Potential of Attosecond Coherent Diffractive Imaging

Topological links and knots of speckled light mediated by coherence singularities

Links and knots are exotic topological structures that have garnered significant interest across multiple branches of natural sciences. Coherent links and knots, such as those constructed by phase or polarization singularities of coherent light, have been observed in various three-dimensional optical settings. However, incoherent links and knots-knotted or connected lines of coherence singularities-arise from a fundamentally different concept. They are "hidden" in the statistic properties of a randomly fluctuating field, making their presence often elusive or undetectable. Here, we theoretically construct and experimentally demonstrate such topological entities of incoherent light. By leveraging a state-of-the-art incoherent modal-decomposition scheme, we unveil incoherent topological structures from fluctuating light speckles, including Hopf links and Trefoil knots of coherence singularities that are robust against coherence and intensity fluctuations. Our work is applicable to diverse wave systems where incoherence or practical coherence is prevalent, and may pave the way for design and implementation of statistically-shaped topological structures for various applications such as high-dimensional optical information encoding and optical communications.

Robust broadband ptychography algorithms for high-harmonic soft X-ray supercontinua

We demonstrate PaCMAN, a ptychography algorithm that can reconstruct high quality images with broadband illumination sources while being robust to shot, detector, and parasitic noise. We extend prior monochromatization work to improve accuracy, especially for discrete spectra, and also demonstrate how PaCMAN can be converted into Ms. PaCMAN, a multi-spectral variant that outperforms multi-spectral ePIE. When comparing speed-optimized ePIE and PaCMAN, we achieve high reconstruction quality in 4x less time, and when they are dose-optimized, we achieve high reconstruction quality in 1.5-2x less dose. These algorithms will enable rapid sub-10 nm imaging with table-top soft X-ray high harmonic supercontinua, advance attosecond coherent diffractive imaging, and reduce the dose needed to image radiation sensitive materials.

A high-performance reconstruction method for partially coherent ptychography

Ptychography is now integrated as a tool in mainstream microscopy allowing quantitative and high-resolution imaging capabilities over a wide field of view. However, its ultimate performance is inevitably limited by the available coherent flux when implemented using electrons or laboratory X-ray sources. We present a universal reconstruction algorithm with high tolerance to low coherence for both far-field and near-field ptychography. The approach is practical for partial temporal and spatial coherence and requires no prior knowledge of the source properties. Our initial visible-light and electron data show that the method can dramatically improve the reconstruction quality and accelerate the convergence rate of the reconstruction. The approach also integrates well into existing ptychographic engines. It can also improve mixed-state and numerical monochromatisation methods, requiring a smaller number of coherent modes or lower dimensionality of Krylov subspace while providing more stable and faster convergence. We propose that this approach could have significant impact on ptychography of weakly scattering samples.

Spectral multiplexing based on multi-distance lensless imaging

We have demonstrated the capability of spectral multiplexing in multi-distance diffractive imaging, enabling the reconstruction of samples with diverse spectral responses. While previous methods such as ptychography utilize redundancy in radial diffraction data to achieve information multiplexing, they typically require capturing a substantial amount of diffraction data. In contrast, our approach effectively harnesses the redundancy information in axial diffraction data. This significantly reduces the amount of diffraction data required and relaxes the stringent requirements on optical path stability.

Ultra-broadband diffractive imaging with unknown probe spectrum

Strict requirement of a coherent spectrum in coherent diffractive imaging (CDI) architectures poses a significant obstacle to achieving efficient photon utilization across the full spectrum. To date, nearly all broadband computational imaging experiments have relied on accurate spectroscopic measurements, as broad spectra are incompatible with conventional CDI systems. This paper presents an advanced approach to broaden the scope of CDI to ultra-broadband illumination with unknown probe spectrum, effectively addresses the key challenges encountered by existing state-of-the-art broadband diffractive imaging frameworks. This advancement eliminates the necessity for prior knowledge of probe spectrum and relaxes constraints on non-dispersive samples, resulting in a significant extension in spectral bandwidth, achieving a nearly fourfold improvement in bandlimit compared to the existing benchmark. Our method not only monochromatizes a broadband diffraction pattern from unknown illumination spectrum, but also determines the compressive sampled profile of spectrum of the diffracted radiation. This superiority is experimentally validated using both CDI and ptychography techniques on an ultra-broadband supercontinuum with relative bandwidth exceeding 40%, revealing a significantly enhanced coherence and improved reconstruction with high fidelity under ultra-broadband illumination.

