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Single-shot ptychography is a quantitative phase imaging method wherein overlapping beams of light arranged in a grid pattern simultaneously illuminate a sample, allowing a full ptychographic dataset to be collected in a single shot. It is primarily used at optical wavelengths, but there is interest in using it for X-ray imaging. However, the constraints imposed by X-ray optics have limited the resolution achievable to date. In this work, we reinterpret single-shot ptychography as a structured illumination method by viewing the grid of beams as a single, highly structured illumination function. Pre-calibrating this illumination and reconstructing single-shot data using the randomized probe imaging algorithm allows us to account for the overlap and coherent interference between the diffraction arising from each beam. We achieve a resolution 3.5 times finer than the numerical aperture-based limit imposed by traditional algorithms for single-shot ptychography. We argue that this reconstruction method will work better for most single-shot ptychography experiments and discuss the implications for the design of future single-shot X-ray microscopes., Comment: 4 pages, 3 figures

High-harmonic generation (HHG) is a nonlinear process in which a material sample is irradiated by intense laser pulses, causing the emission of high harmonics of the incident light. HHG has historically been explained by theories employing a classical electromagnetic field, successfully capturing its spectral and temporal characteristics. However, recent research indicates that quantum-optical effects naturally exist, or can be artificially induced, in HHG. Even though the fundamental equations of motion for quantum electrodynamics (QED) are well-known, a unifying framework for solving them to explore HHG is missing. So far, numerical solutions employed a wide range of basis-sets and untested approximations. Based on methods originally developed for cavity polaritonics, here we formulate a numerically accurate QED model consisting of a single active electron and a single quantized photon mode. Our framework can in principle be extended to higher electronic dimensions and multiple photon modes to be employed in ab initio codes. We employ it as a model of an atom interacting with a photon mode and predict a characteristic minimum structure in the HHG yield vs. phase-squeezing. We find that this phenomenon, which can be used for novel ultrafast quantum spectroscopies, is partially captured by a multi-trajectory Ehrenfest dynamics approach, with the exact minima position sensitive to the level of theory. On the one hand, this motivates using multi-trajectory approaches as an alternative for costly exact calculations. On the other hand, it suggests an inherent limitation of the multi-trajectory formalism, indicating the presence of entanglement. Our work creates a road-map for a universal formalism of QED-HHG that can be employed for benchmarking approximate theories, predicting novel phenomena for advancing quantum applications, and for the measurements of entanglement and entropy., Comment: 10 pages, 7 figures

Dynamical symmetries of laser-dressed matter determine selection rules that determine its absorption spectrum. We explore selection rules for polarization-sensitive absorption in Floquet matter, using Floquet group theory in synthetic dimensions. We present comprehensive tables of selection rules that polarization-structured light impose on Floquet dark states and Floquet dark bands. Notably, our tables encompass nonlinear absorption, to all nonlinear orders, revealing that different nonlinear orders follow distinct polarization selection rules, potentially leading to polarization-tunable optical filters.

We demonstrate that phase-matched frequency upconversion of ultrafast laser light can be extended to shorter wavelengths by using longer driving laser wavelengths. Experimentally, we show that the phase-matching cutoff for harmonic generation in argon increases from 45 to 100 eV when the driving laser wavelength is increased from 0.8 to 1.3 micrometers. Phase matching is also obtained at higher pressures using a longer-wavelength driving laser, mitigating the unfavorable scaling of the single-atom response. Theoretical calculations suggest that phase-matched high harmonic frequency upconversion driven by mid-infrared pulses could be extended to extremely high photon energies., Comment: 10 pages, 3 figures

We show how bright, fully coherent, hard x-ray beams can be generated through nonlinear upconversion of femtosecond laser light. By using longer-wavelength mid-infrared driving lasers of moderate peak intensity, full phase matching of the high harmonic generation process can extend, in theory, into the hard x-ray region of the spectrum. We identify the dominant phase matching mechanism for long wavelength driving lasers, and verify our predictions experimentally by demonstrating phase-matched up-conversion into the soft x-ray region of the spectrum around 330 eV using an extended, high-pressure, gas medium that is weakly ionized by the laser. Scaling of the overall conversion efficiency is surprisingly favorable as the wavelength of the driving laser is increased, making useful, fully coherent, multi-keV x-ray sources feasible. Finally, we show that the rapidly decreasing microscopic single-atom yield at longer driving wavelengths is compensated macroscopically by an increasing optimal pressure for phase matching and a rapidly decreasing reabsorption of the generated light at higher photon energies., Comment: 43 pages, 8 figures, 1 table

