scattered
fields through a novel application of the Betti-Rayleigh reciprocity theorem.
We present several numerical examples showing a rich scattering spectrum. In
one particularly intriguing example, we point out wave behavior which may be
related to the phenomenon of resonance trapping. We also show that there exists
a deep connection between energy flux conservation and the biorthogonality
relationship of the non self-adjoint problem. The proof applies to the general
class of scattering problems involving elastic waves (under self-adjoint or non
self-adjoint operators).