Fast spectroscopic imaging using extreme ultraviolet interferometry

Extreme ultraviolet pulses as generated by high harmonic generation (HHG) are a powerful tool for both time-resolved spectroscopy and coherent diffractive imaging. However, the integration of spectroscopy and microscopy to harness the unique broadband spectra provided by HHG is hardly explored due to the challenge to decouple spectroscopic and microscopic information. Here, we present an interferometric approach to this problem that combines Fourier transform spectroscopy (FTS) with Fourier transform holography (FTH). This is made possible by the generation of phase-locked pulses using a pair of HHG sources. Crucially, in our geometry the number of interferometric measurements required is at most equal to the number of high-harmonics in the illumination, and can be further reduced by incorporating prior knowledge about the structure of the FTH sample. Compared to conventional FTS, this approach achieves over an order of magnitude increase in acquisition speed for full spectro-microscopic data, and furthermore allows high-resolution computational imaging.

Four-dimensional experimental characterization of partially coherent light using incoherent modal decomposition

The intensity distributions and statistics of partially coherent light fields with random fluctuations have proven to be more robust than for coherent light. However, its full potential in practical applications has not been realized due to the lack of four-dimensional optical field measurement. Here, a general incoherent modal decomposition method of partially coherent light field is proposed and demonstrated experimentally. The decomposed random modes can be used to, but not limited to, reconstruct average intensity, cross-spectral density, and orthogonal decomposition properties of the partially coherent light fields. The versatility and flexibility of this method allows it to reveal the invariance of light fields and to retrieve embedded information after propagation through complex media. The Gaussian-shell-model beam and partially coherent Gaussian array are used as examples to demonstrate the reconstruction and even prediction of second-order statistics. This method is expected to pave the way for applications of partially coherent light in optical imaging, optical encryption, and antiturbulence optical communication.

Phase retrieval with a dual recursive scheme

Since optical sensors cannot detect the phase information of the light wave, recovering the missing phase from the intensity measurements, called phase retrieval (PR), is a natural and important problem in many imaging applications. In this paper, we propose a learning-based recursive dual alternating direction method of multipliers, called RD-ADMM, for phase retrieval with a dual and recursive scheme. This method tackles the PR problem by solving the primal and dual problems separately. We design a dual structure to take advantage of the information embedded in the dual problem that can help with solving the PR problem, and we show that it is feasible to use the same operator for both the primal and dual problems for regularization. To demonstrate the efficiency of this scheme, we propose a learning-based coded holographic coherent diffractive imaging system to generate the reference pattern automatically according to the intensity information of the latent complex-valued wavefront. Experiments on different kinds of images with a high noise level indicate that our method is effective and robust, and can provide higher-quality results than other commonly-used PR methods for this setup.

Deep-Learning Electron Diffractive Imaging

We report the development of deep-learning coherent electron diffractive imaging at subangstrom resolution using convolutional neural networks (CNNs) trained with only simulated data. We experimentally demonstrate this method by applying the trained CNNs to recover the phase images from electron diffraction patterns of twisted hexagonal boron nitride, monolayer graphene, and a gold nanoparticle with comparable quality to those reconstructed by a conventional ptychographic algorithm. Fourier ring correlation between the CNN and ptychographic images indicates the achievement of a resolution in the range of 0.70 and 0.55 Å. We further develop CNNs to recover the probe function from the experimental data. The ability to replace iterative algorithms with CNNs and perform real-time atomic imaging from coherent diffraction patterns is expected to find applications in the physical and biological sciences.

Extension of the bright high-harmonic photon energy range via nonadiabatic critical phase matching

The concept of critical ionization fraction has been essential for high-harmonic generation, because it dictates the maximum driving laser intensity while preserving the phase matching of harmonics. In this work, we reveal a second, nonadiabatic critical ionization fraction, which substantially extends the phase-matched harmonic energy, arising because of the strong reshaping of the intense laser field in a gas plasma. We validate this understanding through a systematic comparison between experiment and theory for a wide range of laser conditions. In particular, the properties of the high-harmonic spectrum versus the laser intensity undergoes three distinctive scenarios: (i) coincidence with the single-atom cutoff, (ii) strong spectral extension, and (iii) spectral energy saturation. We present an analytical model that predicts the spectral extension and reveals the increasing importance of the nonadiabatic effects for mid-infrared lasers. These findings are important for the development of high-brightness soft x-ray sources for applications in spectroscopy and imaging.

