  We introduce a theoretical formalism to describe disorder-induced extrinsic
scattering in slow-light photonic crystal waveguides. This work details and
extends the optical scattering theory used in a recent \emph{Physical Review
Letter} [M. Patterson \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{102},
103901 (2009)] to describe coherent scattering phenomena and successfully
explain complex experimental measurements. Our presented theory, that combines
Green function and coupled mode methods, allows one to self-consistently
account for arbitrary multiple scattering for the propagating electric field
and recover experimental features such as resonances near the band edge. The
technique is fully three-dimensional and can calculate the effects of disorder
on the propagating field over thousands of unit cells. As an application of
this theory, we explore various sample lengths and disordered instances, and
demonstrate the profound effect of multiple scattering in the waveguide
transmission. The spectra yield rich features associated with disorder-induced
localization and multiple scattering, which are shown to be exasperated in the
slow light propagation regime.