For decades, most research on high harmonic generation (HHG) considered matter as quantum but light as classical, leaving the quantum-optical nature of the harmonics an open question. Here we explore the quantum properties of high harmonics. We derive a formula for the quantum state of the high harmonics, when driven by arbitrary quantum light states, and then explore specific cases of experimental relevance. Specifically, for a moderately squeezed pump, HHG driven by squeezed coherent light results in squeezed high harmonics. Harmonic squeezing is optimized by syncing ionization times with the pump's squeezing phase. Beyond this regime, as pump squeezing is increased, the harmonics initially acquire squeezed thermal photon statistics, and then occupy an intricate quantum state which strongly depends on the semi-classical nonlinear response function of the interacting system. Our results pave the way for the generation of squeezed extreme-ultraviolet ultrashort pulses, and, more generally, quantum frequency conversion into previously inaccessible spectral ranges, which may enable ultrasensitive attosecond metrology.

Conservation laws are one of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization and frequencies of the emitted radiation. Here we present a new scheme to derive conservation laws in optical parametric processes in which many photons are annihilated and a single new photon is emitted. We then utilize it to derive two new such conservation laws. Conservation of reflection-parity (RP) arises from a generalized reflection symmetry of the polarization in a superspace, analogous to the superspace employed in the study of quasicrystals. Conservation of space-time-parity (STP) similarly arises from space-time reversal symmetry in superspace. We explore these new conservation laws numerically in the context of high harmonic generation and outline experimental set-ups where they can be tested.

Entangled photon pairs are a vital resource for quantum information, computation, and metrology. Although these states are routinely generated at optical frequencies, sources of quantum of light are notably lacking at extreme ultraviolet (XUV) and soft X-ray frequencies. Here, we show that strongly driven systems used for high harmonic generation (HHG) can become versatile sources of entangled photon pairs at these high frequencies. We present a general theory of photon pair emission from non-perturbatively driven systems, which we refer to as "strong field pair generation" (SFPG). We show that strongly driven noble gases can generate thousands of entangled pairs per shot over a large XUV bandwidth. The emitted pairs have distinctive properties in angle and frequency, which can be exploited to discriminate them from the background HHG signal. We connect SFPG theory to the three-step-model of HHG, showing that this pair emission originates from the impact of high frequency vacuum fluctuations on electron recombination. The light produced by SFPG exhibits attosecond Hong-Ou-Mandel correlations, and can be leveraged as a source of heralded single photon attosecond pulses. Our findings aid ongoing efforts to propel quantum optics into the XUV and beyond.

The motion of laser-driven electrons quivers with an average energy termed pondermotive energy. We explore electron dynamics driven by bright squeezed vacuum (BSV), finding that BSV induces width oscillations, akin to electron quivering in laser light, with an equivalent ponderomotive energy. In the case of bound electrons, width oscillations may lead to tunnel ionization with noisy sub-cycle structure. Our results are foundational for strong-field and free-electron quantum optics, as they shed light on tunnel ionization, high harmonic generation, and nonlinear Compton scattering in BSV.

