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Publications by
Prof. Dr. Gerhard G. Paulus

All publications of HI Jena


S. Ringleb, M. Kiffer, N. Stallkamp, S. Kumar, J. Hofbrucker, B. Reich, B. Arndt, G. Brenner, M. Ruiz-Lopéz, S. Düsterer, M. Vogel, K. Tiedtke, W. Quint, T. Stöhlker, and G. G. Paulus
High-intensity laser experiments with highly charged ions in a Penning trap
Physica Scripta 97, 084002 (2022)

Abstract: We have conceived and built the HILITE (High-Intensity Laser-Ion Trap Experiment) Penning-trap setup for the production, confinement and preparation of pure ensembles of highly charged ions in a defined quantum state as a target for various high-intensity lasers. This enables a broad suite of laser-ion interaction studies at high photon energies and/or intensities, such as non-linear photo-ionisation studies. The setup has now been used to perform experiments at one such laser facility, namely the FLASH Free-Electron Laser at DESY in Hamburg, Germany. We describe the experimental possibilities of the apparatus, the results of the first measurements and future experiments at other laser facilities.

B. Marx-Glowna, B. Grabiger, R. Loetzsch, I. Uschmann, A. T. Schmitt, K. S. Schulze, A. Last, T. Roth, S. Antipov, H.-P. Schlenvoigt, I. Sergueev, O. Leupold, R. Roehlsberger, and G. G. Paulus
Scanning high-sensitive x-ray polarization microscopy
New Journal of Physics 24, 053051 (2022)

Abstract: We report on the realization of an extremely sensitive x-ray polarization microscope, allowing to detect tiniest polarization changes of 1 in 100 billion (10(-11)) with a mu m-size focused beam. The extreme degree of polarization purity places the most stringent requirements on the orientation of the polarizer and analyzer crystals as well as the composition and the form fidelity of the lenses, which must not exhibit any birefringence. The results show that these requirements are currently only met by polymer lenses. Highly sensitive scanning x-ray polarization microscopy thus is established as a new method. It can provide new insights in a wide range of applications ranging from quantum electrodynamics and quantum optics to x-ray spectroscopy, materials research, and laser physics.

S. Haedrich, E. Shestaev, M. Tschernajew, F. Stutzki, N. Walther, F. Just, M. Kienel, I. Seres, P. Jojart, Z. Bengery, B. Gilicze, Z. Varallyay, A. Borzsonyi, M. Mueller, C. Grebing, A. Klenke, D. Hoff, G. Paulus, T. Eidam, and J. Limpert
Carrier-envelope phase stable few-cycle laser system delivering more than 100 W, 1 mJ, sub-2-cycle pulses
Optics Letters 47, 1537 (2022)

Abstract: Two-stage multipass-cell compression of a fiber-chirpedpulse amplifier system to the few-cycle regime is presented. The output delivers a sub-2-cycle (5.8 fs), 107W average power, 1.07 mJ pulses at 100kHz centered at 1030nm with excellent spatial beam quality (M-2 =1.1, Strehl ratio S = 0.98), pointing stability (2.3 mu rad), and superior long-term average power stability of 0.1% STD over more than 8 hours. This is combined with a carrier-envelope phase stability of 360mrad in the frequency range from 10Hz to 50kHz, 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

K. Schulze, B. Grabiger, R. Loetzsch, B. Marx-Glowna, A. Schmitt, A. Garcia, W. Hippler, L. Huang, F. Karbstein, Z. Konopková, H.-P. Schlenvoigt, J.-P. Schwinkendorf, C. Strohm, T. Toncian, I. Uschmann, H.-C. Wille, U. Zastrau, R. Röhlsberger, T. Stöhlker, T. Cowan, and G. Paulus
Towards perfectly linearly polarized x-rays
Physical Review Research 4, 013220 (2022)

Abstract: In recent years, high-precision x-ray polarimeters have become a key method for the investigation of fundamental physical questions from solid-state physics to quantum optics. Here, we report on the verification of a polarization purity of better than 8×10−11 at an x-ray free-electron laser, which implies a suppression of the incoming photons to the noise level in the crossed polarizer setting. This purity provides exceptional sensitivity to tiny polarization changes and offers intriguing perspectives for fundamental tests of quantum electrodynamics.

S. Fuchs, J. Abel, J. Nathanael, J. Reinhard, F. Wiesner, M. Wuensche, S. Skruszewicz, C. Roedel, D. Born, H. Schmidt, and G. Paulus
Photon counting of extreme ultraviolet high harmonics using a superconducting nanowire single-photon detector
Applied Physics B 128, 26 (2022)

Abstract: Laser-driven light sources in the extreme ultraviolet range (EUV) enable nanoscopic imaging with unique label-free elemental contrast. However, to fully exploit the unique properties of these new sources, novel detection schemes need to be developed. Here, we show in a proof-of-concept experiment that superconducting nanowire single-photon detectors (SNSPD) can be utilized to enable photon counting of a laser-driven EUV source based on high harmonic generation (HHG). These detectors are dark-count free and accommodate very high count rates-a perfect match for high repetition rate HHG sources. In addition to the advantages of SNSPDs for classical imaging applications with laser-driven EUV sources, the ability to count single photons paves the way for very promising applications in quantum optics and quantum imaging with high energetic radiation like, e.g., quantum ghost imaging with nanoscale resolution.

N. Dimitrov, M. Zhekova, Y. Zhang, G. Paulus, and A. Dreischuh
Background-free femtosecond autocorrelation in collinearly-aligned inverted field geometry using optical vortices
OPTICS COMMUNICATIONS 504, 127493 (2022)

Abstract: Among the existing techniques for measuring ultrashort pulse durations, the two classical second-order methods - interferometric and the background-free autocorrelation - are distinguished due to their simplicity and reliability. In this work we report on a technique that allows realignment-free switching between these two modes of autocorrelation. It is based on a collinearly aligned inverted-field interferometer and an optical vortex plate that is added/removed in front of the device in order to switch between both modes. Experiment and theoretical modeling confirm the effectiveness of the technique down to the 10-fs range.

L. Stoyanov, G. Maleshkov, I. Stefanov, G. Paulus, and A. Dreischuh
Focal beam structuring by triple mixing of optical vortex lattices
Optical and Quantum Electronics 54, 34 (2022)

Abstract: On-demand generation and reshaping of arrays of focused laser beams is highly desired in many areas of science and technology. In this work, we present a versatile approach for laser beam structuring in the focal plane of a lens by triple mixing of square and/or hexagonal optical vortex lattices (OVLs). In the artificial far field the input Gaussian beam is reshaped into ordered arrays of bright beams with flat phase profiles. This is remarkable, since the bright focal peaks are surrounded by hundreds of OVs with their dark cores and two-dimensional phase dislocations. Numerical simulations and experimental evidences for this are shown, including a broad discussion of some of the possible scenarios for such mixing: triple mixing of square-shaped OVLs, triple mixing of hexagonal OVLs, as well as the two combined cases of mixing square-hexagonal-hexagonal and square-square-hexagonal OVLs. The particular ordering of the input phase distributions of the OV lattices on the used spatial light modulators is found to affect the orientation of the structures ruled by the hexagonal OVL. Reliable control parameters for the creation of the desired focal beam structures are the respective lattice node spacings. The presented approach is flexible, easily realizable by using a single spatial light modulator, and thus accessible in many laboratories.


M. Almassarani, S. Meng, B. Beleites, F. Ronneberger, G. Paulus, and A. Gopal
Parametric Study of Proton Acceleration from Laser-Thin Foil Interaction
Plasma 4, 670 (2021)

Abstract: We experimentally investigated the accelerated proton beam characteristics such as maximum energy and number by varying the incident laser parameters. For this purpose, we varied the laser energy, focal spot size, polarization, and pulse duration. The proton spectra were recorded using a single-shot Thomson parabola spectrometer equipped with a microchannel plate and a high-resolution charge-coupled device with a wide detection range from a few tens of keV to several MeV. The outcome of the experimental findings is discussed in detail and compared to other theoretical works.

B. Ying, F. Machalett, V. Huth, M. Kuebel, A. Sayler, T. Stoehlker, G. Paulus, and P. Wustelt
Experimental study of the laser-induced ionization of heavy metal and metalloid ions: Au+ and Si2+ in intense and sculpted femtosecond laser fields
Journal of Physics B: Atomic, Molecular and Optical Physics 54, 174002 (2021)

Abstract: We implement a liquid metal ion source in a 3D coincidence momentum spectroscopy setup for studying the interaction of ionic targets with intense laser pulses. Laser intensities of up to 4 . 10(16) W cm(-2) allow for the observation of up to ten-fold ionization of Au+-ions and double ionization of Si2+-ions. Further, by utilizing two-color sculpted laser fields to control the ionization process on the attosecond time scale, we demonstrate the capability to resolve the recoil ion momenta of heavy metal atoms. Simulations based on a semiclassical model assuming purely sequential ionization reproduce the experimental data well. This work opens up the use of a range of metallic and metalloid ions, which have hardly been investigated in strong-field laser physics so far.

F. Karbstein, C. Sundqvist, K. S. Schulze, I. Uschmann, H. Gies, and G. G. Paulus
Vacuum birefringence at x-ray free-electron lasers
New Journal of Physics 23, 095001 (2021)

Abstract: We study the perspectives of measuring the phenomenon of vacuum birefringence predicted by quantum electrodynamics using an x-ray free-electron laser (XFEL) alone. We devise an experimental scheme allowing two consecutive XFEL pulses to collide under a finite angle, and thus act as both pump and probe field for the effect. The signature of vacuum birefringence is encoded in polarization-flipped signal photons to be detected with high-purity x-ray polarimetry. Our findings for idealized scenarios underline that the discovery potential of solely XFEL-based setups can be comparable to those involving optical high-intensity lasers. For currently achievable scenarios, we identify several key details of the x-ray optical ingredients that exert a strong influence on the magnitude of the desired signatures.

P. Wustelt, F. Oppermann, S. Mhatre, M. Kuebel, A. Sayler, M. Lein, S. Graefe, and G. Paulus
Laser-Driven Anharmonic Oscillator: Ground-State Dissociation of the Helium Hydride Molecular Ion by Midinfrared Pulses
Physical Review Letters 127, 043202 (2021)

Abstract: 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.

S. Skruszewicz, S. Fuchs, J. J. Abel, J. Nathanael, J. Reinhard, C. Rödel, F. Wiesner, M. Wuensche, P. Wachulak, A. Bartnik, K. Janulewicz, H. Fiedorowicz, and G. G. Paulus
Coherence tomography with broad bandwidth extreme ultraviolet and soft X-ray radiation
Applied Physics B 127, 55 (2021)

Abstract: We present an overview of recent results on optical coherence tomography with the use of extreme ultraviolet and soft X-ray radiation (XCT). XCT is a cross-sectional imaging method that has emerged as a derivative of optical coherence tomography (OCT). In contrast to OCT, which typically uses near-infrared light, XCT utilizes broad bandwidth extreme ultraviolet (XUV) and soft X-ray (SXR) radiation (Fuchs et al in Sci Rep 6:20658, 2016). As in OCT, XCT\textquotesingle s axial resolution only scales with the coherence length of the light source. Thus, an axial resolution down to the nanometer range can be achieved. This is an improvement of up to three orders of magnitude in comparison to OCT. XCT measures the reflected spectrum in a common-path interferometric setup to retrieve the axial structure of nanometer-sized samples. The technique has been demonstrated with broad bandwidth XUV/SXR radiation from synchrotron facilities and recently with compact laboratory-based laser-driven sources. Axial resolutions down to 2.2 nm have been achieved experimentally. XCT has potential applications in three-dimensional imaging of silicon-based semiconductors, lithography masks, and layered structures like XUV mirrors and solar cells.

H. Kang, S. Chen, J. Chen, and G. Paulus
Frustrated double ionization of atoms in circularly polarized laser fields
New Journal of Physics 23, 033041 (2021)

Abstract: We theoretically study frustrated double ionization (FDI) of atoms subjected to intense circularly polarized laser pulses using a three-dimensional classical model. We find a \textasciigrave knee\textquotesingle structure of FDI probability as a function of intensity, which is similar to the intensity dependence of nonsequential double ionization probability. The observation of FDI is more favourable when using targets with low ionization potentials and short driving laser wavelengths. This is attributed to the crucial role of recollision therein, which can be experimentally inferred from the photoelectron momentum distribution generated by FDI. This work provides novel physical insights into FDI dynamics with circular polarization.

L. Stoyanov, Y. Zhang, A. Dreischuh, and G. Paulus
Long-range quasi-non-diffracting Gauss-Bessel beams in a few-cycle laser field
Optics Express 29, 10997 (2021)

Abstract: 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 mu rad and reach propagation distances in excess of 1.5 m.

