Non-linear x-ray coherent diffractive imaging

Abstract X-ray coherent diffractive imaging has emerged as a key technique with modern coherent x-ray sources, enabling lensless reconstruction of nanoscale structure and dynamics with high spatial and temporal resolution with even a single x-ray pulse. However, there are many types of nanoscale orderings which are not directly resolvable using linear x-ray contrast mechanisms, for instance the orientation of ferroelectric domains, where systems with identical alignments but different orientations exhibit different topologies. The advent of nonlinear x-ray processes like sum-frequency generation and four-wave mixing raises the possibility of non-linear x-ray imaging, combining the high-resolution and elemental specificity of x-ray imaging with the state selectivity and vector sensitivity of non-linear optical imaging. In this work, we propose a coherent diffractive approach to imaging using x-ray nonlinear processes, leveraging the property of mutual incoherence between different wavelengths to isolate the nonlinear component from the overall diffraction pattern. We numerically demonstrate the approach, and discuss the feasibility of the proposed method in the presence of experimental noise, most relevantly shot noise. This analysis method is applicable in both static and dynamic imaging, including for single-shot imaging, offering a pathway beyond traditional spectroscopy for extreme ultraviolet/x-ray coherent imaging of spatio-temporal dynamics in quantum materials and biological systems.