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

Abstract

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 (ng = 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.

Automated optimization of photonic crystal slab cavities

“…1, but for the value S 1 x = 0.327 a corresponding to our optimal design (the white cross indicates where the design lies with respect to S 2 x and S 3 x ). In this plot, we observe that the width of the maximum is larger than the typical uncertainty in the hole positions (smaller than 0.005 a for Si42). Furthermore, in Fig.…”

Effect of hole-shape irregularities on photonic crystal waveguides

“…Disorder sets a severe limitation to the quality factor of high-Q PHC cavities [2][3][4], and degrades the performance of PHC waveguides by inducing extrinsic radiation losses [5][6][7][8] and light localization [9] in the vicinity of the guided band edge (which has also been advocated as a useful resource for applications [10]). For these reasons, disorder in PHCs has been the subject of increasingly intense theoretical [2][3][4][5][6][7][8]11,12] and experimental [3,4,[13][14][15] studies in the last decade. Several theoretical works [3][4][5]8,11] have considered the simplest possible disorder model, namely, circular holes with randomly fluctuating radii and/or positions, and studied the spectral properties as a function of the fluctuation amplitude.…”

High-Q silicon photonic crystal cavity for enhanced optical nonlinearities

“…1(e), computed for a disorder amplitude r ¼ 0.003a, which is a very reasonable estimate of the largest fluctuations introduced in the fabrication process. 31 Finally, we note that Fig. 2(a) also shows that at short distances, where the Q-factor is still very high (%100 000), losses are fully dominated by coupling into the waveguide channel, which highlights the potential for photonic applications.…”