M. Kübel, P. Wustelt, Y. Zhang, S. Skruszewicz, D. Hoff, D. Würzler, H. Kang, D. Zille, D. Adolph, G. Paulus, A. Sayler, M. Dumergue, A. Nayak, R. Flender, L. Haizer, M. Kurucz, B. Kiss, S. Kühn, B. Fetić, and D. Milošević
High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau
Physical Review Letters 126, 113201 (2021)

Abstract: Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1  μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

F. Wiesner, M. Wünsche, J. Reinhard, J. Abel, J. Nathanael, S. Skruszewicz, C. Rödel, S. Yulin, A. Gawlik, G. Schmidl, U. Huebner, J. Plentz, G. Paulus, and S. Fuchs
Material-specific imaging of nanolayers using extreme ultraviolet coherence tomography
Optica 8, 230 (2021)

Abstract: Scientific and technological progress depend substantially on the ability to image on the nanoscale. In order to investigate complex, functional, nanoscopic structures like, e.g., semiconductor devices, multilayer optics, or stacks of 2D materials, the imaging techniques not only have to provide images but should also provide quantitative information. We report the material-specific characterization of nanoscopic buried structures with extreme ultraviolet coherence tomography. The method is demonstrated at a laser-driven broadband extreme ultraviolet radiation source, based on high-harmonic generation. We show that, besides nanoscopic axial resolution, the spectral reflectivity of all layers in a sample can be obtained using algorithmic phase reconstruction. This provides localized, spectroscopic, material-specific information of the sample. The method can be applied in, e.g., semiconductor production, lithographic mask inspection, or quality control of multilayer fabrication. Moreover, it paves the way for the investigation of ultrafast nanoscopic effects at functional buried interfaces. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License.

L. Stoyanov, M. Zhekova, A. Stefanov, B. Ivanov, I. Stefanov, G. Paulus, and A. Dreischuh
Generation of long range low-divergent Gauss-Bessel beams by annihilating optical vortices
Optics Communications 480, 126510 (2021)

Abstract: Bessel beams are remarkable since they do not diverge. Accordingly, they have numerous applications ranging from precision laser micro-machining to laser particle acceleration. We demonstrate a novel approach for generating long-range Gauss-Bessel beams. A ring-shaped beam is produced by imprinting a vortex with high topological charge in a Gaussian beam. The phase singularities are thereafter removed and the ring-shaped beam focused/Fourier-transformed by a thin lens. This results in a remarkably good realization of a Gauss- Bessel beam. Divergence angles in the microradian range and Gauss-Bessel beam lengths up to 2.5 m behind the focal plane of the lens are demonstrated.

B. Marx-Glowna, I. Uschmann, K. Schulze, H. Marschner, H.-C. Wille, K. Schlage, T. Stöhlker, R. Röhlsberger, and G. Paulus
Advanced X-ray polarimeter design for nuclear resonant scattering
Journal of Synchrotron Radiation 28, 120 (2021)

Abstract: This work presents the improvements in the design and testing of polarimeters based on channel-cut crystals for nuclear resonant scattering experiments at the 14.4 keV resonance of Fe-57. By using four asymmetric reflections at asymmetry angles of alpha(1) = -28 degrees, alpha(2) = 28 degrees, alpha(3) = -28 degrees and alpha(4) = 28 degrees, the degree of polarization purity could be improved to 2.2 x 10(-9). For users, an advanced polarimeter without beam offset is now available at beamline P01 of the storage ring PETRA III.

K. S. Schulze, R. Lötzsch, R. Rüffer, I. Uschmann, R. Röhlsberger, and G. G. Paulus
X-ray dichroism in polyimide caused by non-resonant scattering
Journal of Synchrotron Radiation 28, 176 (2021)

Abstract: Dichroism is one of the most important optical effects in both the visible and the X-ray range. Besides absorption, scattering can also contribute to dichroism. This paper demonstrates that, based on the example of polyimide, materials can show tiny dichroism even far from electronic resonances due to scattering. Although the effect is small, it can lead to a measurable polarization change and might have influence on highly sensitive polarimetric experiments.

A. T. Schmitt, Y. Joly, K. S. Schulze, B. Marx-Glowna, I. Uschmann, B. Grabiger, H. Bernhardt, R. Lötzsch, A. Juhin, J. Debray, H.-C. Wille, H. Yavaş, G. G. Paulus, and R. Röhlsberger
Disentangling x-ray dichroism and birefringence via high-purity polarimetry
Optica 8, 56 (2021)

Abstract: High-brilliance synchrotron radiation sources have opened new avenues for x-ray polarization analysis that go far beyond conventional polarimetry in the optical domain. With linear x-ray polarizers in a crossed setting, polarization extinction ratios down to 10⁻¹⁰ can be achieved. This renders the method sensitive to probe the tiniest optical anisotropies that would occur, for example, in strong-field quantum electrodynamics due to vacuum birefringence and dichroism. Here we show that high-purity polarimetry can be employed to reveal electronic anisotropies in condensed matter systems with utmost sensitivity and spectral resolution. Taking CuO and La₂CuO₄ as benchmark systems, we present a full characterization of the polarization changes across the Cu K-absorption edge and their separation into dichroic and birefringent contributions. At diffraction-limited synchrotron radiation sources and x-ray lasers, where polarization extinction ratios of 10⁻¹² can be achieved, our method has the potential to assess birefringence and dichroism of the quantum vacuum in extreme electromagnetic fields.


P. Wustelt, M. Kübel, G. Paulus, and A. Sayler
Strong-field laser-induced fragmentation of small molecules from fast to slow
Advances in Atomic, Molecular and Optical Physics 69, 67 (2020)

Abstract: The structure and dynamics of molecules are governed by the electric forces acting between electrons and nuclei. Intense, ultrashort laser pulses offer the possibility to manipulate these forces, on the time scales relevant for the motion of a molecule's constituents. Thus, laser fields can act, not only as a mechanism to trigger molecular dynamics, but also controlling them. The fragmentation patterns that result from the interaction testify to the laser-induced processes occurring in the molecule. In this review, we examine how a laser addresses the different degrees of freedom of a molecule, from electronic excitation to vibrations of nuclei, to rotations of the molecule. We will focus the discussion on the most fundamental systems, particularly H2+, H2, and HeH+. These simple systems allow for accurate theoretical analysis of experimental results, and extrapolation of the conclusions to more complex systems. Since some of the most fundamental molecules, such as HeH+ and H3+ do not exist in the neutral form, we put an emphasis on experiments starting from molecular ions, but do not restrict the discussion to these. Strong-field interactions of small molecules are a test ground, not only for experimental but also for theoretical methods. The joint effort of the two scientific disciplines have delivered deep insights into fundamental concepts of molecular science. The recent developments of novel laser sources with longer wavelength, higher peak power, or repetition rates, as well as more complex targets and detection schemes, promise that the field will remain highly relevant in the decades to come.

N. Stallkamp, S. Ringleb, B. Arndt, M. Kiffer, S. Kumar, G. Paulus, W. Quint, T. Stöhlker, and M. Vogel
HILITE-A well-defined ion target for laser experiments
Journal of Physics: Conference Series 1412, 092009 (2020)

Abstract: We present a Penning-trap-based setup for the study of light-matter interactions in the high-power and/or high-intensity laser regime, such as multi-photon ionization and field ionization. The setup applies ioncloud formation techniques to highly charged ions to the end of specific target preparation, as well as nondestructive detection techniques to identify and quantify the interaction educts and products.

L. Stoyanov, M. Zhekova, A. Stefanov, I. Stefanov, G. Paulus, and A. Dreischuh
Zeroth- and first-order long range non-diffracting Gauss-Bessel beams generated by annihilating multiple-charged optical vortices
Scientific Reports 10, 21981 (2020)

Abstract: We demonstrate an alternative approach for generating zeroth- and first-order long range non-diffracting Gauss-Bessel beams (GBBs). Starting from a Gaussian beam, the key point is the creation of a bright ring-shaped beam with a large radius-to-width ratio, which is subsequently Fourier-transformed by a thin lens. The phase profile required for creating zeroth-order GBBs is flat and helical for first-order GBBs with unit topological charge (TC). Both the ring-shaped beam and the required phase profile can be realized by creating highly charged optical vortices by a spatial light modulator and annihilating them by using a second modulator of the same type. The generated long-range GBBs are proven to have negligible transverse evolution up to 2 m and can be regarded as non-diffracting. The influences of the charge state of the TCs, the propagation distance behind the focusing lens, and the GBB profiles on the relative intensities of the peak/rings are discussed. The method is much more efficient as compared to this using annular slits in the back focal plane of lenses. Moreover, at large propagation distances the quality of the generated GBBs significantly surpasses this of GBBs created by low angle axicons. The developed analytical model reproduces the experimental data. The presented method is flexible, easily realizable by using a spatial light modulator, does not require any special optical elements and, thus, is accessible in many laboratories.

B. Grabiger, B. Marx-Glowna, I. Uschmann, R. Loetzsch, G. Paulus, and K. Schulze
A highly sensitive imaging polarimeter in the x-ray regime
Applied Physics Letters 117, 201102 (2020)

Abstract: We report on the development of a highly sensitive imaging polarimeter that allows for the investigation of polarization changing properties of materials in the x-ray regime. By combining a microfocus rotating anode, collimating multilayer mirrors, and two germanium polarizer crystals, we achieved a polarization purity of the two orthogonal linear polarization states of 8 × 10−8. This enables the detection of an ellipticity on the same order or a rotation of the polarization plane of 6 arcsec. The high sensitivity combined with the imaging techniques allows us to study the microcrystalline structure of materials. As an example, we investigated beryllium sheets of different grades, which are commonly used for fabricating x-ray lenses, with a spatial resolution of 200 μm, and observed a strong degradation of the polarization purity due to the polycrystalline nature of beryllium. This makes x-ray lenses made of beryllium unsuitable for imaging polarimeter with higher spatial resolution. The results are important for the development of x-ray optical instruments that combine high spatial resolution and high sensitivity to polarization.

D. Zille, D. Adolph, S. Skruszewicz, A. M. Sayler, and G. G. Paulus
Species-dependent tunneling ionization of weakly bound atoms in the short-wave infrared regime
New Journal of Physics 22, 083021 (2020)
No abstract availableLinkBibTeX
S. Chen, J. Chen, G. Paulus, and H. Kang
Strong-field frustrated double ionization of argon atoms
Physical Review A 102, 023103 (2020)

Abstract: Using a three-dimensional semiclassical method, we theoretically investigate frustrated double ionization (FDI) of Ar atoms subjected to strong laser fields. The double-hump photoelectron momentum distribution generated from FDI observed in a recent experiment [S. Larimian, Phys. Rev. Research 2, 013021 (2020)2643-156410.1103/PhysRevResearch.2.013021] is reproduced by our simulation. We confirm that the observed spectrum is due to recollision. The laser intensity dependence of FDI is investigated. We reveal that the doubly excited states of Ar atoms and excited states of Ar+ are the dominant pathways for producing FDI at relatively low and high intensities, respectively. The information of which pathway leads to FDI is encoded in the electron momentum distributions. Our work demonstrates that FDI is a general strong-field physical process accompanied with nonsequential double ionization and it can be well understood within the context of recollision scenario.

F. Oppermann, P. Wustelt, T. Florin, S. Mhatre, S. Gräfe, G. Paulus, and M. Lein
Dissociation and ionization of HeH+in sub-cycle-controlled intense two-color fields
Journal of Physics B: Atomic, Molecular and Optical Physics 53, 174001 (2020)

Abstract: Using quantum-mechanical, one-dimensional, non-Born-Oppenheimer simulations we study the control over the strong-field dynamics of the helium hydride molecular ion HeH+ due to interaction driven by short and strong two-color laser pulses. We calculate yields of two competing fragmentation channels: electron removal and dissociation. We find that by changing the relative phase of the two colors, we can select the dominating channel. Nuclear motion is decisive for explaining ionization in this target. Ionization yields are vastly underestimated when nuclear motion is excluded and they are substantially reduced in the heavier isotopologue HeD+. Coupling of the two lowest electronic states is crucial even for the ground-state dissociation process.

H. Bernhardt, A. Schmitt, B. Grabiger, B. Marx-Glowna, R. Loetzsch, H.-C. Wille, D. Bessas, A. Chumakov, R. Rüffer, R. Röhlsberger, T. Stöhlker, I. Uschmann, G. Paulus, and K. Schulze
Ultra-high precision x-ray polarimetry with artificial diamond channel cuts at the beam divergence limit
Physical Review Research 2, 023365 (2020)

Abstract: We report on the use of synthetic single-crystal diamonds for high definition x-ray polarimetry. The diamonds are precision mounted to form artificial channel-cut crystals (ACCs). Each ACC supports four consecutive reflections with a scattering angle 2ΘB of 90°. We achieved a polarization purity of 3.0×10−10 at beamline ID18 of the European Synchrotron Radiation Facility (ESRF). When the x-ray beam's horizontal divergence was reduced through additional collimation from 17 to 8.4μrad, the polarization purity improved to 1.4×10−10. Precision x-ray polarimetry thus has reached the limit, where the purity is determined by the divergence of the beam. In particular, this result is important for polarimetry at fourth generation x-ray sources, which provide diffraction-limited x-ray beams. The sensitivity expected as a consequence of the present work will pave the way for exploring new physics such as the investigation of vacuum birefringence.

