  The interplay between order and disorder in photonic lattices opens up a wide
range of novel optical scattering mechanisms, resonances, and applications that
can be obscured by typical ordered design approaches to photonics. Striking
examples include Anderson localization, random lasers, and visible light
scattering in biophotonic structures such as butterfly wings. In this work, we
present a profound example of light localization in photonic crystal waveguides
by introducing long-range correlated disorder. Using a rigorous
three-dimensional Bloch mode expansion technique, we demonstrate how inter-hole
correlations have a negative contribution to the total out-of-plane radiative
losses, leading to a pronounced enhancement of the quality factor, $Q$, and
$Q/V$ cavity figures of merit in the long-range correlation regime.
Subsequently, the intensity fluctuations of the system are shown to globally
increase with the correlation length, highlighting the non-trivial role of
long-range disorder on the underlying scattering mechanisms. We also explore
the possibility of creating ultra-high quality cavity modes via inter-hole
correlations, which have various functionalities in chip-based nonlinear optics
and waveguide cavity-quantum electrodynamics.
