Imaging via Correlation of X-Ray Fluorescence Photons.

We demonstrate that x-ray fluorescence emission, which cannot maintain a stationary interference pattern, can be used to obtain images of structures by recording photon-photon correlations in the manner of the stellar intensity interferometry of Hanbury Brown and Twiss. This is achieved utilizing femtosecond-duration pulses of a hard x-ray free-electron laser to generate the emission in exposures comparable to the coherence time of the fluorescence. Iterative phasing of the photon correlation map generated a model-free real-space image of the structure of the emitters. Since fluorescence can dominate coherent scattering, this may enable imaging uncrystallised macromolecules.

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles.

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Form factor determination of biological molecules with X-ray free electron laser small-angle scattering (XFEL-SAS).

Free-electron lasers (FEL) are revolutionizing X-ray-based structural biology methods. While protein crystallography is already routinely performed at FELs, Small Angle X-ray Scattering (SAXS) studies of biological macromolecules are not as prevalent. SAXS allows the study of the shape and overall structure of proteins and nucleic acids in solution, in a quasi-native environment. In solution, chemical and biophysical parameters that have an influence on the structure and dynamics of molecules can be varied and their effect on conformational changes can be monitored in time-resolved XFEL and SAXS experiments. We report here the collection of scattering form factors of proteins in solution using FEL X-rays. The form factors correspond to the scattering signal of the protein ensemble alone; the scattering contributions from the solvent and the instrument are separately measured and accurately subtracted. The experiment was done using a liquid jet for sample delivery. These results pave the way for time-resolved studies and measurements from dilute samples, capitalizing on the intense and short FEL X-ray pulses.

Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging.

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Mid infrared polarization engineering via sub-wavelength biaxial hyperbolic van der Waals crystals.

Mid-infrared (IR) spectral region is of immense importance for astronomy, medical diagnosis, security and imaging due to the existence of the vibrational modes of many important molecules in this spectral range. Therefore, there is a particular interest in miniaturization and integration of IR optical components. To this end, 2D van der Waals (vdW) crystals have shown great potential owing to their ease of integration with other optoelectronic platforms and room temperature operation. Recently, 2D vdW crystals of [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] have been shown to possess the unique phenomenon of natural in-plane biaxial hyperbolicity in the mid-infrared frequency regime at room temperature. Here, we report a unique application of this in-plane hyperbolicity for designing highly efficient, lithography free and extremely subwavelength mid-IR photonic devices for polarization engineering. In particular, we show the possibility of a significant reduction in the device footprint while maintaining an enormous extinction ratio from [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] [Formula: see text] based mid-IR polarizers. Furthermore, we investigate the application of sub-wavelength thin films of these vdW crystals towards engineering the polarization state of incident mid-IR light via precise control of polarization rotation, ellipticity and relative phase. We explain our results using natural in-plane hyperbolic anisotropy of [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] [Formula: see text] via both analytical and full-wave electromagnetic simulations. This work provides a lithography free alternative for miniaturized mid-infrared photonic devices using the hyperbolic anisotropy of [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] [Formula: see text].

A cyclical deep learning based framework for simultaneous inverse and forward design of nanophotonic metasurfaces.

The conventional approach to nanophotonic metasurface design and optimization for a targeted electromagnetic response involves exploring large geometry and material spaces. This is a highly iterative process based on trial and error, which is computationally costly and time consuming. Moreover, the non-uniqueness of structural designs and high non-linearity between electromagnetic response and design makes this problem challenging. To model this unintuitive relationship between electromagnetic response and metasurface structural design as a probability distribution in the design space, we introduce a framework for inverse design of nanophotonic metasurfaces based on cyclical deep learning (DL). The proposed framework performs inverse design and optimization mechanism for the generation of meta-atoms and meta-molecules as metasurface units based on DL models and genetic algorithm. The framework includes consecutive DL models that emulate both numerical electromagnetic simulation and iterative processes of optimization, and generate optimized structural designs while simultaneously performing forward and inverse design tasks. A selection and evaluation of generated structural designs is performed by the genetic algorithm to construct a desired optical response and design space that mimics real world responses. Importantly, our cyclical generation framework also explores the space of new metasurface topologies. As an example application of the utility of our proposed architecture, we demonstrate the inverse design of gap-plasmon based half-wave plate metasurface for user-defined optical response. Our proposed technique can be easily generalized for designing nanophtonic metasurfaces for a wide range of targeted optical response.