R. Hollinger, D. Hoff, P. Wustelt, S. Skruszewicz, Y. Zhang, H. Kang, D. Würzler, T. Jungnickel, M. Dumergue, A. Nayak, R. Flender, L. Haizer, M. Kurucz, B. Kiss, S. Kühn, E. Cormier, C. Spielmann, G. G. Paulus, P. Tzallas, and M. Kübel
Carrier-envelope-phase measurement of few-cycle mid-infrared laser pulses using high harmonic generation in ZnO
Optics Express 28, 7314 (2020)

Abstract: 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 3.1 µm. 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.

D. Würzler, S. Skruszewicz, A. M. Sayler, D. Zille, M. Möller, P. Wustelt, Y. Zhang, J. Tiggesbäumker, and G. G. Paulus
Accurate retrieval of ionization times by means of the phase-of-the-phase spectroscopy, and its limits
Physical Review A 101, 033416 (2020)

Abstract: By applying recently introduced, phase-of-the-phase spectroscopy [S. Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015)], we analyze the phase-dependent photoelectron signal from Xe ionized in intense, parallel, two-color (1800 nm and 900 nm) laser fields. With such a field configuration, tuning of the relative phase between the ionizing, ω , and the perturbative, 2ω, field results in a modulation of the ionization rate, as well as modifications of the trajectories of electrons propagating in the laser-dressed continuum. Based on a semiclassical model, we confirm that phase dependencies, due to the perturbation of the ionization rate, encode the ionization times of the electrons. Here, using the fork structure, a well-known feature originating from well-defined dynamics allows us to distinguish between electrons ionized within distinct time windows. However, due to the simultaneous perturbation of the electron trajectories, the assignment of the ionization times can be distorted by up to 80 as, i.e., a 10° phase shift, which is independent of the degree of the perturbation.

Y. Zhang, D. Zille, D. Hoff, P. Wustelt, D. Würzler, M. Möller, A. M. Sayler, and G. Paulus
Observing the Importance of the Phase-Volume Effect for Few-Cycle Light-Matter Interactions
Physical Review Letters 124, 133202 (2020)

Abstract: 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?

N. Dimitrov, M. Zhekova, G. Paulus, and A. Dreischuh
Inverted field interferometer for measuring the topological charges of optical vortices carried by short pulses
Optics Communications 456, 124530 (2020)

Abstract: In this work, we present an improved technique for measuring both the magnitude and sign of the topological charge of input optical vortex beams carried by short laser pulses. Numerical simulations and experimental evidences for the interference signal obtainable at the output of an inverted field interferometer (IFI) valid for both continuous wave and femtosecond optical vortex beams and pulses with an eventual pulse front tilt are in an excellent agreement. An IFI also appears to be a valuable tool for calibrating a built-in variable delay line and for estimating an eventual pulse front tilt of the input ultrashort laser pulses without any realignments. As a trivial side effect, by blocking alternatively one of the two arms of the interferometer, one can use OV beams/pulses of opposite TCs, which are well located in the plane of a desired target, eventually — at precisely known time delays.

N. Stallkamp, S. Ringleb, B. Arndt, M. Kiffer, S. Kumar, T. Morgenroth, G. G. Paulus, W. Quint, Th. Stöhlker, and M. Vogel
HILITE—A tool to investigate interactions of matter and light
X-Ray Spectrometry 49, 188 (2020)

Abstract: Detailed investigations of laser–ion interactions require well‐defined ion targets and detection techniques for high‐sensitivity measurements of reaction educts and products. To this end, we have designed and built the High‐Intensity Laser‐Ion Trap Experiment Penning trap setup, which features various ion‐target preparation techniques including selection, cooling, compression, and positioning as well as destructive and non‐destructive measurement techniques to determine the number of stored ions for all charge states individually and simultaneously. We have recently performed first commissioning experiments of ion deceleration and dynamic ion capture with highly charged ion bunches from an electron beam ion source. We have characterized our single‐pass non‐destructive ion counter in detail and were able to determine the ion velocity as well as the number of ions from the signals acquired.

E. Shestaev, D. Hoff, A. M. Sayler, A. Klenke, S. Hädrich, F. Just, T. Eidam, P. Jójárt, Z. Várallyay, K. Osvay, G. G. Paulus, A. Tünnermann, and J. Limpert
High-power ytterbium-doped fiber laser delivering few-cycle, carrier-envelope phase-stable 100 µJ pulses at 100 kHz
Optics Letters 45, 97 (2020)

Abstract: We present a carrier-envelope phase (CEP)-stable Yb-doped fiber laser system delivering 100 µJ few-cycle pulses at a repetition rate of 100 kHz. The CEP stability of the system when seeded by a carrier-envelope offset-locked oscillator is 360 mrad, as measured pulse-to-pulse with a stereographic above-threshold ionization (stereo-ATI) phase meter. Slow CEP fluctuations have been suppressed by implementing a feedback loop from the phase meter to the pulse picking acousto-optic modulator. To the best of our knowledge, this is the highest CEP stability achieved to date with a fiber-based, high-power few-cycle laser.

S. Fuchs, F. Wiesner, M. Wünsche, J. Nathanael, J. Abel, J. Reinhard, C. Rodel, and G. Paulus
Quantitative nanoscale coherence tomography with extreme ultraviolet light

Abstract: We present nanoscale coherence tomography (XCT) in the extreme ultraviolet range driven by a high-harmonic generation (HHG) light source. Using a novel phase retrieval algorithm, XCT enables non-destructive, quantitative, cross-sectional imaging, of, e.g., semiconductor devices.


L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, G. Paulus, and A. Dreischuh
Multi-spot focal pattern formation and beam reshaping by mixing square-shaped and hexagonal vortex lattices
Proceedings of SPIE 11332, 18 (2019)

Abstract: Here we will present a reliable (experimentally and numerically proved) technique for multi-spot pattern formation in the focus of a lens (i.e. in the artificial far field). This was done using large square-shaped and/or hexagonal optical vortex (OV) lattices generated by spatial light modulators. Experimental and numerical results showing a controllable far-field beam reshaping when such lattices are generated in the Fourier plane will be discussed. Even more interesting bright structures can be obtained by combining OV lattices (of any type) with different node spacings. We show that the small-scale structure of the observed patterns results from the OV lattice with the larger array node spacing, whereas the large-scale structure stems from the OV lattice with the smaller array node spacing. The orientation of the mixed far-field structures is proven to rotate by 180 degrees when all TCs are inverted.

L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, G. Paulus, and A. Dreischuh
Controllable beam reshaping by mixing square-shaped and hexagonal optical vortex lattices
Scientific Reports 9, 2128 (2019)

Abstract: In the present work we show experimentally and by numerical calculations a substantial far-field beam reshaping by mixing square-shaped and hexagonal optical vortex (OV) lattices composed of vortices with alternatively changing topological charges. We show that the small-scale structure of the observed pattern results from the OV lattice with the larger array node spacing, whereas the large-scale structure stems from the OV lattice with the smaller array node spacing. In addition, we demonstrate that it is possible to host an OV, a one-dimensional, or a quasi-two-dimensional singular beam in each of the bright beams of the generated focal patterns. The detailed experimental data at different square-to-hexagonal vortex array node spacings shows that this quantity could be used as a control parameter for generating the desired focused structure. The experimental data are in excellent agreement with the numerical simulations.

J. Nathanael, M. Wünsche, S. Fuchs, T. Weber, J. Abel, J. Reinhard, F. Wiesner, U. Hübner, S. Skruszewicz, G. Paulus, and C. Rödel
Laboratory setup for extreme ultraviolet coherence tomography driven by a high-harmonic source
Review of Scientific Instruments 90, 113702 (2019)

Abstract: We present a laboratory beamline dedicated to nanoscale subsurface imaging using extreme ultraviolet coherence tomography (XCT). In this setup, broad-bandwidth extreme ultraviolet (XUV) radiation is generated by a laser-driven high-harmonic source. The beamline is able to handle a spectral range of 30-130 eV and a beam divergence of 10 mrad (full width at half maximum). The XUV radiation is focused on the sample under investigation, and the broadband reflectivity is measured using an XUV spectrometer. For the given spectral window, the XCT beamline is particularly suited to investigate silicon-based nanostructured samples. Cross-sectional imaging of layered nanometer-scale samples can be routinely performed using the laboratory-scale XCT beamline. A depth resolution of 16 nm has been achieved using the spectral range of 36-98 eV which represents a 33% increase in resolution due to the broader spectral range compared to previous work.

M. Zhekova, G. Maleshkov, L. Stoyanov, I. Stefanov, G. Paulus, and A. Dreischuh
Formation of multi-spot focal arrays by square-shaped optical vortex lattices
Optics Communications 449, 110 (2019)

Abstract: In this work, we present numerical simulations and experimental evidence for the creation of controllable multi-spot focal arrays composed of bright beams with flat phase profiles. The input phase structures sent to spatial light modulators were square-shaped optical vortex (OV) lattices containing hundreds of vortices. In order to stabilize each of these lattices in space, all used OVs were singly charged and their topological charges varied alternatively across the structures. It is proven that the OV lattice node spacing can be used as a control parameter for reshaping the generated multi-spot focal arrays. Each peak of these arrays is shown to be able to additionally host a singular beam.

M. Wünsche, S. Fuchs, T. Weber, J. Nathanael, J. Abel, J. Reinhard, F. Wiesner, U. Hübner, S. Skruszewicz, G. Paulus, and C. Rödel
A high resolution extreme ultraviolet spectrometer system optimized for harmonic spectroscopy and XUV beam analysis
Review of Scientific Instruments 90, 023108 (2019)

Abstract: We present a modular extreme ultraviolet (XUV) spectrometer system optimized for a broad spectral range of 12-41 nm (30-99 eV) with a high spectral resolution of lambda/Delta lambda greater than or similar to 784 +/- 89. The spectrometer system has several operation modes for (1) XUV beam inspection, (2) angular spectral analysis, and (3) imaging spectroscopy. These options allow for a versatile use in high harmonic spectroscopy and XUV beam analysis. The high performance of the spectrometer is demonstrated using a novel cross-sectional imaging method called XUV coherence tomography.

D. Hoff, M. Krueger, L. Maisenbacher, A. Sayler, P. Hommelhoff, and G. Paulus
Tracing the phase of focused broadband laser pulses
No abstract availableLinkBibTeX
S. Fuchs, M. Wünsche, J. Nathanael, J. Abel, J. Reinhard, F. Wiesner, S. Skruszewicz, C. Rödel, and G. Paulus
XUV coherence tomography with nanoscale resolution using one-dimensional phase retrieval

Abstract: We present XUV Coherence Tomography (XCT) driven by a high-harmonic generation (HHG) light source. Using a novel one-dimensional phase retrieval algorithm, XCT enables non-destructive, artifact-free, nanoscale, cross-sectional imaging, of, e.g., semiconductor devices.


L. Yue, P. Wustelt, A. Sayler, F. Oppermann, M. Lein, G. Paulus, and S. Gräfe
Strong-field polarizability-enhanced dissociative ionization
Physical Review A 98, 043418 (2018)

Abstract: We investigate dissociative single and double ionization of HeH^+ induced by intense femtosecond laser pulses. By employing a semiclassical model with nuclear trajectories moving on field-dressed surfaces and ionization events treated as stochastical jumps, we identify a strong-field mechanism wherein the molecules dynamically align along the laser polarization axis and stretch towards a critical internuclear distance before dissociative ionization. As the tunnel-ionization rate is larger for larger internuclear distances and for aligned samples, ionization is enhanced. The strong dynamical rotation originates from the anisotropy of the internuclear distance-dependent polarizability tensor, which features a maximum at certain internuclear distances. Good qualitative agreement with our experimental observations is found. Finally, we investigate under which experimental conditions isotope effects of different isotopologues of HeH^+ can be observed.

D. Hoff, F. J. Furch, T. Witting, K. Rühle, D. Adolph, A. M. Sayler, M. J. J. Vrakking, G. G. Paulus, and C. P. Schulz
Continuous every-single-shot carrier-envelope phase measurement and control at 100 kHz
Optics Letters 43, 3850 (2018)

Abstract: 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.

P. Wustelt, F. Oppermann, L. Yue, M. Möller, T. Stöhlker, M. Lein, S. Gräfe, G. Paulus, and A. Sayler
Heteronuclear Limit of Strong-Field Ionization: Fragmentation of HeH⁺ by Intense Ultrashort Laser Pulses
Physical Review Letters 121, 073203 (2018)

Abstract: 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.