High harmonic generation (HHG) is an extreme nonlinear process where intense pulses of light drive matter to emit high harmonics of the driving frequency, reaching the extreme ultraviolet (XUV) and x-ray spectral ranges. So far, the HHG process was always generated by intense laser pulses that are well described as a classical electromagnetic field. Advances in the generation of intense squeezed light motivate us to revisit the fundamentals of HHG and ask how the photon statistics of light may alter this process, and more generally alter the field of extreme nonlinear optics. The role of photon statistics in non-perturbative interactions of intense light with matter has remained unexplored in both experiments and theory. Here we show that the defining spectral characteristics of HHG, such as the plateau and cutoff, are sensitive to the photon statistics of the driving light. While coherent (classical) and Fock light states induce the established HHG cutoff law, thermal and squeezed states substantially surpass it, extending the cutoff compared to classical light of the same intensity. Hence, shaping the photon statistics of light enables producing far higher harmonics in HHG. We develop the theory of extreme nonlinear optics driven by squeezed light, and more generally by arbitrary quantum states of light. Our work introduces quantum optical concepts to strong-field physics as new degrees of freedom in the creation and control of HHG, and finally shows that experiments in this field are feasible. Looking forward, HHG driven by quantum light creates quantum states of XUV and X-rays, enabling applications of quantum optics in new spectral regimes.

In strong-field physics and attosecond science, intense light induces ultrafast electron dynamics. Such ultrafast dynamics of electrons in matter is at the core of phenomena such as high harmonic generation (HHG), where these dynamics lead to emission of extreme UV bursts with attosecond duration. So far, all ultrafast dynamics of matter were understood to originate purely from the classical vector potential of the driving light, disregarding the influence of the quantum nature of light. Here we show that dynamics of matter driven by bright (intense) light significantly depend on the quantum state of the driving light, which induces an effective photon-statistics force. To provide a unified framework for the analysis & control over such a force, we extend the strong-field approximation (SFA) theory to account for non-classical driving light. Our quantum SFA (qSFA) theory shows that in HHG, experimentally feasible squeezing of the driving light can shift & shape electronic trajectories and attosecond pulses at the scale of hundreds of attoseconds. Our work presents a new degree-of-freedom for attosecond spectroscopy, by relying on nonclassical electromagnetic fields, and more generally, introduces a direct connection between attosecond science and quantum optics.

Synthetic chiral light fields were recently introduced as a novel source of chirality [Ayuso et al. Nat. Phot. 13, 866 (2019)]. This locally-chiral light spans a three-dimensional polarization that plots a chiral trajectory in space-time, leading to huge nonlinear chiral signals upon interactions with chiral media. The degree of chirality of this new form of light was defined, characterized, and shown to be proportional to the chiral signal conversion efficiency. However, the sign of the light's chirality - its 'handedness' - has not yet been defined. Standard definitions of helicity are inapplicable for locally-chiral light due to its complex three-dimensional structure. Here, we define an unambiguous handedness for locally-chiral fields and employ it in practical calculations., Comment: 7 pages, 3 figures

Characterizing chirality is highly important for applications in the pharmaceutical industry, as well as in the study of dynamical chemical and biological systems. However, this task has remained challenging, especially due to the ongoing increasing complexity and size of the molecular structure of drugs and active compounds. In particular, large molecules with many active chirality centers are today ubiquitous, but remain difficult to structurally analyze due to their high number of stereoisomers. Here we theoretically explore the sensitivity of high harmonic generation (HHG) to the chirality of molecules with a varying number of active chiral centers. We find that HHG driven by bi-chromatic non-collinear lasers is a sensitive probe for the stereo-configuration of a chiral molecule. We first show through calculations (from benchmark chiral molecules with up to three chirality centers) that the HHG spectrum is imprinted with information about the handedness of each chirality center in the driven molecule. Next, we show that using both classical- and deep-learning-based reconstruction algorithms, the composition of an unknown mixture of stereoisomers can be reconstructed with high fidelity by a single-shot HHG measurement. Our work illustrates how the combination of non-linear optics and machine learning might open routes for ultra-sensitive sensing in chiral systems., Comment: 8 pages, 6 figures, 1 page SM

Symmetries and their associated selection rules are extremely useful in all fields of science. In particular, for system that include electromagnetic (EM) fields interacting with matter, it has been shown that both of symmetries of matter and EM field's time-dependent polarization play a crucial role in determining the properties of linear and nonlinear responses. The relationship between the system's symmetry and the properties of its excitations facilitate precise control over light emission and enable ultrafast symmetry-breaking spectroscopy of variety of properties. Here. we formulate the first general theory that describes the macroscopic dynamical symmetries (including quasicrystal-like symmetries) of an EM vector field, revealing many new symmetries and selection rules in light-matter interactions. We demonstrate an example of multi-scale selection rules experimentally in the framework of high harmonic generation (HHG). This work waves the way for novel spectroscopic techniques in multi-scale system as well as for imprinting complex structures in EUV-X-ray beams, attosecond pulses, or the interacting medium itself., Comment: 27 pages, 5 figures

