High order diffraction suppression by quasi-periodic two-dimensional gratings

Abstract

We propose quasi-periodic two-dimensional gratings comprised of a large number of circular holes for the high order diffraction suppression. By using Kirchhoff’s diffraction theory, we analytically investigate the diffraction property of the grating and optimize the structure parameters to suppress the high order diffractions. We analyze the dependence of the high order diffractions on the hole location and size. Notably, theoretical analysis reveals that the 3rd and even order diffractions can be completely suppressed, and the 5th order diffraction is as low as 0.02% of the 1st order diffraction, thereby allowing to submerge in the background noise for most practical applications. The desired diffraction pattern containing the 0th and ± 1st order diffractions results from the constructive interference of lights from different holes, which locate according to some statistical law distribution. The experimental results are also presented, confirming the theoretical predictions. Especially, our gratings have two advantages: the ability to form free-standing structures and large tolerance up to ± 10% deviation of the hole size. The former is highly desired for the x-ray and extreme ultraviolet regions, while the latter ease the fabrication difficulties of the current planar silicon technology. Our results should possess broad potential applications in a wide spectrum unscrambling from the infrared to the x-ray region.