A. Woldegeorgis, T. Kurihara, B. Beleites, J. Bossert, R. Grosse, G. G. Paulus, F. Ronneberger, and A. Gopal
THz Induced Nonlinear Effects in Materials at Intensities above 26 GW/cm2
Journal of Infrared, Millimeter, and Terahertz Waves 39, 667 (2018)

Abstract: Nonlinear refractive index and absorption coefficient are measured for common semiconductor material such as silicon and organic molecule such as lactose in the terahertz (THz) spectral regime extending from 0.1 to 3 THz. Terahertz pulses with field strengths in excess of 4.4 MV/cm have been employed. Transmittance and the transmitted spectrum were measured with Z-scan and single shot noncollinear electro-optic pump-probe techniques. The THz-induced change in the refractive index (Deltan) shows frequency-dependence and a maximum change of -0.128 at 1.37 THz in lactose and up to +0.169 at 0.15 THz in silicon was measured for a peak incident THz intensity of 26 GW/cm2. Furthermore, the refractive index variation shows a quadratic dependence on the incident THz field, implying the dominance of third-order nonlinearity.

W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus
The plateau in above-threshold ionization: the keystone of rescattering physics
Journal of Physics B: Atomic, Molecular and Optical Physics 51, 162002 (2018)

Abstract: A review is presented of the rescattering plateau in laser-induced above-threshold ionization and its various features as they were discovered over time. Several theoretical explanations are discussed, from simple momentum conservation to the quantum-mechanical improved strong-field approximation and the inherent quantum orbits or, alternatively, entirely classical methods. Applications of the plateau to the extraction of atomic or molecular potentials and to the characterization of the driving laser pulse are also surveyed.

S. Herzer, A. Woldegeorgis, J. Polz, A. Reinhard, M. Almassarani, B. Beleites, F. Ronneberger, R. Grosse, G. G. Paulus, U. Huebner, T. May, and A. Gopal
An investigation on THz yield from laser-produced solid density plasmas at relativistic laser intensities
New Journal of Physics 20, 063019 (2018)

Abstract: We experimentally characterize the generation of high-power terahertz radiation (THz) at the rear surface of a target irradiated by multiple laser pulses. A detailed dependence of the THz yield as a function of laser pulse duration, energy, target material and thickness is presented. We studied the THz radiation emitted mainly in two directions from the target rear surface, namely target normal (acceptance angle 0.87 sr) and non-collinear direction (perpendicular to the target normal direction—acceptance angle 4.12 sr). Independent measurements based on electro-optic diagnostics and pyroelectric detector were employed to estimate the THz yield. Most of the energy is emitted at large angles relative to the target normal direction. THz yield increases with incident laser intensity and thinner targets are better emitters of THz radiation compared to thicker ones.

D. Zille, D. Adolph, M. Möller, A. M. Sayler, and G. G. Paulus
Chirp and carrier-envelope-phase effects in the multiphoton regime: measurements and analytical modeling of strong-field ionization of sodium
New Journal of Physics 20, 063018 (2018)

Abstract: We investigate the influence of chirp on carrier-envelope-phase (CEP)-dependent strong-field few-cycle laser-induced photoelectron spectra of sodium, well within the multiphoton regime. Our measurements and analytical model of this process reveal a simple chirp-dependence, which has the potential to be utilized as an online monitor of laser chirp. Moreover, this effect could extend single-shot measurements of the CEP using above-threshold ionization to longer, chirped pulses, and significantly lower the required pulse energies. Specifically, at a wavelength of 775 nm and an intensity of 6.5 x 10^{12} W/cm^{2} the CEP- and energy-dependent left-right asymmetries of emitted electrons are measured in a time-of-flight spectrometer. In these asymmetry maps, inclined stripe-like structures emerge, where the inclination is tunable with the chirp of the pulse. We report a simple analytical model, explaining the effect as the interference of electrons with even and odd angular momenta, located at energies in between adjacent above-threshold ionization peaks. As we demonstrate, the analytical model is in good agreement with the measurement, as well as with solutions of the three-dimensional time-dependent Schrödinger equation. Further, the analytical model, which can easily be extended to other atoms, allows us to derive an equation, describing the relation between the slope of the inclined stripes and the chirp of the laser.

M. Cerchez, M. Swantusch, M. Toncian, X. M. Zhu, R. Prasad, T. Toncian, Ch. Rödel, O. Jäckel, G. G. Paulus, A. A. Andreev, and O. Willi
Enhanced energy absorption of high intensity laser pulses by targets of modulated surface
Applied Physics Letters 112, 221103 (2018)

Abstract: Investigations of energy transfer of high intensity (I=5x10^19 W/cm2), ultrashort (<30 fs) Ti:Sa laser pulses to solid targets with a randomly rough surface have been performed. We investigated the influence of the target surface morphology on the efficiency of energy transfer of p-polarized laser pulses characterized by a very high contrast. Targets with a roughness r larger than 20% of the laser wavelength proved to absorb a remarkably large fraction of energy reaching up to 70%, almost independent of the incidence angle. Numerical simulations of various interaction conditionsare in agreement with the experimental data and confirm the effect of the target morphology and its surface parameters on the enhanced energy absorbed fraction.

A. M. Sayler, E. Eckner, J. McKenna, B. D. Esry, K. D. Carnes, I. Ben-Itzhak, and G. G. Paulus
Nonunique and nonuniform mapping in few-body Coulomb-explosion imaging
Physical Review A 97, 033412 (2018)

Abstract: Much of our knowledge of molecular geometry and interaction dynamics comes from indirect measurements of the molecular fragments following breakup. This technique—Coulomb-explosion imaging (CEI), i.e., determining the initial molecular configuration of a system from the momenta of the resulting fragments using knowledge of the particle interactions—is one of the fundamental tools of molecular physics. Moreover, CEI has been a staple of molecular studies for decades. Here we show that one often cannot assign a unique initial configuration to the few-body breakup of a polyatomic molecule given the measurement of the resulting fragments' momenta. Specifically, multiple initial configurations can result in identical momenta for a molecule breaking into three or more parts. Further, the nonunique and nonuniform mapping from the initial configuration to the measured momenta also significantly complicates the determination of molecular alignment at the time of breakup.

L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, D. N. Neshev, G. G. Paulus, and A. Dreischuh
Far-field pattern formation by manipulating the topological charges of square-shaped optical vortex lattices
Journal of the Optical Society of America B 35, 402 (2018)

Abstract: In this work, we demonstrate experimentally the formation of 10 different structures consisting of bright beams with flat phase fronts in the focus of a lens (i.e., in the artificial far field). The basic structure used is a large, stable, square-shaped optical vortex (OV) array composed of vortices with alternating topological charges (TCs). The TCs of one individual OV, of a subarray of OVs, or of the complete OV lattice were erased/doubled in the cases of perfect superposition (on-site alignment) or are manipulated in phase in the cases of an offset between the vortices (off-site alignment). A dramatic reshaping of the beam is observed in the far field and shown to be in excellent agreement with numerical simulations.


Y. Zhang, P. Kellner, D. Adolph, D. Zille, P. Wustelt, D. Würzler, S. Skruszewicz, M. Möller, A. M. Sayler, and G. G. Paulus
Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths
Optics Letters 42, 5150 (2017)

Abstract: 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.

D. Hoff, M. Krüger, L. Maisenbacher, G. Paulus, P. Hommelhoff, and A. Sayler
Using the focal phase to control attosecond processes
Journal of Optics 19, 124007 (2017)

Abstract: The spatial evolution of the electric field of focused broadband light is crucial for many emerging attosecond technologies. Here the effects of the input beam parameters on the evolution of few-cycle laser pulses in the focus are discussed. Specifically, we detail how the frequency-dependent input beam geometry, chirp and chromatic aberration can affect the spatial dependence of the carrier-envelope phase (CEP), central frequency and pulse duration in the focus. These effects are confirmed by a direct, three-dimensional measurement of the CEP-evolution in the focus of a typical few-cycle pulse laser using electron rescattering at metal nanotips in combination with a CEP-metre. Moreover, we demonstrate a simple measurement technique to estimate the focal CEP evolution by input-beam parameters. These parameters can be used in novel ways in order to control attosecond dynamics and tailor highly nonlinear light–matter interactions.

D. Würzler, N. Eicke, M. Möller, D. Seipt, A. M. Sayler, S. Fritzsche, M. Lein, and G. G. Paulus
Velocity map imaging of scattering dynamics in orthogonal two-color fields
Journal of Physics B: Atomic, Molecular and Optical Physics 51, 015001 (2017)

Abstract: In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.

M. Kübel, Z. Dube, A. Yu. Naumov, M. Spanner, G. G. Paulus, M. F. Kling, D. M. Villeneuve, P. B. Corkum, and A. Staudte
Streak Camera for Strong-Field Ionization
Physical Review Letters 119, 183201 (2017)

Abstract: Ionization of an atom or molecule by a strong laser field produces suboptical cycle wave packets whose control has given rise to attosecond science. The final states of the wave packets depend on ionization and deflection by the laser field, which are convoluted in conventional experiments. Here, we demonstrate a technique enabling efficient electron deflection, separate from the field driving strong-field ionization. Using a midinfrared deflection field permits one to distinguish electron wave packets generated at different field maxima of an intense few-cycle visible laser pulse. We utilize this capability to trace the scattering of low-energy electrons driven by the midinfrared field. Our approach represents a general technique for studying and controlling strong-field ionization dynamics on the attosecond time scale.

S. Fuchs, M. Wünsche, J. Nathanael, J. J. Abel, C. Rödel, J. Biedermann, J. Reinhard, U. Hübner, and G. G. Paulus
Optical coherence tomography with nanoscale axial resolution using a laser-driven high-harmonic source
Optica 4, 903 (2017)

Abstract: Extreme ultraviolet microscopy is technologically demanding and thus largely confined to synchrotron radiation facilities. However, specific benefits like high resolution and exceptional material contrast provide strong motivation for the development of table-top alternatives. We report on the first demonstration of coherence tomography, i.e., noninvasive cross-sectional imaging, with high harmonics. A depth resolution of 24 nm and very good material contrast are achieved. Excessively demanding optics for extreme ultraviolet radiation are avoided and artifacts due to the elementary geometry are suppressed with a novel three-step one-dimensional phase-retrieval algorithm. The images are recorded in reflection geometry, facilitating the analysis of, e.g., operating semiconductor samples.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff
Tracing the phase of focused broadband laser pulses
Nature Physics 13, 947 (2017)

Abstract: Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago, an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase. Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today. Based on electron backscattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength spatial resolution and sub-optical-cycle time resolution. Here we report such a direct, three-dimensional measurement of the spatial dependence of the optical phase of a focused, 4-fs, near-infrared pulsed laser beam. The observed optical phase deviates substantially from the monochromatic Gouy phase—exhibiting a much more complex spatial dependence, both along the propagation axis and in the radial direction. In our measurements, these significant deviations are the rule and not the exception for focused, broadband laser pulses. Therefore, we expect wide ramifications for all broadband laser–matter interactions, such as in high-harmonic and attosecond pulse generation, femtochemistry, ophthalmological optical coherence tomography and light-wave electronics.

D. Zille, D. Seipt, M. Möller, S. Fritzsche, G. G. Paulus, and D. B. Milošević
Spin-dependent quantum theory of high-order above-threshold ionization
Physical Review A 95, 063408 (2017)

Abstract: The strong-field-approximation theory of high-order above-threshold ionization of atoms is generalized to include the electron spin. The obtained rescattering amplitude consists of a direct and exchange part. On the examples of excited He atoms as well as Li^+ and Be^2+ ions, it is shown that the interference of these two amplitudes leads to an observable difference between the photoelectron momentum distributions corresponding to different initial spin states: Pronounced minima appear for singlet states, which are absent for triplet states.

M. Wünsche, S. Fuchs, S. Aull, J. Nathanael, M. Möller, C. Rödel, and G. G. Paulus
Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation
Optics Express 25, 6936 (2017)

Abstract: 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 4×10^9 photons/s in the range of 30 eV to 100 eV and 1×10^7photons/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).

D. Adolph, M. Möller, J. Bierbach, M. Schwab, A. Sävert, M. Yeung, A. M. Sayler, M. Zepf, M. C. Kaluza, and G. G. Paulus
Real-time, single-shot, carrier-envelope-phase measurement of a multi-terawatt laser
Applied Physics Letters 110, 081105 (2017)

Abstract: We present the single-shot carrier-envelope phase (CEP) determination of a 1 Hz, multi-terawatt (TW) laser system with a setup based on spectral broadening in a hollow-core fiber and a stereographic measurement of the energy-dependent above-threshold ionization plateau. The latter is extremely sensitive to variations in CEP. As compared to the f-2f interferometers, this technique reduces the uncertainties due to the shot-to-shot intensity fluctuations, which are prevalent in the TW laser systems. The experimental results pave the way towards the investigation and control over CEP-sensitive processes at ultra-high intensities.

D. Zille, D. Seipt, M. Möller, S. Fritzsche, S. Gräfe, C. Müller, and G. G. Paulus
Spin-dependent rescattering in strong-field ionization of helium
Journal of Physics B: Atomic, Molecular and Optical Physics 50, 065001 (2017)

Abstract: We investigate the influence of singlet and triplet spin states on rescattered photoelectrons in strong-field ionization of excited helium. Choosing either a symmetric or antisymmetric spatial wave function as the initial state results in different scattering cross sections for the 1s2s¹S and ³S states. These cross sections are used in the semi-classical model of strong-field ionization. Our investigations show that the photoelectron momentum distributions of rescattered electrons exhibit a significant dependence on the relative spin state of the projectile and the bound electron which should be observable in experiments. The proposed experimental approach can be understood as a testbed for probing the spin dynamics of electrons during strong-field ionization and the presented results as a baseline for their identification.