Selection rules are often considered a hallmark of symmetry. When a symmetry is broken, e.g., by an external perturbation, the system exhibits selection rule deviations which are often analyzed by perturbation theory. Here, we employ symmetry-breaking degrees of freedom as synthetic dimensions, to demonstrate that symmetry-broken systems systematically exhibit a new class of symmetries and selection rules. These selection rules determine the scaling of a system's observables (to all orders in the strength of the symmetry-breaking perturbation) as it transitions from symmetric to symmetry-broken. We specifically analyze periodically driven (Floquet) systems subject to two driving fields, where the first field imposes a spatio-temporal symmetry, and the second field breaks it, imposing a symmetry in synthetic dimensions. We tabulate the resulting synthetic symmetries for (2+1)D Floquet group symmetries and derive the corresponding selection rules for high harmonic generation (HHG) and above-threshold ionization (ATI). Finally, we observe experimentally HHG selection rules imposed by symmetries in synthetic dimensions. The new class of symmetries & selection rules extends the scope of existing symmetry breaking spectroscopy techniques, opening new routes for ultrafast spectroscopy of phonon-polarization, spin-orbit coupling, and more.

We propose a simple all-in-line single-shot scheme for diagnostics of ultrashort laser pulses, consisting of a multi-mode fiber, a nonlinear crystal and a CCD camera. The system records a 2D spatial intensity pattern, from which the pulse shape (amplitude and phase) are recovered, through a fast Deep Learning algorithm. We explore this scheme in simulations and demonstrate the recovery of ultrashort pulses, robustness to noise in measurements and to inaccuracies in the parameters of the system components. Our technique mitigates the need for commonly used iterative optimization reconstruction methods, which are usually slow and hampered by the presence of noise. These features make our concept system advantageous for real time probing of ultrafast processes and noisy conditions. Moreover, this work exemplifies that using deep learning we can unlock new types of systems for pulse recovery.

High harmonic generation (HHG) is an extremely nonlinear effect, where a medium is driven by a strong laser field, generating coherent broadband radiation with photon energies ranging up to the X-ray and pulse durations reaching attosecond timescales. Conventional models of HHG treat the medium quantum mechanically, while the driving and emitted fields are treated classically. Such models are usually very successful, but inherently cannot capture the quantum-optical nature of the process. Despite prior works considering quantum HHG, it is still not known in what circumstances the spectral and statistical properties of the radiation considerably depart from the known phenomenology of HHG. Finding such regimes in HHG could lead to novel sources of attosecond light with intrinsically quantum statistics such as squeezing and entanglement. In this work, we present a fully quantum electrodynamical theory of extreme nonlinear optics with which we predict new quantum effects that alter both spectral and statistical properties of HHG. We predict the emission of shifted frequency combs resulting from transitions between perturbed states of the driven atom, and identify new spectral features that arise from the breakdown of the dipole approximation for the emission. Moreover, we find that each HHG emitted photon is a superposition of all frequencies in the spectrum - e.g., HHG creates single photon combs. We also describe how the HHG process changes in the single atom regime, and discuss how our various predictions can be tested experimentally. Our approach is also applicable to a wide range of nonlinear optical processes, paving the way toward novel quantum information techniques in the EUV and X-ray, and in ultrafast quantum optics., Comment: 19 pages, 4 figures

