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It is well-known that the wave of a freely propagating Gaussian beam experiences an additional π phase shift compared to a plane wave. This phase shift, known as the Gouy phase, has significant consequences in, e.g., nonlinear optics, since the nonlinear processes require high peak intensity and phase matching of the focused beams. Hence, determining and controlling the Gouy phase is crucial in many fields of modern optics and photonics. Here, we develop an analytical model for the Gouy phase of long-range Bessel-Gaussian beams obtained by annihilating highly charged optical vortices. The model accounts for the influence of the relevant experimental parameters (topological charge, radius-to-width ratio of the initial ring-shaped beam, and focal length of the Fourier-transforming lens). We find an evolution of the Gouy phase varying nearly linearly with propagation distance and confirm this result experimentally.
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We report on a combined experimental and numerical study of photoelectron circular dichroism (PECD) induced by intense few-cycle laser pulses, using methyloxirane as the molecular example. Our experiments reveal a remarkably pronounced sensitivity of the PECD strength of double-ionization on the carrier-envelope phase (CEP) of the laser pulses. By comparison to the simulations, which reproduce the measured CEP-dependence for specific orientations of the molecules in the lab frame, we attribute the origin of the observed CEP-dependence of PECD to the CEP-induced modulation of ionization from different areas of the wave functions of three dominant orbitals.
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Correlative microscopy is a powerful technique that combines the advantages of multiple imaging modalities to achieve a comprehensive understanding of investigated samples. For example, fluorescence microscopy provides unique functional contrast by imaging only specifically labeled components, especially in biological samples. However, the achievable structural information on the sample in its full complexity is limited. Here, the intrinsic label-free carbon contrast of water window soft X-ray microscopy can complement fluorescence images in a correlative approach ultimately combining nanoscale structural resolution with functional contrast. However, soft X-ray microscopes are complex and elaborate, and are usually installed on large-scale synchrotron radiation sources due to the demanding photon flux requirements. Yet, with modern high-power lasers it has become possible to generate sufficient photon flux from laser-produced plasmas, thus enabling laboratory-based setups. Here, we present a compact table-top soft X-ray microscope with an integrated epifluorescence modality for "in situ" correlative imaging. Samples remain in place when switching between modalities, ensuring identical measurement conditions and avoiding sample alteration or destruction. We demonstrate our new method by multimodal images of several exemplary samples ranging from nanoparticles to various multicolor labeled cell types. A structural resolution of down to 50 nm was reached.
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Many applications of two-dimensional materials such as graphene require the encapsulation in bulk material. While a variety of methods exist for the structural and functional characterization of uncovered 2D materials, there is a need for methods that image encapsulated 2D materials as well as the surrounding matter. In this work, we use extreme ultraviolet coherence tomography to image graphene flakes buried beneath 200â nm of silicon. We show that we can identify mono-, bi-, and trilayers of graphene and quantify the thickness of the silicon bulk on top by measuring the depth-resolved reflectivity. Furthermore, we estimate the quality of the graphene interface by incorporating a model that includes the interface roughness. These results are verified by atomic force microscopy and prove that extreme ultraviolet coherence tomography is a suitable tool for imaging 2D materials embedded in bulk materials.
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We present a tabletop setup for extreme ultraviolet (EUV) reflection spectroscopy in the spectral range from 40 to 100 eV by using high-harmonic radiation. The simultaneous measurements of reference and sample spectra with high energy resolution provide precise and robust absolute reflectivity measurements, even when operating with spectrally fluctuating EUV sources. The stability and sensitivity of EUV reflectivity measurements are crucial factors for many applications in attosecond science, EUV spectroscopy, and nano-scale tomography. We show that the accuracy and stability of our in situ referencing scheme are almost one order of magnitude better in comparison to subsequent reference measurements. We demonstrate the performance of the setup by reflective near-edge x-ray absorption fine structure measurements of the aluminum L2/3 absorption edge in α-Al2O3 and compare the results to synchrotron measurements.
