Non-linear X-ray Coherent Diffractive Imaging

Abstract: 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 sensitivity of non-linear optical imaging. While scanning imaging methods may be feasible, for linear X-ray processes coherent diffractive imaging has emerged as a key approach, enabling lensless reconstruction of nanoscale structure and dynamics with high spatial and temporal resolution. In this work, we propose a coherent diffractive approach to imaging using X-ray nonlinear processes, introducing an analysis method to isolate the nonlinear component from the overall diffraction pattern by leveraging the property of mutual incoherence between different wavelengths. For examples such as sum-frequency generation in ferroelectrics, this method reveals both domain structure and orientation through the retrieved amplitude and phase of the nonlinear signal. We 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, offering a pathway beyond traditional spectroscopy toward XUV/X-ray coherent imaging of spatio-temporal dynamics in quantum materials and biological systems.