P. Hansinger, P. Töpfer, N. Dimitrov, D. Adolph, D. Hoff, T. Rathje, A. M. Sayler, A. Dreischuh, and G. G. Paulus
Refractive index dispersion measurement using carrier-envelope phasemeters
New Journal of Physics 19, 023040 (2017)

Abstract: We introduce a novel method for direct and accurate measurement of refractive index dispersion based on carrier-envelope phase detection of few-cycle laser pulses, exploiting the difference between phase and group velocity in a dispersive medium. In a layout similar to an interferometer, two carrier-envelope phasemeters are capable of measuring the dispersion of a transparent or reflective sample, where one phasemeter serves as the reference and the other records the influence of the sample. Here we report on proof-of-principle measurements that already reach relative uncertainties of a few 10^−4 . Further development is expected to allow for unprecedented precision.

P. Wustelt, M. Möller, M. Schöffler, X. Xie, V. Hanus, A. Sayler, A. Baltuska, G. Paulus, and M. Kitzler
Numerical investigation of the sequential-double-ionization dynamics of helium in different few-cycle-laser-field shapes
Physical Review A 95, 023411 (2017)

Abstract: We investigate sequential double ionization of helium by intense near-circularly polarized few-cycle laser pulses using a semiclassical ionization model with two independent electrons. Simulated He^2+ ion momentum distributions are compared to those obtained in recent benchmark experiments. We study the influence of a number of pulse parameters such as peak intensity, carrier-envelope phase, pulse duration, and second- and third-order spectral phase on the shape of the ion momentum distributions. Good agreement is found in the main features of these distributions and of their dependence on the laser pulse duration, peak intensity, and carrier-envelope phase. Furthermore, we find that for explaining certain fine-scale features observed in the experiments, it becomes important to consider subtle timing variations in the two-electron emissions introduced by small values of chirp. This result highlights the possibility of measuring and controlling multielectron dynamics on the attosecond time scale by fine tuning the field evolution of intense close-to-single-cycle laser pulses.


M. Yeung, S. Rykovanov, J. Bierbach, L. Li, E. Eckner, S. Kuschel, A. Woldegeorgis, C. Rödel, A. Sävert, G. G. Paulus, M. Coughlan, B. Dromey, and M. Zepf
Experimental observation of attosecond control over relativistic electron bunches with two-colour fields
Nature Photonics 32, 11 (2016)

Abstract: Energy coupling during relativistically intense laser–matter interactions is encoded in the attosecond motion of strongly driven electrons at the pre-formed plasma–vacuum boundary. Studying and controlling this motion can reveal details about the microscopic processes that govern a vast array of light–matter interaction phenomena, including those at the forefront of extreme laser–plasma science such as laser-driven ion acceleration, bright attosecond pulse generation and efficient energy coupling for the generation and study of warm dense matter. Here we experimentally demonstrate that by precisely adjusting the relative phase of an additional laser beam operating at the second harmonic of the driving laser it is possible to control the trajectories of relativistic electron bunches formed during the interaction with a solid target at the attosecond scale. We observe significant enhancements in the resulting high-harmonic yield, suggesting potential applications for sources of ultra-bright, extreme ultraviolet attosecond radiation to be used in atomic and molecular pump–probe experiments.

H. Li, X. M. Tong, N. Schirmel, G. Urbasch, K. J. Betsch, S. Zherebtsov, F. Süßmann, A. Kessel, S. A. Trushin, G. G. Paulus, K.-M. Weitzel, and M. F. Kling
Intensity dependence of the dissociative ionization of DCl in few-cycle laser fields
Journal of Physics B: Atomic, Molecular and Optical Physics 49, 015601 (2016)

Abstract: We have studied the dissociative ionization of DCl in 4 fs laser fields at 720 nm central wavelength using intensities in the range (1.3–3.1) × 10^14 W cm−2 . By employing the phase-tagged velocity-map imaging technique, information about the angular distribution of deuterium ions as a function of their kinetic energy and the carrier-envelope phase is obtained. On the basis of the experimental data and semi-classical simulations, three regions are distinguished for the resulting D+ ions with different kinetic energies. The one with the lowest kinetic energy, around 5–7 eV, is from dissociation involving the X-state of DCl+ , populated through direct ionization with the laser field. The second region, around 7–11 eV, originates from rescattering induced dissociative ionization. Above 2 × 10^14 W cm−2 D+ ions with kinetic energies exceeding 15 eV are obtained, which we ascribe to double ionization induced by rescattered electrons.

H. Bernhardt, B. Marx-Glowna, K. Schulze, B. Grabiger, J. Haber, C. Detlefs, R. Lötzsch, T. Kämpfer, R. Röhlsberger, E. Förster, Th. Stöhlker, I. Uschmann, and G. G. Paulus
High purity x-ray polarimetry with single-crystal diamonds
Applied Physics Letters 109, 121106 (2016)

Abstract: We report on the use of synthetic single-crystal diamonds for high purity x-ray polarimetry to improve the polarization purity of present-day x-ray polarimeters. The polarimeter setup consists of a polarizer and an analyzer, each based on two parallel diamond crystals used at a Bragg angle close to 45°. The experiment was performed using one (400) Bragg reflection on each diamond crystal and synchrotron undulator radiation at an x-ray energy of 9838.75 eV. A polarization purity of 8.9 × 10−10 was measured at the European Synchrotron Radiation Facility, which is the best value reported for two-reflection polarizer/analyzer setups. This result is encouraging and is a first step to improve the resolution of x-ray polarimeters further by using diamond crystal polarizers and analyzers with four or six consecutive reflections.

M. Lestinsky, V. Andrianov, B. Aurand, V. Bagnoud, D. Bernhardt, H. Beyer, S. Bishop, K. Blaum, A. Bleile, At. Borovik, F. Bosch, C. Bostock, C. Brandau, A. Bräuning-Demian, I. Bray, T. Davinson, B. Ebinger, A. Echler, P. Egelhof, A. Ehresmann, M. Engström, C. Enss, N. Ferreira, D. Fischer, A. Fleischmann, E. Förster, S. Fritzsche, R. Geithner, S. Geyer, J. Glorius, K. Göbel, O. Gorda, J. Goullon, P. Grabitz, R. Grisenti, A. Gumberidze, S. Hagmann, M. Heil, A. Heinz, F. Herfurth, R. Heß, P.-M. Hillenbrand, R. Hubele, P. Indelicato, A. Källberg, O. Kester, O. Kiselev, A. Knie, C. Kozhuharov, S. Kraft-Bermuth, T. Kühl, G. Lane, Y. Litvinov, D. Liesen, X. Ma, R. Märtin, R. Moshammer, A. Müller, S. Namba, P. Neumayer, T. Nilsson, W. Nörtershäuser, G. G. Paulus, N. Petridis, M. Reed, R. Reifarth, P. Reiß, J. Rothhardt, R. Sanchez, M. Sanjari, S. Schippers, H. Schmidt, D. Schneider, P. Scholz, R. Schuch, M. Schulz, V. Shabaev, A. Simonsson, J. Sjöholm, Ö. Skeppstedt, K. Sonnabend, U. Spillmann, K. Stiebing, M. Steck, T. Stöhlker, A. Surzhykov, S. Torilov, E. Träbert, M. Trassinelli, S. Trotsenko, X. Tu, I. Uschmann, P. Walker, G. Weber, D. Winters, P. Woods, H. Zhao, and Y. Zhang
Physics book: CRYRING@ESR
European Physical Journal Special Topics 225, 797 (2016)

Abstract: The exploration of the unique properties of stored and cooled beams of highly-charged ions as provided by heavy-ion storage rings has opened novel and fascinating research opportunities in the realm of atomic and nuclear physics research. Since the late 1980s, pioneering work has been performed at the CRYRING at Stockholm and at the Test Storage Ring (TSR) at Heidelberg. For the heaviest ions in the highest charge-states, a real quantum jump was achieved in the early 1990s by the commissioning of the Experimental Storage Ring (ESR) at GSI Helmholtzzentrum für Schwerionenforschung (GSI) in Darmstadt where challenging experiments on the electron dynamics in the strong field regime as well as nuclear physics studies on exotic nuclei and at the borderline to atomic physics were performed. Meanwhile also at Lanzhou a heavy-ion storage ring has been taken in operation, exploiting the unique research opportunities in particular for medium-heavy ions and exotic nuclei.

N. Dimitrov, L. Stoyanov, I. Stefanov, A. Dreischuh, P. Hansinger, and G. Paulus
Pulse front tilt measurement of femtosecond laser pulses
Optics Communications 371, 51 (2016)

Abstract: In this work we report experimental investigations of an intentionally introduced pulse front tilt on femtosecond laser pulses by using an inverted field correlator/interferometer. A reliable criterion for the precision in aligning (in principle) dispersionless systems for manipulating ultrashort pulses is developed, specifically including cases when the pulse front tilt is a result of a desired spatio-temporal coupling. The results obtained using two low-dispersion diffraction gratings are in good qualitative agreement with the data from a previously developed analytical model and from an independent interferometric measurement.

M. Schöffler, X. Xie, P. Wustelt, M. Möller, S. Roither, D. Kartashov, A. Sayler, A. Baltuska, G. G. Paulus, and M. Kitzler
Laser-subcycle control of sequential double-ionization dynamics of helium
Physical Review A 93, 063421 (2016)

Abstract: We present measured momentum distributions on the double ionization of helium with intense, near-circularly-polarized few-cycle laser pulses with a known carrier-envelope offset phase (CEP). The capability of obtaining CEP-resolved momentum distributions enables us to observe signatures of the various combinations of laser-half-cycle two-electron emissions. By comparison to semiclassical trajectory simulations, we succeed in assigning the corresponding structures in the measured distributions to certain two-electron emission dynamics. Based on this possibility, we demonstrate that the sequential double-ionization dynamics can be sensitively controlled with the pulse duration and the laser peak intensity. For the shortest pulse durations and not too high intensities we find that the two electrons are dominantly emitted with a delay of roughly a laser half cycle. For a just slightly increased intensity we find evidence that at least one of the two electrons is surprisingly likely emitted in between the peaks of the laser field oscillations rather than at the field maxima. The simulations reproduce the signatures of these kinds of two-electron emissions overall relatively well.

J. Haber, K. Schulze, K. Schlage, R. Loetzsch, L. Bocklage, T. Gurieva, H. Bernhardt, H.-C. Wille, R. Rüffer, I. Uschmann, G. G. Paulus, and R. Röhlsberger
Collective strong coupling of X-rays and nuclei in a nuclear optical lattice
Nature Photonics 10, 445 (2016)

Abstract: The advent of third-generation synchrotron radiation sources and X-ray free-electron lasers has opened up the opportunity to perform quantum optical experiments with high-energy X-rays. The prime atomic system for experiments in this energy range is the strongly nuclear resonant 57Fe Mössbauer isotope. Experiments have included measurements of the collective Lamb shift, observation of electromagnetically induced transparency, subluminal propagation of X-rays and spontaneously generated coherences. In these experiments, however, the nuclei were only weakly coupled to the light field. Collective strong coupling of nuclei and X-rays, which is desirable for many quantum optical applications, has eluded researchers so far. Here, we observe collective strong coupling between X-rays and matter excitations in a periodic array of alternating 57Fe and 56Fe layers. Our experiment extends the range of methods for X-ray quantum optics and paves the way for the observation and exploitation of strong-coupling-related phenomena at X-ray energies.

M. Kübel, C. Burger, N. Kling, T. Pischke, L. Beaufore, I. Ben-Itzhak, G. G. Paulus, J. Ullrich, T. Pfeifer, R. Moshammer, M. F. Kling, and B. Bergues
Complete characterization of single-cycle double ionization of argon from the nonsequential to the sequential ionization regime
Physical Review A 93, 053422 (2016)

Abstract: Selected features of nonsequential double ionization have been qualitatively reproduced by a multitude of different (quantum and classical) approaches. In general, however, the typical uncertainty of laser pulse parameters and the restricted number of observables measured in individual experiments leave room for adjusting theoretical results to match the experimental data. While this has been hampering the assessment of different theoretical approaches leading to conflicting interpretations, comprehensive experimental data that would allow such an ultimate and quantitative assessment have been missing so far. To remedy this situation we have performed a kinematically complete measurement of single-cycle multiple ionization of argon over a one order of magnitude range of intensity. The momenta of electrons and ions resulting from the ionization of the target gas are measured in coincidence, while each ionization event is tagged with the carrier-envelope phase and intensity of the 4-fs laser pulse driving the process. The acquired highly differential experimental data provide a benchmark for a rigorous test of the many competing theoretical models used to describe nonsequential double ionization.

