  We present a fully three-dimensional Bloch mode expansion technique and
photon Green function formalism to compute the quality factor, mode volume, and
Purcell enhancement distributions of a disordered W1 photonic crystal slab
waveguide in the slow-light Anderson localization regime. By considering
fabrication (intrinsic) and intentional (extrinsic) disorder we find that the
quality factor and Purcell enhancement statistics are well described by
log-normal distributions without any fitting parameters. We also compare
directly the effects of hole size fluctuations as well as fluctuations in the
hole position. The functional dependence of the mean and standard deviation of
the quality factor and Purcell enhancement distributions is found to decrease
exponentially on the square root of the extrinsic disorder parameter. The
strong coupling probability between a single quantum dot and an
Anderson-localized mode is numerically computed and found to exponential
decrease with the squared extrinsic disorder parameter, where low disordered
systems give rise to larger probabilities when state-of-art quantum dots are
considered. The optimal regions to position quantum dots in the W1 waveguide
are also discussed. These theoretical results are fundamental interesting and
connect to recent experimental works on photonic crystal slab waveguides in the
slow-light regime.
