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

Abstract

Laser-generated XUV and soft x-ray radiation sources using high-harmonic generation, typically producing 108 photons per pulse per harmonic (~5 nm to ~50 nm) in a coherent low-divergence beam, are a promising source for nanometer scale imaging. Here we present XUV diffraction from a single-layer self-assembled hexagonal close-packed (HCP) array of 200 nm diameter PMMA nanospheres. Such a lattice is too small to diffract from using visible light, and hence XUV wavelengths are required. We observe a hexagonal diffraction pattern for three diffraction orders - the result of illuminating a single crystal. The observed 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 hence providing useful information on the quality of the crystal and the 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 the scattering function from a single sphere, which can be calculated using the Mie solution to Maxwell's equations. We compare the measured intensity for each of the eighteen observed interference peaks for the harmonic at 27.6 nm, against the theoretical intensity. The excellent agreement over four orders of magnitude indicates that Mie scattering predicts an appropriate form factor for this analysis and also enables us to extract the complex refractive index of PMMA at this wavelength