Anderson Localization in Disordered LN Photonic Crystal Slab Cavities

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 (N = 3-35 cavity lengths), using a fully three-dimensional Bloch mode expansion technique. We compute the optical density of states (DOS), quality factors and effective mode volumes of the cavity modes, with and without lattice 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 find Anderson-like 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 away 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 Anderson localization. Surprisingly, we find that the Anderson-like 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 (e.g., open vs mirrors) on finite-size slow-light waveguides. They also point out the limits of using models based on the cavity boundaries/mirrors and a single slow-light Bloch mode to describe cavity systems with large N.