Single-stranded RNA viruses co-assemble their capsid with the genome, and variations in capsid structures can have significant functional relevance. In particular, viruses need to respond to a dehydrating environment to prevent genomic degradation and remain active upon rehydration. Theoretical work has predicted low-energy buckling transitions in icosahedral capsids, which could protect the virus from further dehydration. However, there has been no direct experimental evidence, nor a molecular mechanism, for such behavior. Here, we observe this transition using X-ray single particle imaging of MS2 bacteriophages after aerosolization. Using a combination of machine learning tools, we classify hundreds of thousands of single-particle diffraction patterns to learn the structural landscape of the capsid morphology as a function of time spent in the aerosol phase. We found a previously unreported compact conformation as well as intermediate structures that suggest an incoherent buckling transition that does not preserve icosahedral symmetry. Finally, we propose a mechanism for this buckling, where a single 19-residue loop is destabilized, leading to the large observed morphological change. Our results provide experimental evidence for a mechanism by which viral capsids may protect themselves from dehydration upon aerosolization. In the process, these findings also demonstrate the power of single-particle X-ray imaging and machine learning methods in studying biomolecular structural dynamics.

Single-particle small-angle X-ray scattering (SP-SAXS) at X-ray free electron lasers (XFELs) enables quantitative analysis of morphological heterogeneity that is fundamentally inaccessible to ensemble-averaged in situ techniques. By recording diffraction snapshots from isolated particles, SP-SAXS resolves low-contrast, less abundant, or transient species within heterogeneous particle populations that would otherwise remain hidden to conventional X-ray techniques. We demonstrate this unique capability by investigating the solvothermal formation of CoO nanocrystal assemblies from a Co(acac)₃ precursor in benzyl alcohol. The single-particle data revealed amorphous, uniform-density Co(acac)₂ spheres as transient intermediates that directly crystallize into cavernous CoO nanocrystal assemblies, explaining why CoO forms as hierarchical aggregates rather than as isolated nanocrystals. These results establish SP-SAXS as a uniquely powerful framework for uncovering nonclassical nanoparticle formation pathways hidden in ensemble measurements.

X-ray single particle imaging (SPI) has offered the potential to visualize structures of biomolecules at near-atomic resolution. However, state-of-the-art structures at X-ray free electron lasers (XFELs) are limited to moderate resolution, primarily due to background scattering. We computationally explore a modified SPI technique based on holographic enhancement from a strongly scattering 2D crystal lattice placed near the object. The Bragg peaks from the crystal enable structure retrieval even for background levels up to 10⁵ times higher than the object signal. This method could enable SPI at more widely accessible synchrotron sources, where even detection of objects before radiation damage is nearly impossible currently, supports practical fixed-target sample delivery, and enables high-resolution imaging under near-native conditions. Numerical simulations with a custom reconstruction algorithm to recover the latent parameters show the potential to improve the achievable resolution while also expanding the accessibility to the technique.

This dissertation presents methods to improve X-ray single-particle imaging (SPI) for recovering detailed 3D structures of nanoscale biomolecules — such as viruses and proteins — at synchrotrons and X-ray free-electron laser sources (XFELs). Specifically, it addresses challenges posed by structural heterogeneity in the sample of interest and high background noise akin to experiments, both of which significantly limit the achievable near-atomic resolution.

Advancements in optical quantum technologies have been enabled by the generation, manipulation, and characterization of light, with identification based on its photon statistics. However, characterizing light and its sources through single photon measurements requires efficient detectors and longer measurement times to obtain high-quality photon statistics. Here, a deep learning-based variational autoencoder (VAE) method is introduced for classifying single photon added coherent state (SPACS), single photon added thermal state (SPATS), and mixed states between coherent and SPACS as well as between thermal and SPATS of light. The semi-supervised learning-based VAE efficiently maps the photon statistics features of light to a lower dimension, enabling quasi-instantaneous classification with low average photon counts. The proposed VAE method is robust and maintains classification accuracy in the presence of losses inherent in an experiment, such as finite collection efficiency, non-unity quantum efficiency, finite number of detectors, etc. Additionally, leveraging the transfer learning capabilities of VAE enables successful classification of data of any quality using a single trained model. It is envisioned that such a deep learning methodology will enable better classification of quantum light and light sources even in poor detection.

