Two-dimensional gratings of hexagonal holes for high order diffraction suppression

Abstract

We propose two-dimensional gratings comprised of a large number of identical and similarly oriented hexagonal holes for the high order diffraction suppression. An analytical study of the diffraction property for such gratings, based on both square and triangle arrays, is described. The dependence of the high order diffraction property on the hole shape and size is investigated. Notably, theoretical calculation reveals that the 2nd, 3rd and 4th order diffractions adjacent to the 1st order diffraction can be completely suppressed, and the 5th order diffraction efficiency is as low as 0.01%, which will be submerged in the background noise for most practical applications. The 1st order diffraction intensity efficiency 6.93% can be achieved as the hexagonal holes along y-axis connect with each other. For the case of b=P_y/3, the 1st order diffraction intensity efficiency is 3.08%. The experimental results are also presented, confirming the theoretical predictions. Especially, our two-dimensional gratings have the ability to form free-standing structures which are highly desired for the x-ray region. Comparing with the grating of the square array, the grating of the triangle array is easy to be fabricated by silicon planar process due to the large spacing between any two adjacent holes. Our results should be of great interest in a wide spectrum unscrambling from the infrared to the x-ray region.

High-efficiency V-shaped phase gratings to suppress high order diffractions

“…Based on the basic sinusoidal amplitude grating, twodimensional binary gratings utilizing the amplitude sinusoidal transmission function along one direction have been proposed. [14][15][16][17][18][19][20][21] The idea is that the average transmission effect along one direction is obtained by integrating the transmission function along the other directions. The average sinusoidal transmission function of binary gratings arises from complexshaped holes, such as sinusoidal or trapezoidal, 14,15 or the modulation of the hole positions.…”

“…[14][15][16][17][18][19][20][21] The idea is that the average transmission effect along one direction is obtained by integrating the transmission function along the other directions. The average sinusoidal transmission function of binary gratings arises from complexshaped holes, such as sinusoidal or trapezoidal, 14,15 or the modulation of the hole positions. [14][15][16][17][18][19][20][21] The absolute efficiency AIP Advances 9, 015308 (2019); doi: 10.1063/1.…”

“…The average sinusoidal transmission function of binary gratings arises from complexshaped holes, such as sinusoidal or trapezoidal, 14,15 or the modulation of the hole positions. [14][15][16][17][18][19][20][21] The absolute efficiency AIP Advances 9, 015308 (2019); doi: 10.1063/1. of the 1 st order diffraction is limited to 6.93% of the trapezoidal grating.…”

“…15 Moreover, the complex shapes or small gaps between holes increases the fabrication difficulty when using current nanofabrication techniques. In addition, modulated gratings [14][15][16][17][18][19][20][21] introduce background noise, which decreases the signal-to-noise ratio of the 1 st order diffraction. Therefore, we desire a grating that has a high 1 st order diffraction efficiency (not lower than the traditional sinusoidal grating) and large feature sizes (comparable to the traditional binary grating).…”

“…Moreover, the feature size of the V-shaped grating is half of the period, which makes the grating much easier to fabricate than other approaches. [10][11][12][13][14][15][16] We investigate the dependencies of the 1 st order diffraction efficiency on the wavelength and the grating depth. The diffraction patterns of the fabricated grating have been measured with both a 532 nm laser and a broadband xenon lamp.…”