XUV diffraction from a self-assembled 2D array of close-packed 200nm diameter PMMA spheres

Abstract

Laser-generated XUV and soft x-ray radiation sources using high-harmonic generation (HHG), typically producing 108 photons per pulse per harmonic (~5nm to ~50nm) in a coherent low-divergence beam [1], are a promising source for nanometer scale imaging [2]. Here we present XUV diffraction from a single-layer self-assembled hexagonal-close-packed (HCP) array of 200nm diameter PMMA nanospheres. Such a lattice is too small to diffract from using visible light, and hence XUV wavelengths are required. Figure (a) shows the far-field pattern from the single crystal at a 22µm focus, and overlaid with 100 mrad contours. The interference peaks are a convolution of a Bragg peak with both the distribution of lattice planes (due to crystal defects) and the harmonic spectra. However, as these convolutions are in orthogonal directions, they can be independently resolved (figures b & c), providing information on the crystal quality and generated wavelengths.The far-field diffraction pattern from a single-layer HCP array of spheres is the Fourier Transform (FT) of a hexagonal grid of delta functions multiplied by the FT of a the scattering function from a single sphere, which can be calculated using Mie theory. Figure (d) shows, (+) the measured intensity for each of the eighteen interference peaks for the harmonic at 27.6nm, (.) the theoretical intensity versus angle distribution for a single sphere, and (o) the predicted intensity at each interference peak. The excellent agreement indicates that Mie scattering predicts an appropriate form factor for this analysis and enables us to extract the complex refractive index of PMMA at this wavelength