Fig. 1. Schematic of the distribution of holes in the array: from δ-function to arbitrary positive function

Fig. 2. (a) Design for a quasi-periodical hole array: in each lattice (d×d square), a rectangular hole with side lengths of d/6 and d is positioned randomly on the ξ_n axis and has a trapezoidal distribution profile shown in (b)

Fig. 3. Comparison between far-field diffraction patterns of a quasi-periodical array shown in Fig. 2 when H＝L＝100 and a periodic grating with a duty cycle of 1∶5 and 201 periods

Fig. 4. (a) Intensity profiles of Fig. 3(a)–(c) across the line q＝λ/2d (indicated by yellow dashed lines in Fig. 3); (b) numerical results of Eq. (1) across the p-axis for the rectangular holes with side lengths of d/5 and d (red dot), and 2d/15 and d (black line).