P. Hansinger, G. Maleshkov, I. L. Garanovich, D. V. Skryabin, D. N. Neshev, A. Dreischuh, and G. G. Paulus
White light generated by femtosecond optical vortex beams
Journal of the Optical Society of America B 33, 681 (2016)

Abstract: In this work we report detailed experimental and numerical investigation of the white light generation by singly and doubly charged optical vortices propagating in a Kerr medium, where spectral broadening and transfer of topological charge (TC) into emerging spectral satellites take place due to self-phase modulation and degenerate four-wave frequency mixing (FWFM). Experiments performed with different pump beams show excellent agreement with theory. Singly and doubly charged white light vortices are observed within more than ±200  nm bandwidth after nonlinear propagation in Argon gas. Our experiment and theory data confirm that the TC transformation of the newly generated spectral components follows a law analogous to the one for energy conservation in the FWFM process. We also present results on the white light vortex stability.

A. Gopal, A. H. Woldegeorgis, S. Herzer, G. G. Paulus, P. Singh, W. Ziegler, and T. May.
Smith–Purcell radiation in the terahertz regime using charged particle beams from laser–matter interactions
Laser and Particle Beams 34, 187 (2016)

Abstract: We report on the experimental observation of Smith–Purcell (SP) radiation generation by charged particle beam from laser–matter interactions. High-power laser pulses were focused onto a thin metal foil target to generate proton beams with energies up to 1.7 MeV via the target normal sheath acceleration (TNSA) process. The particle beam from the TNSA process was sent close to a periodic structure to generate SP radiation. Sub-μJ terahertz pulses were recorded using a pyroelectric detector. Simultaneous measurement of the ion spectra allowed us to estimate the power of the emitted radiation and compare it with the experimental results. The distance between the grating and the particle beam was varied and its effect on the emitted radiation was studied.

T. Kämpfer, I. Uschmann, Z. W. Wu, A. Surzhykov, S. Fritzsche, E. Förster, and G. G. Paulus
Linear polarization of the characteristic x-ray lines following inner-shell photoionization of tungsten
Physical Review A 93, 033409 (2016)

Abstract: The linear polarization of the characteristic lines Lα1 (3d5/2→2p3/2) and Lα2 (3d3/2→2p3/2), following inner-shell photoionization of neutral tungsten, is analyzed both experimentally and theoretically. In the experiment, a tungsten target is photoionized by the primary emission of an x-ray tube with incident photon energies in the range of 10.2–30 keV. The σ and π components of the emitted fluorescence are measured by using a spectropolarimeter, based on x-ray diffraction at Bragg angles close to 45∘. The degree of linear polarization of the Lα1 and Lα2 lines is determined to be +(1.6±0.5)% and −(7±2)%, respectively. In addition, this degree of polarization is calculated within the framework of the density-matrix theory as a function of the incident photon energy. These calculations are in good agreement with the experimental results and show only a weak dependence of the degree of polarization on the energy of the incident photoionizing photon.

S. Fuchs, C. Rödel, A. Blinne, U. Zastrau, M. Wünsche, V. Hilbert, L. Glaser, J. Viefhaus, E. Frumker, P. Corkum, E. Förster, and G. G. Paulus
Nanometer resolution optical coherence tomography using broad bandwidth XUV and soft x-ray radiation
Scientific Reports 6, 20658 (2016)

Abstract: Optical coherence tomography (OCT) is a non-invasive technique for cross-sectional imaging. It is particularly advantageous for applications where conventional microscopy is not able to image deeper layers of samples in a reasonable time, e.g. in fast moving, deeper lying structures. However, at infrared and optical wavelengths, which are commonly used, the axial resolution of OCT is limited to about 1 μm, even if the bandwidth of the light covers a wide spectral range. Here, we present extreme ultraviolet coherence tomography (XCT) and thus introduce a new technique for non-invasive cross-sectional imaging of nanometer structures. XCT exploits the nanometerscale coherence lengths corresponding to the spectral transmission windows of, e.g., silicon samples. The axial resolution of coherence tomography is thus improved from micrometers to a few nanometers. Tomographic imaging with an axial resolution better than 18 nm is demonstrated for layer-type nanostructures buried in a silicon substrate. Using wavelengths in the water transmission window, nanometer-scale layers of platinum are retrieved with a resolution better than 8 nm. XCT as a nondestructive method for sub-surface tomographic imaging holds promise for several applications in semiconductor metrology and imaging in the water window.

I. C. E. Turcu, F. Negoita, D. A. Jaroszynski, P. Mckenna, S. Balascuta, D. Ursescu, I. Dancus, M. O. Cernaianu, M. V. Tataru, P. Ghenuche, D. Stutman, A. Boianu, M. Risca, M. Toma, C. Petcu, G. Acbas, S. R. Yoffe, A. Noble, B. Ersfeld, E. Brunetti, R. Capdessus, C. Murphy, C. P. Ridgers, D. Neely, S. P. D. Mangles, R. J. Gray, A. G. R. Thomas, J. G. Kirk, A. Ilderton, M. Marklund, D. F. Gordon, B. Hafizi, D. Kaganovich, J. P. Palastro, E. D'Humieres, M. Zepf, G. Sarri, H. Gies, F. Karbstein, J. Schreiber, G. G. Paulus, B. Dromey, C. Harvey, A. Di Piazza, C. H. Keitel, M. C. Kaluza, S. Gales, and N. V. Zamfir
High Field Physics and QED Experiments at ELI-NP
Romanian Reports In Physics 68, S145 (2016)

Abstract: ELI-NP facility will enable for the first time the use of two 10 PW laser beams for quantum electrodynamics (QED) experiments. The first beam will accelerate electrons to relativistic energies. The second beam will subject relativistic electrons to the strong electromagnetic field generating QED processes: intense gamma ray radiation and electron-positron pair formation. The laser beams will be focused to intensities above 10^21 W/cm^2 and reaching 10^22–10^23 W/cm^2 for the first time. We propose to use this capability to investigate new physical phenomena at the interfaces of plasma, nuclear and particle physics at ELI-NP. This High Power Laser System Technical Design Report (HPLS-TDR2) presents the experimental area E6 at ELI-NP for investigating high field physics and quantum electrodynamics and the production of electron-positron-pairs and of energetic gamma-rays. The scientific community submitted 12 commissioning runs for E6 interaction chamber with two 10 PW laser beams and one proposal for the CETAL interaction chamber with 1 PW laser. The proposals are representative of the international high field physics community being written by 48 authors from 14 European and US organizations. The proposals are classified according to the science area investigated into: Radiation Reaction Physics: Classical and Quantum; Compton and Thomson Scattering Physics: Linear and Non Linear Regimes; QED in Vacuum; Atoms in Extreme Fields. Two pump-probe colliding 10 PW laser beams are proposed for the E6 interaction chamber. The focused pump laser beam accelerates the electrons to relativistic energies. The accelerated electron bunches interact with the very high electro-magnetic field of the focused probe laser beam. We propose two main types of experiments with: (a) gas targets in which the pump laser-beam is focused by a long focal length mirror and drives a wakefield in which the electron bunch is accelerated to multi-GeV energies and then exposed to the EM field of the probe laser which is tightly focused; (b) solid targets in which both the pump and probe laser beams are focused on the solid target, one accelerating the electrons in the solid and the other, delayed, providing the high electric field to which the relativistic electrons are subjected. We propose four main focusing configurations for the pump and probe laser beams, two for each type of target: counter-propagating 10 PW focused laser beams and the two 10 PW laser beams focused in the same direction. For solid targets we propose an additional configuration with plasma-mirror on the pump laser beam: the plasma mirror placed between the focusing mirror and target. It is proposed that the 10 PW laser beams will have polarization control and focus control by means of adaptive optics. Initially only one 10 PW may have polarization control and adaptive optics. In order to accommodate the two laser beams and diagnostics the proposed interaction chamber is quasi-octagonal with a diameter of 4.5 m. A large electron-spectrometer is proposed for multi-GeV electrons. Other diagnostics are requested for: gamma-rays, electrons and positrons, protons and ions, plasma characterization, transmitted and reflected laser beam. Targets will be provided by the ELI-NP Target Laboratory or purchased. The E6 experiments and diagnostics will benefit from the ELI-NP Electronics Laboratory, the Workshop and the Optics Laboratory. In order to ensure radiation-protection, a large beam-dump is planned for both multi-GeV electrons and multi-100 MeV protons.


S. Ringleb, M. Vogel, S. Kumar, W. Quint, G. G. Paulus, and Th. Stöhlker
HILITE—ions in intense photon fields
Physica Scripta 2015, 014067 (2015)

Abstract: We are currently devising the open-endcap Penning trap experiment (high-intensity laser ion-trap experiment) as a tool for ion confinement, manipulation and detection to be used at high-energy and/or high-intensity laser facilities. This instrument will allow studies of laser–ion interactions with well-defined ion targets, and to detect the reaction products non-destructively. The ion target may be controlled concerning the constituent species, the density, shape and position with respect to the laser focus. For commissioning experiments, we optimize the focusing parameters to achieve a high number of ionized particles per shot. The detection electronics is designed to measure all charge states of all nuclei up to xenon. We plan first experiments with argon and xenon irradiated by a titanium:sapphire chirped-pulse-amplification laser system with 10 mJ pulse energy and a pulse duration of 30 fs.

M. Yeung, J. Bierbach, E. Eckner, S. Rykovanov, S. Kuschel, A. Sävert, M. Förster, C. Rödel, G. Paulus, S. Cousens, M. Coughlan, B. Dromey, and M. Zepf
Noncollinear Polarization Gating of Attosecond Pulse Trains in the Relativistic Regime
Physical Review Letters 115, 193903 (2015)

Abstract: High order harmonics generated at relativistic intensities have long been recognized as a route to the most powerful extreme ultraviolet pulses. Reliably generating isolated attosecond pulses requires gating to only a single dominant optical cycle, but techniques developed for lower power lasers have not been readily transferable. We present a novel method to temporally gate attosecond pulse trains by combining noncollinear and polarization gating. This scheme uses a split beam configuration which allows pulse gating to be implemented at the high beam fluence typical of multi-TW to PW class laser systems. Scalings for the gate width demonstrate that isolated attosecond pulses are possible even for modest pulse durations achievable for existing and planned future ultrashort high-power laser systems. Experimental results demonstrating the spectral effects of temporal gating on harmonic spectra generated by a relativistic laser plasma interaction are shown.

B. Marx-Glowna, K. Schulze, I. Uschmann, T. Kämpfer, G. Weber, C. Hahn, H.-C. Wille, K. Schlage, R. Röhlsberger, E. Förster, Th. Stöhlker, and G. Paulus
Influence of higher harmonics of the undulator in X-ray polarimetry and crystal monochromator design
Journal of Synchrotron Radiation 22, 1151 (2015)

Abstract: 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.

A. M. Sayler, M. Arbeiter, S. Fasold, D. Adolph, M. Möller, D. Hoff, T. Rathje, B. Fetić, D. B. Milošević, T. Fennel, and G. G. Paulus
Accurate determination of absolute carrier-envelope phase dependence using photo-ionization
Optics Letters 40, 3137 (2015)

Abstract: The carrier-envelope phase (CEP) dependence of few-cycle above-threshold ionization (ATI) of Xe is calibrated for use as a reference measurement for determining and controlling the absolute CEP in other interactions. This is achieved by referencing the CEP-dependent ATI measurements of Xe to measurements of atomic H, which are in turn referenced to ab initio calculations for atomic H. This allows for the accurate determination of the absolute CEP dependence of Xe ATI, which enables relatively easy determination of the offset between the relative CEP measured and/or controlled by typical devices and the absolute CEP in the interaction.

A. Sävert, S. P. D. Mangles, M. Schnell, E. Siminos, J. M. Cole, M. Leier, M. Reuter, M. B. Schwab, M. Möller, K. Poder, O. Jäckel, G. G. Paulus, C. Spielmann, S. Skupin, Z. Najmudin, and M. C. Kaluza
Direct Observation of the Injection Dynamics of a Laser Wakefield Accelerator Using Few-Femtosecond Shadowgraphy
Physical Review Letters 115, 055002 (2015)

Abstract: We present few-femtosecond shadowgraphic snapshots taken during the nonlinear evolution of the plasma wave in a laser wakefield accelerator with transverse synchronized few-cycle probe pulses. These snapshots can be directly associated with the electron density distribution within the plasma wave and give quantitative information about its size and shape. Our results show that self-injection of electrons into the first plasma-wave period is induced by a lengthening of the first plasma period. Three-dimensional particle-in-cell simulations support our observations.

