Statistical analysis of subnanometer residual disorder in photonic crystal waveguides: Correlation between slow light properties and structural properties

The authors present a statistical study of residual disorder in nominally identical planar photonic crystal waveguides operating in the slow light regime. The focus is on the role played by the subnanometer scaled residual disorder inherent to state-of-the-art electron-beam (EB) lithography systems, in particular, on the impact of the nature of the residual disorder on the maximum value of the guided mode group index. The authors analyze the statistical properties of the surface area, the position, and the shape of the air holes that define the photonic crystal with optimized scanning electron microscope micrographs. The authors identify the hole-area fluctuation as the main source of degradation of the dispersive slow light regime by correlating such a microscopic analysis of the structural disorder with large field-of-view optical characterizations based on a Fourier space imaging technique. The structure with the largest group index (n_g = 40) exhibits a standard deviation σ of the radius of the hole as low as 0.4 nm. Such a low value of σ, which already significantly limits the maximum achievable group index of the guided mode, stresses the drastic impact of the residual disorder on the performances of the slow light regime. A mean square analysis of the electronic micrographs reveals that the standard deviation of the hole position is lower than an upper limit of 0.6 nm. This upper bound comes from the intrinsic imperfections of the scanning electronic microscope itself, which hinders to quantify the position disorder induced by the EB lithography system. The authors have identified no correlation between the shape of the holes and the group index as for the hole position. As a result, the hole-area fluctuation is currently the main parameter to control in order to improve the performance of the slow light regime.