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The development of the broad-bandwidth photon sources emitting in the soft X-ray range has attracted great attention for a long time due to the possible applications in high-resolution spectroscopy, nano-metrology, and material sciences. A high photon flux accompanied by a broad, smooth spectrum is favored for the applications such as near-edge X-ray absorption fine structure (NEXAFS), extended X-ray absorption fine structure (EXAFS), or XUV/X-ray coherence tomography (XCT). So far, either large-scale facilities or technologically challenging systems providing only limited photon flux in a single shot dominate the suitable sources. Here, we present a soft, broad-band (1.5 nm - 10.7 nm) soft X-ray source. The source is based on the interaction of very intense laser pulses with a target formed by a cluster mixture. A photon yield of 2.4 × 1014 photons/pulse into 4π (full space) was achieved with a medium containing Xe clusters of moderate-size mixed with a substantial amount of extremely large ones. It is shown that such a cluster mixture enhances the photon yield in the soft X-ray range by roughly one order of magnitude. The size of the resulting source is not beneficial (≤500 µm but this deficit is compensated by a specific spectral structure of its emission fulfilling the specific needs of the spectroscopic (broad spectrum and high signal dynamics) and metrological applications (broad and smoothed spectrum enabling a sub-nanometer resolution limit for XCT).
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Two-stage multipass-cell compression of a fiber-chirped-pulse amplifier system to the few-cycle regime is presented. The output delivers a sub-2-cycle (5.8â fs), 107â W average power, 1.07â mJ pulses at 100â kHz centered at 1030â nm with excellent spatial beam quality (M2 = 1.1, Strehl ratio S = 0.98), pointing stability (2.3â µrad), and superior long-term average power stability of 0.1% STD over more than 8â hours. This is combined with a carrier-envelope phase stability of 360â mrad in the frequency range from 10â Hz to 50â kHz, i.e., measured on a single-shot basis. This unique system will serve as an HR1 laser for the Extreme Light Infrastructure Attosecond Light Pulse Source research facility to enable high repetition rate isolated attosecond pulse generation.
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This work presents the improvements in the design and testing of polarimeters based on channel-cut crystals for nuclear resonant scattering experiments at the 14.4â keV resonance of 57Fe. By using four asymmetric reflections at asymmetry angles of α1 = -28°, α2 = 28°, α3 = -28° and α4 = 28°, the degree of polarization purity could be improved to 2.2 × 10-9. For users, an advanced polarimeter without beam offset is now available at beamline P01 of the storage ring PETRA III.
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Many applications ranging from nonlinear optics to material processing would benefit from pulsed ultrashort (quasi-)non-diffracting Gauss-Bessel beams (GBBs). Here we demonstrate a straightforward yet efficient method for generating such zeroth- and first-order GBBs using a single reflective spatial light modulator. Even in the sub-8-fs range there are no noticeable consequences for the measured pulse duration. The only effect is a weak "coloring" of the outer-lying satellite rings of the beams due to the spectrum spanning over more than 300 nm. The obtained beams have diffraction half-angles below 40 µrad and reach propagation distances in excess of 1.5 m.
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The vibrational motion of molecules represents a fundamental example of an anharmonic oscillator. Using a prototype molecular system, HeH^{+}, we demonstrate that appropriate laser pulses make it possible to drive the nuclear motion in the anharmonic potential of the electronic ground state, increasing its energy above the potential barrier and facilitating dissociation by purely vibrational excitation. We find excellent agreement between the frequency-dependent response of the helium hydride molecular cation to both classical and quantum mechanical simulations, thus removing any ambiguities through electronic excitation. Our results provide access to the rich dynamics of anharmonic quantum oscillator systems and pave the way to state-selective control schemes in ground-state chemistry by the adequate choice of the laser parameters.
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High-harmonic generation (HHG) in crystals offers a simple, affordable and easily accessible route to carrier-envelope phase (CEP) measurements, which scales favorably towards longer wavelengths. We present measurements of HHG in ZnO using few-cycle pulses at 3.1µm. Thanks to the broad bandwidth of the driving laser pulses, spectral overlap between adjacent harmonic orders is achieved. The resulting spectral interference pattern provides access to the relative harmonic phase, and hence, the CEP.
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The spatially dependent phase distribution of focused few-cycle pulses, i.e., the focal phase, is much more complex than the well-known Gouy phase of monochromatic beams. As the focal phase is imprinted on the carrier-envelope phase (CEP), for accurate modeling and interpretation of CEP-dependent few-cycle laser-matter interactions, both the coupled spatially dependent phase and intensity distributions must be taken into account. In this Letter, we demonstrate the significance of the focal phase effect via comparison of measurements and simulations of CEP-dependent photoelectron spectra. Moreover, we demonstrate the impact of this effect on few-cycle light-matter interactions as a function of their nonlinear intensity dependence to answer the general question: if, when, and how much should one be concerned about the focal phase?