Self-probed ptychography from semiconductor high-harmonic generation

We demonstrate a method to image an object using a self-probing approach based on semiconductor high-harmonic generation. On the one hand, ptychography enables high-resolution imaging from the coherent light diffracted by an object. On the other hand, high-harmonic generation from crystals is emerging as a new source of extreme-ultraviolet ultrafast coherent light. We combine these two techniques by performing ptychography measurements with nanopatterned crystals serving as the object as well as the generation medium of the harmonics. We demonstrate that this strong field in situ approach can provide structural information about an object. With the future developments of crystal high harmonics as a compact short-wavelength light source, our demonstration can be an innovative approach for nanoscale imaging of photonic and electronic devices in research and industry.

Temporal and spectral multiplexing for EUV multibeam ptychography with a high harmonic light source

We demonstrate temporally multiplexed multibeam ptychography implemented for the first time in the EUV, by using a high harmonic based light source. This allows for simultaneous imaging of different sample areas, or of the same area at different times or incidence angles. Furthermore, we show that this technique is compatible with wavelength multiplexing for multibeam spectroscopic imaging, taking full advantage of the temporal and spectral characteristics of high harmonic light sources. This technique enables increased data throughput using a simple experimental implementation and with high photon efficiency.

A Nonlinear Magnetoelastic Energy Model and Its Application in Domain Wall Velocity Prediction

In this letter, we propose a nonlinear Magnetoelastic Energy (ME) with a material parameter related to electron interactions. An attenuating term is contained in the formula of the proposed nonlinear ME, which can predict the variation in the anisotropic magneto-crystalline constants induced by external stress more accurately than the classical linear ME. The domain wall velocity under stress and magnetic field can be predicted accurately based on the nonlinear ME. The proposed nonlinear ME model is concise and easy to use. It is important in sensor analysis and production, magneto-acoustic coupling motivation, magnetoelastic excitation, etc.

Spatiospectral characterization of ultrafast pulse-beams by multiplexed broadband ptychography

Ultrafast pulse-beam characterization is critical for diverse scientific and industrial applications from micromachining to generating the highest intensity laser pulses. The four-dimensional structure of a pulse-beam, E~(x,y,z,ω), can be fully characterized by coupling spatiospectral metrology with spectral phase measurement. When temporal pulse dynamics are not of primary interest, spatiospectral characterization of a pulse-beam provides crucial information even without spectral phase. Here we demonstrate spatiospectral characterization of pulse-beams via multiplexed broadband ptychography. The complex spatial profiles of multiple spectral components, E~(x,y,ω), from modelocked Ti:sapphire and from extreme ultra-violet pulse-beams are reconstructed with minimum intervening optics and no refocusing. Critically, our technique does not require spectral filters, interferometers, or reference pulses.

Quantitative hyperspectral coherent diffractive imaging spectroscopy of a solid-state phase transition in vanadium dioxide

Solid-state systems can host a variety of thermodynamic phases that can be controlled with magnetic fields, strain, or laser excitation. Many phases that are believed to exhibit exotic properties only exist on the nanoscale, coexisting with other phases that make them challenging to study, as measurements require both nanometer spatial resolution and spectroscopic information, which are not easily accessible with traditional x-ray spectromicroscopy techniques. Here, we use coherent diffractive imaging spectroscopy (CDIS) to acquire quantitative hyperspectral images of the prototypical quantum material vanadium oxide across the vanadium L 2,3 and oxygen K x-ray absorption edges with nanometer-scale resolution. We extract the full complex refractive indices of the monoclinic insulating and rutile conducting phases of VO2 from a single sample and find no evidence for correlation-driven phase transitions. CDIS will enable quantitative full-field x-ray spectromicroscopy for studying phase separation in time-resolved experiments and other extreme sample environments where other methods cannot operate.

Agile spectral tuning of high order harmonics by interference of two driving pulses

In this work, the experimental realization of a tunable high photon flux extreme ultraviolet light source is presented. This is enabled by high harmonic generation of two temporally delayed driving pulses with a wavelength of 1030 nm, resulting in a tuning range of 0.8 eV at the 19th harmonic at 22.8 eV. The implemented approach allows for fast tuning of the spectrum, is highly flexible and is scalable towards full spectral coverage at higher photon energies.