J. Bierbach, M. Yeung, E. Eckner, C. Roedel, S. Kuschel, M. Zepf, and G. G. Paulus
Long-term operation of surface high-harmonic generation from relativistic oscillating mirrors using a spooling tape
Optics Express 23, 12321 (2015)

Abstract: Surface high-harmonic generation in the relativistic regime is demonstrated as a source of extreme ultra-violet (XUV) pulses with extended operation time. Relativistic high-harmonic generation is driven by a frequency-doubled high-power Ti:Sapphire laser focused to a peak intensity of 3·10^19 W/cm2 onto spooling tapes. We demonstrate continuous operation over up to one hour runtime at a repetition rate of 1 Hz. Harmonic spectra ranging from 20 eV to 70 eV (62 nm to 18 nm) were consecutively recorded by an XUV spectrometer. An average XUV pulse energy in the µJ range is measured. With the presented setup, relativistic surface high-harmonic generation becomes a powerful source of coherent XUV pulses that might enable applications in, e.g. attosecond laser physics and the seeding of free-electron lasers, when the laser issues causing 80-% pulse energy fluctuations are overcome.

K. Heeg, J. Haber, D. Schumacher, L. Bocklage, H.-C. Wille, K. Schulze, R. Loetzsch, I. Uschmann, G. Paulus, R. Rüffer, R. Röhlsberger, and J. Evers
Tunable Subluminal Propagation of Narrow-band X-Ray Pulses
Physical Review Letters 114, 203601 (2015)

Abstract: Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Subluminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of Fe57 Mössbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.

M. Vogel, G. Birkl, M. Ebrahimi, D. von Lindenfels, A. Martin, G. Paulus, W. Quint, S. Ringleb, Th. Stöhlker, and M. Wiesel
Extreme-field physics in Penning traps
Hyperfine Interactions 236, 65 (2015)

Abstract: We present two Penning trap experiments concerned with different aspects of the physics of extreme electromagnetic fields, the ARTEMIS experiment designed for bound-electron magnetic moment measurements in the presence of the extremely strong fields close to the nucleus of highly charged ions, and the HILITE experiment, in which well-defined ion targets are to be subjected to high-intensity laser fields.

P. Wustelt, M. Möller, T. Rathje, A. M. Sayler, T. Stöhlker, and G. G. Paulus
Momentum-resolved study of the saturation intensity in multiple ionization
Physical Review A 91, 031401 (2015)

Abstract: We present a momentum-resolved study of strong field multiple ionization of ionic targets. Using a deconvolution method we are able to reconstruct the electron momenta from the ion momentum distributions after multiple ionization up to four sequential ionization steps. This technique allows an accurate determination of the saturation intensity as well as of the electron release times during the laser pulse. The measured results are discussed in comparison to typically used models of over-the-barrier ionization and tunnel ionization.

T. Hahn, J. Bierbach, C. Rödel, D. Hemmers, M. Yeung, B. Dromey, S. Fuchs, A. Galestian, S. Kuschel, M. Zepf, G. Paulus, and G. Pretzler
Broadband XUV polarimetry of high harmonics from plasma surfaces using multiple Fresnel reflections
Applied Physics B 118, 241 (2015)

Abstract: High-harmonic generation (HHG) by nonlinear interaction of intense laser pulses with gases or plasma surfaces is the most prominent way of creating highly coherent extreme ultraviolet (EUV/XUV) pulses. In the last years, several scientific applications have been found which require the measurement of the polarization of the harmonic radiation. We present a broadband XUV polarimeter based on multiple Fresnel reflections providing an extinction rate of 5–25 for 17–45 nm which is particularly suited for surface harmonics. The device has first been tested at a gas harmonic source providing linearly polarized XUV radiation. In a further experiment using HHG from plasma surfaces, the XUV polarimeter allowed a polarization measurement of high harmonic radiation from plasma surfaces for the first time which reveals a linear polarization state as predicted for our generation parameters. The generation and control of intense polarized XUV pulses - together with the availability of broadband polarizers in the XUV - open the way for a series of new experiments. For instance, dichroism in the XUV, elliptically polarized harmonics from aligned molecules, or the selection rules of relativistic surface harmonics can be studied with the broadband XUV polarimeter.


W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus
Low-energy electron rescattering in laser-induced ionization
Journal of Physics B: Atomic, Molecular and Optical Physics 47, 204022 (2014)

Abstract: The low-energy structure (LES) in the energy spectrum of above-threshold ionization of rare-gas atoms is reinvestigated from three different points of view. First, the role of forward rescattering in the completely classical simple-man model (SMM) is considered. Then, the corresponding classical electronic trajectories are retrieved in the quantum-mechanical ionization amplitude derived in the strong-field approximation augmented to allow for rescattering. Third, classical trajectories in the presence of both the laser field and the Coulomb field are scrutinized in order to see how they are related to the LES. It is concluded that the LES is already rooted in the SMM. The Coulomb field enhances the structure so that it can successfully compete with other contributions and become visible in the total spectrum.

M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević
Off-axis low-energy structures in above-threshold ionization
Physical Review A 90, 023412 (2014)

Abstract: The velocity map of the above-threshold ionization electron spectrum at long laser wavelength exhibits a characteristic structure normal to the laser polarization, which has the appearance of a trident or a three-pronged fork. The forklike structure vanishes for few-cycle laser pulses. It is explained in terms of the classical-electron-trajectories model of strong-field ionization augmented so as to allow for rescattering. The analysis reveals its relation to the so-called low-energy structure, which was recently observed for very small transverse momenta.

B. Marx, K. S. Schulze, I. Uschmann, T. Kämpfer, O. Wehrhan, H. C. Wille, K. Schlage, R. Röhlsberger, E. Weckert, E. Förster, Th. Stöhlker, and G. G. Paulus
High precision measurement of undulator polarization in the regime of hard x-rays
Applied Physics Letters 105, 024103 (2014)

Abstract: We have measured the polarization purity of undulator radiation at 12.9 keV, with hitherto unachievable precision. We could measure a polarization purity of 1.8 × 10−4 by using a silicon channel-cut crystal with six Bragg reflections at 45° as analyzer.

M. Kübel, A. S. Alnaser, B. Bergues, T. Pischke, J. Schmidt, Y. Deng, C. Jendrzejewski, J. Ullrich, G. G. Paulus, A. M. Azzeer, U. Kleineberg, R. Moshammer, and M. F. Kling
Strong-field control of the dissociative ionization of N 2 O with near-single-cycle pulses
New Journal of Physics 16, 065017 (2014)

Abstract: The dissociative ionization of N 2 O by near-single-cycle laser pulses is studied using phase-tagged ion–ion coincidence momentum imaging. Carrier–envelope phase (CEP) dependences are observed in the absolute ion yields and the emission direction of nearly all ionization and dissociation pathways of the triatomic molecule. We find that laser-field-driven electron recollision has a significant impact on the dissociative ionization dynamics and results in pronounced CEP modulations in the dication yields, which are observed in the product ion yields after dissociation. The results indicate that the directional emission of coincident ##IMG## [http://ej.iop.org/images/1367-2630/16/6/065017/njp494655ieqn1.gif] {{N^+}} and ##IMG## [http://ej.iop.org/images/1367-2630/16/6/065017/njp494655ieqn2.gif] {\rm N{{\rm O}^+}} ions in the denitrogenation of the dication can be explained by selective ionization of oriented molecules. The deoxygenation of the dication with the formation of coincident ##IMG## [http://ej.iop.org/images/1367-2630/16/6/065017/njp494655ieqn3.gif] N₂^{+} + ##IMG## [http://ej.iop.org/images/1367-2630/16/6/065017/njp494655ieqn4.gif] {{O^+}} ions exhibits an additional shift in its CEP dependence, suggesting that this channel is further influenced by laser interaction with the dissociating dication. The experimental results demonstrate how few-femtosecond dynamics can drive and steer molecular reactions taking place on (much) longer time scales.

P. Hansinger, G. Maleshkov, I. L. Garanovich, D. V. Skryabin, D. N. Neshev, A. Dreischuh, and G. G. Paulus
Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams
Optics Express 22, 11079 (2014)

Abstract: Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

K. S. Schulze, B. Marx, I. Uschmann, E. Förster, Th. Stöhlker, and G. G. Paulus
Determination of the polarization state of x rays with the help of anomalous transmission
Applied Physics Letters 104, 151110 (2014)

Abstract: Besides intensity and direction, the polarization of an electromagnetic wave provides characteristic information on the crossed medium. Here, we present two methods for the determination of the polarization state of x rays by polarizers based on anomalous transmission (Borrmann effect). Using a polarizer-analyzer setup, we have measured a polarization purity of less than 1.5 × 10^−5, three orders of magnitude better than obtained in earlier work. Using the analyzer crystal in multiple-beam case with slightly detuned azimuth, we show how the first three Stokes parameters can be determined with a single angular scan. Thus, polarization analyzers based on anomalous transmission make it possible to detect changes of the polarization in a range from degrees down to arcseconds.

N. I. Shvetsov-Shilovski, E. Räsänen, G. G. Paulus, and L. B. Madsen
Asymmetric photoelectron momentum distributions due to quantum interference in strong-field ionization by a few-cycle pulse
Physical Review A 89, 043431 (2014)

Abstract: We calculate the left-right asymmetry of the photoelectron momentum distributions generated in a hydrogen atom exposed to an intense few-cycle laser pulse as a function of both the carrier-envelope phase and the laser intensity. We present results of the numerical solution of the three-dimensional time-dependent Schrodingere equation, semiclassical simulations accounting for both laser and Coulomb fields, and the strong-field approximation. We predict pronounced oscillations of the asymmetry parameter as a function of the intensity for a particular range of the carrier-envelope phase. In order to reveal the mechanism underlying these oscillations, we investigate in detail the electron momentum distributions in the one-dimensional case. We show that quantum interference among a large set of both bound and continuum field-free states is responsible for the oscillatory behavior of the left-right asymmetry.

X. Gong, M. Kunitski, K. J. Betsch, Q. Song, L. Ph. H. Schmidt, T. Jahnke, N. Kling, O. Herrwerth, B. Bergues, A. Senftleben, J. Ullrich, R. Moshammer, G. G. Paulus, I. Ben-Itzhak, M. Lezius, M. F. Kling, H. Zeng, R. R. Jones, and J. Wu
Multielectron effects in strong-field dissociative ionization of molecules
Physical Review A 89, 043429 (2014)

Abstract: We study triple-ionization-induced, spatially asymmetric dissociation of N_2 using angular streaking in an elliptically polarized laser pulse in conjunction with few-cycle pump-probe experiments. The kinetic-energyrelease dependent directional asymmetry in the ion sum-momentum distribution reflects the internuclear distance dependence of the fragmentation mechanism. Our results show that for 5-35 fs near-infrared laser pulses with intensities reaching 10^(15) W/cm^(2), charge exchange between nuclei plays aminor role in the triple ionization of N_2. We demonstrate that angular streaking provides a powerful tool for probing multielectron effects in strong-field dissociative ionization of small molecules.

X. Xie, K. Doblhoff-Dier, H. Xu, S. Roither, M. Schöffler, D. Kartashov, S. Erattupuzha, T. Rathje, G. Paulus, K. Yamanouchi, A. Baltuška, S. Gräfe, and M. Kitzler
Selective Control over Fragmentation Reactions in Polyatomic Molecules Using Impulsive Laser Alignment
Physical Review Letters 112, 163003 (2014)

Abstract: We investigate the possibility of using molecular alignment for controlling the relative probability of individual reaction pathways in polyatomic molecules initiated by electronic processes on the few-femtosecond time scale. Using acetylene as an example, it is shown that aligning the molecular axis with respect to the polarization direction of the ionizing laser pulse does not only allow us to enhance or suppress the overall fragmentation yield of a certain fragmentation channel but, more importantly, to determine the relative probability of individual reaction pathways starting from the same parent molecular ion. We show that the achieved control over dissociation or isomerization pathways along specific nuclear degrees of freedom is based on a controlled population of associated excited dissociative electronic states in the molecular ion due to relatively enhanced ionization contributions from inner valence orbitals.

X. Xie, S. Roither, M. Schöffler, E. Lötstedt, D. Kartashov, L. Zhang, G. Paulus, A. Iwasaki, A. Baltuška, K. Yamanouchi, and M. Kitzler
Electronic Predetermination of Ethylene Fragmentation Dynamics
Physical Review X 4, 021005 (2014)

Abstract: We experimentally investigate the dependence of the fragmentation behavior of the ethylene dication on the intensity and duration of the laser pulses that initiate the fragmentation dynamics by strong-field double ionization. Using coincidence momentum imaging for the detection of ionic fragments, we disentangle the different contributions of ionization from lower-valence orbitals and field-driven excitation dynamics to the population of certain dissociative excited ionic states that are connected to one of several possible fragmentation pathways towards a given set of fragment ions. We find that the excitation probability to a particular excited state and therewith the outcome of the fragmentation reaction strongly depend on the parameters of the laser pulse. This, in turn, opens up new possibilities for controlling the outcome of fragmentation reactions of polyatomic molecules in that it may allow one to selectively enhance or suppress individual fragmentation channels, which was not possible in previous attempts of controlling fragmentation processes of polyatomic molecules with strong laser fields.