Light is one of the most powerful and precise tools allowing us to control, shape and create new phases of matter. In this task, the magnetic component of a light wave has so far played a unique role in defining the wave's helicity, but its influence on the optical response of matter is weak. Chiral molecules offer a typical example where the weakness of magnetic interactions hampers our ability to control the strength of their chiral optical response. It is limited several orders of magnitude below the full potential. Here we introduce freely propagating locally and globally chiral electric fields, which interact with chiral quantum systems extremely efficiently. To demonstrate the degree of control enabled by such fields, we focus on the nonlinear optical response of randomly oriented chiral molecules. We show full control over intensity, polarization and propagation direction of the chiral optical response, enabling its background-free detection. This response can be fully suppressed or enhanced at will depending on the molecular handedness, achieving the ultimate limit in chiral discrimination. Our findings open a way to extremely efficient control of chiral matter and to ultrafast imaging of chiral structure and dynamics in gases, liquids and solids., Comment: Major revision of the manuscript that introduces new concepts and considerably extends the scope of the work

We propose and numerically demonstrate a new very robust and highly selective method for femtosecond time-resolved chiral spectroscopy using high harmonic generation (HHG). The method is based on dynamical symmetry breaking from chiral media, and relies only on intense electric-dipole transitions, and not on the interplay of electric and magnetic dipoles. The symmetry breaking results in the emission of a strong chiral signal in the form of otherwise 'forbidden' harmonics (i.e., that are not emitted from achiral media). The intensity of these symmetry-forbidden harmonics is directly correlated to the media's enantiomeric excess, yielding chiral selectivity. On the contrary, the strength of the 'allowed' harmonics is chiral-independent, hence they can be used as a reference to provide chiral selectivity from a single measurement, unlike previous time-resolved schemes that require multiple measurements. We demonstrate numerically 96% discrimination level from microscopic gas phase emission, outperforming by far previous time-resolved methods (the selectivity should be further enhanced when the HHG process is phase matched). We expect the new method to give rise to precise table-top characterization of chiral media in the gas-phase, and for highly sensitive time-resolved ultrafast probing of dynamical chiral processes.

Ultra-short laser pulses with femtosecond to attosecond pulse duration are the shortest systematic events humans can create. Characterization (amplitude and phase) of these pulses is a key ingredient in ultrafast science, e.g., exploring chemical reactions and electronic phase transitions. Here, we propose and demonstrate, numerically and experimentally, the first deep neural network technique to reconstruct ultra-short optical pulses. We anticipate that this approach will extend the range of ultrashort laser pulses that can be characterized, e.g., enabling to diagnose very weak attosecond pulses.

Optical chirality (OC) - one of the fundamental quantities of electromagnetic fields - corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds to that of the pump in the quasi-monochromatic case, but not in multi-chromatic pump cases. We associate this discrepancy to the fact that the polarization OC of multi-chromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, non-instantaneous polarization-associated OC, and timescale-weighted polarization-associated OC, that link the chirality of multi-chromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tri-circular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

This work demonstrates nanoscale magnetic imaging using bright circularly polarized high-harmonic radiation. We utilize the magneto-optical contrast of worm-like magnetic domains in a Co/Pd multilayer structure, obtaining quantitative amplitude and phase maps by lensless imaging. A diffraction-limited spatial resolution of 49 nm is achieved with iterative phase reconstruction enhanced by a holographic mask. Harnessing the unique coherence of high harmonics, this approach will facilitate quantitative, element-specific and spatially-resolved studies of ultrafast magnetization dynamics, advancing both fundamental and applied aspects of nanoscale magnetism., Comment: Ofer Kfir and Sergey Zayko contributed equally to this work. Presented in CLEO 2017 (Oral) doi.org/10.1364/CLEO_QELS.2017.FW1H.8

Symmetry is one of the most generic and useful concepts in physics and chemistry, often leading to conservation laws and selection rules. For example, symmetry considerations have been used to predict selection rules for transitions in atoms, molecules, and solids. Floquet systems also demonstrate a variety of symmetries which are spatiotemporal (i.e. dynamical symmetries (DSs)). However, the derivation of selection rules from DSs has so far been limited to several ad hoc cases. A general theory for deducing the impact of DSs in physical systems has not been formulated yet. Here we explore symmetries exhibited in Floquet systems using group theory, and discover novel DSs and selection rules. We derive the constraints on a general system's temporal evolution, and selection rules that are imposed by the DSs. As an example, we apply the theory to harmonic generation, and derive tables linking (2+1)D and (3+1)D DSs of the driving laser and medium to allowed harmonic emission and its polarization. We identify several new symmetries and selection rules, including an elliptical DS that leads to production of elliptically polarized harmonics where all the harmonics have the same ellipticity, and selection rules that have no explanation based on currently known conservation laws. We expect the theory to be useful for manipulating the harmonic spectrum, and for ultrafast spectroscopy. Furthermore, the presented Floquet group theory should be useful in various other systems, e.g., Floquet topological insulators and photonic lattices, possibly yielding formal and general classification of symmetry and topological properties.

