  We present a detailed theoretical study of the effects of structural disorder
on LN photonic crystal slab cavities, ranging from short to long length scales,
using a fully-3D Bloch mode expansion technique. We compute the optical density
of states, quality factors and effective mode volumes of the cavity modes, with
and without disorder, and compare with the localized modes of the corresponding
disordered photonic crystal waveguide. We demonstrate how the quality factors
and effective mode volumes saturate at a specific cavity length and become
bounded by the corresponding values of the Anderson modes appearing in the
disordered waveguide. By means of the intensity fluctuation criterion, we
observe Anderson localization for cavity lengths larger than around L31, and
show that the field confinement in the disordered LN cavities is mainly
determined by the local characteristics of the structural disorder as long as
the confinement region is far enough from the cavity mirrors and the effective
mode localization length is much smaller than the cavity length; under this
regime, the disordered cavity system becomes insensitive to changes in the
cavity boundaries and a good agreement with the intensity fluctuation criterion
is found for localization. Surprisingly, we find that the Anderson localized
modes do not appear as new disorder-induced resonances in the main spectral
region of the LN cavity modes, and, moreover, the disordered DOS enhancement is
largest for the disordered waveguide system with the same length. These results
are fundamentally interesting for applications such as lasing and cavity-QED,
and provide new insights into the role of the boundary condition on finite-size
slow-light waveguides. They also point out the clear failure of using models
based on the cavity boundaries/mirrors and a single slow-light Bloch mode to
describe cavity systems with large N.
