  Collective effects in the interaction of light with ensembles of identical
scatterers play an important role in many fields of physics. However, often the
term ``identical'' is not accurate due to the presence of hyperfine fields
which induce inhomogeneous transition shifts and splittings. Here we develop a
formalism based on the Green function method to model the linear response of
such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact
formula for the collective spectrum, which exhibits deviations from the uniform
frequency shift and broadening expected of two level systems. In particular, if
the coherent contribution to the collective coupling is large, the effect of
inhomogeneous broadening can be suppressed, with the linewidth approaching that
of the superradiant value. We apply this formalism to describe collective
effects in x-ray scattering off thin-film waveguides for inhomogeneous
hyperfine parameters.

Quantum Physics