Frequency-resolved optical gating (FROG) is probably the most popular technique for complete characterization of ultrashort laser pulses. In FROG, a reconstruction algorithm retrieves the pulse from a measured spectrogram, yet current FROG reconstruction algorithms require and exhibit several restricting features that weaken FROG performances. For example, the delay step must correspond to the spectral bandwidth measured with large enough SNR a condition that limits the temporal resolution of the reconstructed pulse, obscures measurements of weak broadband pulses, and makes measurement of broadband mid-IR pulses hard and slow because the spectrograms become huge. We develop a new approach for FROG reconstruction, based on ptychography (a scanning coherent diffraction imaging technique), that removes many of the algorithmic restrictions. The ptychographic reconstruction algorithm is significantly faster and more robust to noise than current FROG algorithms, which are based on generalized projections (GP). We demonstrate, numerically and experimentally, that ptychographic reconstruction works well with very partial spectrograms, e. g. spectrograms with reduced number of measured delays and spectrograms that have been substantially spectrally filtered. In addition, we implement the ptychogrpahic approach to blind second harmonic generation (SHG) FROG and demonstrate robust and complete characterization of two unknown pulses from a single measured spectrogram and power spectrum of only one of the pulses. We believe that the ptychograpy-based approach will become the standard reconstruction procedure in FROG and related diagnostics methods, allowing successful reconstructions from so far unreconstructable spectrograms., Comment: 11 pages, 9 figures

We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform (STFT). We first show that the redundancy offered by the STFT enables unique recovery for arbitrary nonvanishing inputs, under mild conditions. An efficient algorithm for recovery of a sparse input from the STFT magnitude is then suggested, based on an adaptation of the recently proposed GESPAR algorithm. We demonstrate through simulations that using the STFT leads to improved performance over recovery from the oversampled Fourier magnitude with the same number of measurements., Comment: To appear in IEEE Signal Processing Letters

We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having close central frequencies with isotropic gas leads to the emission of polarization-fan harmonics which are nearly circularly-polarized in one tail of the harmonic peak, linear in the center of the peak and nearly circular with the opposite helicity in the opposite tail. Polarization fan harmonics are obtained as a result of multiple (at least two) head-on recollisions of electrons with their parent ions occurring from different angles. The process can be phase-matched using standard methods (e.g. pressure tuning phase matching) and maintains the single-atom polarization property through propagation. These polarization-fan harmonics may be used for exploring non-repetitive ultrafast chiral phenomena, e.g. dynamics of magnetic domains, in a single shot, Comment: 10 pages, 5 figures

This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art in this area, identify challenges, and suggest vision and areas where signal processing methods can have a large impact on optical imaging and on the world of imaging at large, with applications in a variety of fields ranging from biology and chemistry to physics and engineering.

Circularly-polarized extreme UV and X-ray radiation provides valuable access to the structural, electronic and magnetic properties of materials. To date, this capability was available only at large-scale X-ray facilities such as synchrotrons. Here we demonstrate the first bright, phase-matched, extreme UV circularly-polarized high harmonics and use this new light source for magnetic circular dichroism measurements at the M-shell absorption edges of Co. We show that phase matching of circularly-polarized harmonics is unique and robust, producing a photon flux comparable to the linearly polarized high harmonic sources that have been used very successfully for ultrafast element-selective magneto-optic experiments. This work thus represents a critical advance that makes possible element-specific imaging and spectroscopy of multiple elements simultaneously in magnetic and other chiral media with very high spatial and temporal resolution, using tabletop-scale setups., Comment: 12 text pages, 4 figures, supplamentary information 6 pages