  We prove polynomial and exponential decay at infinity of eigen-vectors of
partial differential operators related to radiation problems for time-harmonic
generalized Maxwell systems in an exterior domain with non-smooth
inhomogeneous, anisotropic coefficients converging near infinity with a certain
rate towards the identity. As a canonical application we show that the
corresponding eigen-values do not accumulate in R \ {0} and that by means of
Eidus' limiting absorption principle a Fredholm alternative holds true.