The outstanding optoelectronic properties of lead halide perovskites have been related to the formation of polarons. Nevertheless, the observation of the atomistic deformation brought about by one electron–hole pair in these materials has remained elusive. Here, we measure the transient structure of single CsPbBr₃ quantum dots (QDs) after resonant excitation in the single exciton limit using serial femtosecond crystallography (SFX). By reconstructing the three-dimensional (3D) differential diffraction pattern and building on density functional theory (DFT) calculations, we assign the lattice distortion after photoexcitation to the combined presence of a delocalized electron and a localized hole, forming a mixed large/small exciton-polaron. This result creates a clear picture of the polaronic deformation in CsPbBr₃ QDs and demonstrates the exceptional sensitivity of SFX to lattice distortions in few-nanometer crystallites. We plan to use this experimental platform for future studies of electron–lattice interactions.

Coherent Diffraction Imaging (CDI) is an experimental technique to image isolated structures by recording the scattered light. The sample density can be recovered from the scattered field through a Fourier Transform operation. However, the phase of the field is lost during the measurement and has to be algorithmically retrieved. Here we present SPRING, an analysis framework tailored to X-ray Free Electron Laser (XFEL) single-shot single-particle diffraction data that implements the Memetic Phase Retrieval method to mitigate the shortcomings of conventional algorithms. We benchmark the approach on data acquired in two experimental campaigns at SwissFEL and European XFEL. Results reveal unprecedented stability and resilience of the algorithm’s behavior on the input parameters, and the capability of identifying the solution in conditions hardly treatable with conventional methods. A user-friendly implementation of SPRING is released as open-source software, aiming at being a reference tool for the CDI community at XFEL and synchrotron facilities.

Materials exposed to intense femtosecond X-ray pulses with energies above their K-shell absorption edge can enter an extremely ionized state, which could give rise to nonlinear phenomena, such as saturable absorption and reverse saturable absorption. In this work, we investigate these effects on single copper nanoparticles irradiated by an X-ray free-electron laser pulse. We study the properties of the Kα fluorescence for two different short pulse durations and three X-ray incident energies below and above the K-shell absorption edge, and correlate these with incident fluence estimates based on coherent diffraction. We observe that the incident fluence of the pulse and not its duration, is the main factor that modulates the nonlinear response, which leads to an effective shortening of the fluorescence emission. Our findings have implications for fluorescence-based methods for imaging single particles using transiently coherent fluorescence, or diffractive imaging through transient resonances.

We demonstrate element-specific incoherent diffractive imaging (IDI) of single copper nanocubes using intensity correlations of Kα 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 10² J/cm², consistent with the assumption of amplified spontaneous emission. Our results reveal fundamental limits for high-fluence nanoimaging towards future single-particle X-ray imaging.

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.

Single-particle imaging (SPI) at x-ray free-electron lasers is a technique to determine the three-dimensional structure of nanoscale objects like biomolecules from a large number of diffraction patterns of copies of these objects in random orientations. The technique has been limited to relatively low resolution due to background noise and heterogeneity of the target particles. A recently introduced reference-enhanced holographic SPI methodology uses strongly scattering holographic references to improve background tolerance, and, thus, the achievable resolution, at the cost of additional latent variables beyond orientation. Here, we describe an improved reconstruction algorithm based on maximum likelihood estimation, which scales better, enabling fine sampling of latent parameters to reach high resolutions, and much better performance in the low signal limit. Furthermore, we show that structural variations within the target particle are averaged in real space, significantly improving robustness to conformational heterogeneity in comparison to conventional SPI. With these computational improvements, we believe reference-enhanced SPI is capable of reaching sub-nanometer resolution biomolecule imaging.

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.

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.

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 (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 α-MoO₃ and α-V₂O₅ 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 α-MoO₃ and α-V₂O₅ 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 α-MoO₃ and α-V₂O₅ 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 α-MoO₃ and α-V₂O₅.

Metasurfaces is an emerging field that enables the manipulation of light by an ultra-thin structure composed of sub-wavelength antennae and fulfills an important requirement for miniaturized optical elements. Finding a new design for a metasurface or optimizing an existing design for a desired functionality is a computationally expensive and time consuming process as it is based on an iterative process of trial and error. We propose a deep learning (DL) architecture dubbed bidirectional autoencoder for nanophotonic metasurface design via a template search methodology. In contrast with the earlier approaches based on DL, our methodology addresses optimization in the space of multiple metasurface topologies instead of just one, in order to tackle the one to many mapping problem of inverse design. We demonstrate the creation of a Geometry and Parameter Space Library (GPSL) of metasurface designs with their corresponding optical response using our DL model. This GPSL acts as a universal design and response space for the optimization. As an example application, we use our methodology to design a multi-band gap-plasmon based half-wave plate metasurface. Through this example, we demonstrate the power of our technique in addressing the non-uniqueness problem of common inverse design. Our network converges aptly to multiple metasurface topologies for the desired optical response with a low mean absolute error between desired optical response and the optical response of topologies searched. Our proposed technique would enable fast and accurate design and optimization of various kinds of metasurfaces with different functionalities.

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.