Single-particle incoherent diffractive imaging and amplified spontaneous emission in copper nanocubes

We demonstrate element-specific incoherent diffractive imaging (IDI) of single copper nanocubes using intensity correlations of K$α$ fluorescence at a hard X-ray free-electron laser. Combining single particle diffraction classification with IDI, we retrieve the form factor of 88 nm cubes with 20 nm resolution, extending IDI to the destructive single-particle regime with a large gain in resolution. IDI visibility drops sharply above a fluence of $10^2$ J/cm$^2$, consistent with the assumption of amplified spontaneous emission. Our results reveal fundamental limits for high-fluence nanoimaging towards future single-particle X-ray imaging.

💡 Research Summary

This groundbreaking study demonstrates, for the first time, element-specific incoherent diffractive imaging (IDI) of single nanoparticles at a hard X-ray free-electron laser (XFEL). The researchers investigated 88-nm copper oxide nanocubes injected into the focus of the European XFEL beam. The key innovation was a hybrid approach: using the coherent small-angle diffraction pattern from the same pulse to classify each particle by its size and orientation, and then applying intensity correlation analysis to the simultaneously measured copper Kα fluorescence at wider angles.

The second-order intensity correlation function, g^(2)(q), of the fluorescence photons was calculated for each pulse. By aligning and averaging the g^(2) signals from thousands of classified single-particle hits, the team successfully retrieved the form factor of the nanocubes, achieving a spatial resolution of approximately 20 nm. This represents a significant advance, extending IDI from bulk foils to the destructive single-particle regime with a substantial gain in resolution.

However, a major and unexpected finding emerged from analyzing the visibility (ν) of the correlation signal. The visibility, which indicates the contrast of the structural information in g^(2), showed a pronounced dip for frames with very high fluorescence signal. This drop at high incident fluence (above ~10² J/cm²) contradicts the expected saturation of visibility and is inconsistent with explanations based solely on background noise.

The paper proposes that Amplified Spontaneous Emission (ASE) is the underlying cause. Under intense XFEL irradiation, rapid ionization can create a population inversion. The spontaneous emission of one Kα photon can then stimulate coherent emission from other excited atoms within the nanocube. While these ASE photons are indistinguishable from spontaneous fluorescence at the detector, they possess partially correlated initial phases, which dilutes the random-phase condition essential for ideal IDI. This reduces the depth of modulation in g^(2) and thus the visibility. Simulations support this by showing that introducing a finite correlation length between emitters’ phases produces g^(2) profiles similar to those observed experimentally.

In conclusion, this work successfully pioneers single-particle IDI, enabling element-specific nanoimaging with meaningful resolution. Simultaneously, it reveals a fundamental limitation: at the high fluences required for such experiments, nonlinear effects like ASE can degrade the imaging signal. This insight is crucial for the future development of high-fluence, single-particle X-ray imaging techniques.