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We report on the unambiguous observation of the subcycle ionization bursts in sequential strong-field double ionization of H_{2} and their disentanglement in molecular frame photoelectron angular distributions. This observation was made possible by the use of few-cycle laser pulses with a known carrier-envelope phase, in combination with multiparticle coincidence momentum imaging. The approach demonstrated here will allow sampling of the intramolecular electron dynamics and the investigation of charge-state-specific Coulomb distortions on emitted electrons in polyatomic molecules.
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We investigate the carrier-envelope phase (CEP) dependences of the single and double ionization processes of methanol (CH3OH) in an intense near-IR few-cycle laser field (2.1 × 1014 W/cm2) by the asymmetry in the ejection direction of CH3 + for the non-hydrogen migration channels and CH2 + for the hydrogen migration channels created through the C-O bond breaking after the ionization. Based on the absolute CEP values at the laser-molecule interaction point, calibrated by the method using intense few-cycle circularly polarized laser pulses [Fukahori et al., Phys. Rev. A 95, 053410-1-053410-14 (2017)], we confirm that methanol cations are produced by tunnel ionization and methanol dications are produced by the recollisional double ionization. We obtain the phase offset for the double ionization accompanying no hydrogen migration to be 1.85π as the absolute CEP at which the extent of the asymmetry becomes maximum. We interpret the phase shift of 0.85π from the phase offset of 1.0π for the tunnel ionization, estimated by a tunnel ionization model incorporating the chemical bond asymmetry, as the corresponding time delay associated with the electron recollisional ionization. The positive phase shift of 0.13π for the single ionization in the non-hydrogen migration channel is interpreted as the additional time (165 as) with which a methanol cation can be excited electronically prior to the decomposition. The additional phase shift of 0.22π for the single ionization in the hydrogen migration channel is interpreted as the additional time (280 as) required for a methanol cation to be excited electronically leading to the hydrogen migration prior to the decomposition.
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We introduce and experimentally demonstrate a method where the two intrinsic timescales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photoelectron photoion coincidence experiment. In our experiment, elliptically polarized, 750 nm, 4.5 fs laser pulses were focused to an intensity of 9×10^{14} W/cm^{2} onto H_{2}. Using coincidence imaging, we directly observe the nuclear wave packet evolving on the 1sσ_{g} state of H_{2}^{+} during its first round-trip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.
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With the emergence of high-repetition-rate few-cycle laser pulse amplifiers aimed at investigating ultrafast dynamics in atomic, molecular, and solid-state science, the need for ever faster carrier-envelope phase (CEP) detection and control has arisen. Here we demonstrate a high-speed, continuous, every-single-shot measurement and fast feedback scheme based on a stereo above-threshold ionization time-of-flight spectrometer capable of detecting the CEP and pulse duration at a repetition rate of up to 400 kHz. This scheme is applied to a 100 kHz optical parametric chirped pulse amplification few-cycle laser system, demonstrating improved CEP stabilization and allowing for CEP tagging.
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The laser-induced fragmentation dynamics of this most fundamental polar molecule HeH^{+} are measured using an ion beam of helium hydride and an isotopologue at various wavelengths and intensities. In contrast to the prevailing interpretation of strong-field fragmentation, in which stretching of the molecule results primarily from laser-induced electronic excitation, experiment and theory for nonionizing dissociation, single ionization, and double ionization both show that the direct vibrational excitation plays the decisive role here. We are able to reconstruct fragmentation pathways and determine the times at which each ionization step occurs as well as the bond length evolution before the electron removal. The dynamics of this extremely asymmetric molecule contrast the well-known symmetric systems leading to a more general picture of strong-field molecular dynamics and facilitating interpolation to systems between the two extreme cases.
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A quasi-supercontinuum source in the extreme ultraviolet (XUV) is demonstrated using a table-top femtosecond laser and a tunable optical parametric amplifier (OPA) as a driver for high-harmonic generation (HHG). The harmonic radiation, which is usually a comb of odd multiples of the fundamental frequency, is generated by near-infrared (NIR) laser pulses from the OPA. A quasi-continuous XUV spectrum in the range of 30 to 100 eV is realized by averaging over multiple harmonic comb spectra with slightly different fundamental frequencies and thus different spectral spacing between the individual harmonics. The driving laser wavelength is swept automatically during an averaging time period. With a total photon flux of 4×109 photons/s in the range of 30 eV to 100 eV and 1×107photons/s in the range of 100 eV to 200 eV, the resulting quasi-supercontinuum XUV source is suited for applications such as XUV coherence tomography (XCT) or near-edge absorption fine structure spectroscopy (NEXAFS).
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A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8 µm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120 mrad for each and every individual laser shot for a 1 kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.
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The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel-cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.