  This work concentrates on numerical simulations of Photonic Crystal
structures using basis-expansion methods, with a main focus on simulating
disorder. The plane-wave and guided-mode expansions are outlined as tools to
compute the Bloch modes of a structure, on the basis of which the Bloch-mode
expansion formalism is outlined - the latter allowing for simulations of large
structures in presence of disorder. As a first illustration of the method, we
apply it to three gentle-confinement cavities, to obtain results for their
quality factors similar to the theoretically predicted in the literature.
Furthermore, we compute that random disorder can drive those factors down to
the experimentally measured values. As a second application, we study the
effect of irregular hole shapes in a PHC waveguide, and find that the
correlation length of the irregularity (i.e. the typical scale of the roughness
of the features) matters: for higher correlation lengths, the computed modes
show both higher band broadening and higher loss rates.