M. Klaiber, E. Yakaboylu, C. Müller, H. Bauke, G. G. Paulus, and K. Z. Hatsagortsyan
Spin dynamics in relativistic ionization with highly charged ions in super-strong laser fields
Journal of Physics B: Atomic, Molecular and Optical Physics 47, 065603 (2014)

Abstract: Spin dynamics and induced spin effects in above-threshold ionization of hydrogenlike highly charged ions in super-strong laser fields are investigated. Spin-resolved ionization rates in the tunnelling regime are calculated by employing two versions of a relativistic Coulomb-corrected strong-field approximation (SFA). An intuitive simpleman model is developed which explains the derived scaling laws for spin flip and spin asymmetry effects. The intuitive model as well as our ab initio numerical simulations support the analytical results for the spin effects obtained in the dressed SFA where the impact of the laser field on the electron spin evolution in the bound state is taken into account. In contrast, the standard SFA is shown to fail in reproducing spin effects in ionization even at a qualitative level. The anticipated spin-effects are expected to be measurable with modern laser techniques combined with an ion storage facility.

M. Kübel, K. J. Betsch, N. G. Kling, A. S. Alnaser, J. Schmidt, U. Kleineberg, Y. Deng, I. Ben-Itzhak, G. G. Paulus, T. Pfeifer, J. Ullrich, R. Moshammer, M. F. Kling, and B. Bergues
Non-sequential double ionization of Ar: from the single- to the many-cycle regime
New Journal of Physics 16, 033008 (2014)

Abstract: The transition from the near-single to the multi-cycle regime in non-sequential double ionization of argon is investigated experimentally. Argon atoms are exposed to intense laser pulses with a center wavelength around 790 nm and the momenta of electrons and ions generated in the double ionization process are measured in coincidence using a reaction microscope. The duration of the near transform-limited pulses is varied from 4 to 30 fs. We observe an abrupt collapse of the cross-shaped two-electron momentum distribution [17] in the few-cycle regime. The transition to longer pulses is further accompanied by a strong increase in the fraction of anti-correlated to correlated electrons.

S. Busold, A. Almomani, V. Bagnoud, W. Barth, S. Bedacht, A. Blažević, O. Boine-Frankenheim, C. Brabetz, T. Burris-Mog, T. Cowan, O. Deppert, M. Droba, H. Eickhoff, U. Eisenbarth, K. Harres, G. Hoffmeister, I. Hofmann, O. Jäckel, R. Jäger, M. Joost, S. Kraft, F. Kroll, M. Kaluza, O. Kester, Z. Lecz, T. Merz, F. Nürnberg, H. Al-Omari, A. Orzhekhovskaya, G. Paulus, J. Polz, U. Ratzinger, M. Roth, G. Schaumann, P. Schmidt, U. Schramm, G. Schreiber, D. Schumacher, T. Stöhlker, A. Tauschwitz, W. Vinzenz, F. Wagner, S. Yaramyshev, and B. Zielbauer
Shaping laser accelerated ions for future applications – The LIGHT collaboration
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 94 (2014)

Abstract: Abstract The generation of intense ion beams from high-intensity laser-generated plasmas has been the focus of research for the last decade. In the LIGHT collaboration the expertise of heavy ion accelerator scientists and laser and plasma physicists has been combined to investigate the prospect of merging these ion beams with conventional accelerator technology and exploring the possibilities of future applications. We report about the goals and first results of the LIGHT collaboration to generate, handle and transport laser driven ion beams. This effort constitutes an important step in research for next generation accelerator technologies.

E. Stambulchik, E. Kroupp, Y. Maron, U. Zastrau, I. Uschmann, and G. G. Paulus
Absorption-aided x-ray emission tomography of planar targets
Physics of Plasmas 21, 033303 (2014)

Abstract: Suggested is a tomography-like method for studying properties of solid-density plasmas with cylindrical symmetry, such as formed in the interaction of high-power lasers with planar targets. The method is based on simultaneous observation of the target x-ray fluorescence at different angles. It can be applied for validation of existing hypotheses and lately for reconstruction of the plasma properties with three-dimensional resolution. The latter becomes straightforward if the resonance x-ray self-absorption is negligible. The utility of the method is demonstrated by examples.

P. Hansinger, G. Maleshkov, N. Gorunski, N. Dimitrov, A. Dreischuh, and G. G. Paulus
Interaction between one-dimensional dark spatial solitons and semi-infinite dark stripes
Optics Communications 313, 106 (2014)

Abstract: In this work we numerically study the evolution and interaction of one-dimensional (1-D) dark spatial solitons and semi-infinite dark stripes (SIDSs) in a local self-defocusing Kerr nonlinear medium. The experimental results in the linear regime of propagation confirm that the SIDS bending and fusion with the infinite 1-D dark beam modeled for negative nonlinearity is due to the opposite phase semi-helicities of SID beam ends. Results for several interaction scenaria show that bending ends of the semi-infinite dark stripes splice to the 1-D dark beam to form structures resembling waveguide couplers/branchers. Well pronounced modulational stability of 1-D dark spatial solitons under strong symmetric background beam modulation from decaying SIDSs is predicted.

X. Xie, S. Roither, M. Schöffler, H. Xu, S. Bubin, E. Lötstedt, S. Erattuphuza, A. Iwasaki, D. Kartashov, K. Varga, G. G. Paulus, A. Baltuška, K. Yamanouchi, and M. Kitzler
Role of proton dynamics in efficient photoionization of hydrocarbon molecules
Physical Review A 89, 023429 (2014)

Abstract: We experimentally investigate the ionization mechanism behind the formation of remarkably high charge states observed in the laser-pulse-induced fragmentation of different hydrocarbon molecules by Roither et al. [Phys. Rev. Lett. 106, 163001 (2011)], who suggested enhanced ionization occurring at multiple C-H bonds as the underlying ionization mechanism. Using multiparticle coincidence momentum imaging we measure the yield of multiply charged fragmenting ethylene and acetylene molecules at several intensities and pulse durations ranging from the few-cycle regime to 25 fs. We observe, at constant intensity, a strong increase of the proton energy with increasing laser pulse duration. It is shown that this is caused by a strong increase in the yield of highly charged parent molecular ions with pulse duration. Based on experimental evidence we explain this increase by the necessary population of precursor states in the parent ion that feature fast C-H stretch dynamics to the critical internuclear distance, where efficient ionization via enhanced ionization takes place. For increasing pulse duration these precursor ionic states are more efficiently populated, which leads in turn to a higher enhanced-ionization probability for longer pulses. Our work provides experimental evidence for the existence of a multiple-bond version of enhanced ionization in polyatomic molecules.


M. B. Schwab, A. Sävert, O. Jäckel, J. Polz, M. Schnell, T. Rinck, L. Veisz, M. Möller, P. Hansinger, G. G. Paulus, and M. C. Kaluza
Few-cycle optical probe-pulse for investigation of relativistic laser-plasma interactions
Applied Physics Letters 103, 191118 (2013)

Abstract: The development of a few-cycle optical probe-pulse for the investigation of laser-plasma interactions driven by a Ti:sapphire, 30 Terawatt (TW) laser system is described. The probe is seeded by a fraction of the driving laser's energy and is spectrally broadened via self-phase modulation in a hollow core fiber filled with a rare gas, then temporally compressed to a few optical cycles via chirped mirrors. Shadowgrams of the laser-driven plasma wave created in relativistic electron acceleration experiments are presented with few-fs temporal resolution, which is shown to be independent of post-interaction spectral filtering of the probe-beam.

A. Gopal, P. Singh, S. Herzer, A. Reinhard, A. Schmidt, U. Dillner, T. May, H.-G. Meyer, W. Ziegler, and G. G. Paulus
Characterization of 700  μJ T rays generated during high-power laser solid interaction
Optics Letters 38, 4705 (2013)

Abstract: Laser-produced solid density plasmas are well-known as table-top sources of electromagnetic radiation. Recent studies have shown that energetic broadband terahertz pulses (T rays) can also be generated from laser-driven compact ion accelerators. Here we report the measurement of record-breaking T-Ray pulses with energies no less than 0.7 mJ. The terahertz spectrum has been characterized for frequencies ranging from 0.1–133  THz. The dependence of T-Ray yield on incident laser energy is linear and shows no tendencies of saturation. The noncollinear emission pattern and the high yield reveal that the T rays are generated by the transient field at the rear surface of the solid target.

V. Hilbert, A. Blinne, S. Fuchs, T. Feigl, T. Kämpfer, C. Rödel, I. Uschmann, M. Wünsche, G. Paulus, E. Förster, and U. Zastrau
An extreme ultraviolet Michelson interferometer for experiments at free-electron lasers
Review of Scientific Instruments 84, 095111 (2013)

Abstract: We present a Michelson interferometer for 13.5 nm soft x-ray radiation. It is characterized in a proof-of-principle experiment using synchrotron radiation, where the temporal coherence is measured to be 13 fs. The curvature of the thin-film beam splitter membrane is derived from the observed fringe pattern. The applicability of this Michelson interferometer at intense free-electron lasers is investigated, particularly with respect to radiation damage. This study highlights the potential role of such Michelson interferometers in solid density plasma investigations using, for instance, extreme soft x-ray free-electron lasers. A setup using the Michelson interferometer for pseudo-Nomarski-interferometry is proposed.

M. Kübel, N. Kling, K. J. Betsch, N. Camus, A. Kaldun, U. Kleineberg, I. Ben-Itzhak, R. R. Jones, G. G. Paulus, T. Pfeifer, J. Ullrich, R. Moshammer, M. F. Kling, and B. Bergues
Nonsequential double ionization of N_{2} in a near-single-cycle laser pulse
Physical Review A 88, 023418 (2013)

Abstract: We present a comparative study of nonsequential double ionization (NSDI) of N_{2} and Ar exposed to near-single-cycle laser pulses. The NSDI process is investigated using carrier-envelope-phase-tagged electron-ion coincidence spectroscopy. The measured NSDI spectra of N_{2} and Ar exhibit a striking resemblance. In particular, the correlated two-electron momentum distribution arising from NSDI of N_{2} also displays a cross-shape very similar to that reported for Ar [Bergues et al., Nat. Commun. 3, 813 (2012)]. We interpret our results in terms of recollision-excitation with subcycle depletion and discuss how this mechanism accounts for the observed similarities and differences in the ionization behavior of the two species.

T. Rathje, A. M. Sayler, S. Zeng, P. Wustelt, H. Figger, B. D. Esry, and G. G. Paulus
Coherent Control at Its Most Fundamental: Carrier-Envelope-Phase-Dependent Electron Localization in Photodissociation of a H₂+ Molecular Ion Beam Target
Physical Review Letters 111, 093002 (2013)

Abstract: Measurements and calculations of the absolute carrier-envelope-phase (CEP) effects in the photodissociation of the simplest molecule, H₂+, with a 4.5-fs Ti:sapphire laser pulse at intensities up to (4 ± 2) × 10^{14}  W/cm^{2} are presented. Localization of the electron with respect to the two nuclei (during the dissociation process) is controlled via the CEP of the ultrashort laser pulses. In contrast to previous CEP-dependent experiments with neutral molecules, the dissociation of the molecular ions is not preceded by a photoionization process, which strongly influences the CEP dependence. Kinematically complete data are obtained by time- and position-resolved coincidence detection. The phase dependence is determined by a single-shot phase measurement correlated to the detection of the dissociation fragments. The experimental results show quantitative agreement with ab initio 3D time-dependent Schrödinger equation calculations that include nuclear vibration and rotation.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus
Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator
Physical Review Letters 111, 074802 (2013)

Abstract: We report the observation of subpicosecond terahertz (T-ray) pulses with energies ≥ 460  μJ from a laser-driven ion accelerator, thus rendering the peak power of the source higher even than that of state-of-the-art synchrotrons. Experiments were performed with intense laser pulses (up to 5 × 10^19  W/cm^2) to irradiate thin metal foil targets. Ion spectra measured simultaneously showed a square law dependence of the T-ray yield on particle number. Two-dimensional particle-in-cell simulations show the presence of transient currents at the target rear surface which could be responsible for the strong T-ray emission.

K. Heeg, H.-C. Wille, K. Schlage, T. Guryeva, D. Schumacher, I. Uschmann, K. S. Schulze, B. Marx, T. Kämpfer, G. Paulus, R. Röhlsberger, and J. Evers
Vacuum-Assisted Generation and Control of Atomic Coherences at X-Ray Energies
Physical Review Letters 111, 073601 (2013)

Abstract: The control of light-matter interaction at the quantum level usually requires coherent laser fields. But already an exchange of virtual photons with the electromagnetic vacuum field alone can lead to quantum coherences, which subsequently suppress spontaneous emission. We demonstrate such spontaneously generated coherences (SGC) in a large ensemble of nuclei operating in the x-ray regime, resonantly coupled to a common cavity environment. The observed SGC originates from two fundamentally different mechanisms related to cooperative emission and magnetically controlled anisotropy of the cavity vacuum. This approach opens new perspectives for quantum control, quantum state engineering and simulation of quantum many-body physics in an essentially decoherence-free setting.

B. Marx, K. S. Schulze, I. Uschmann, T. Kämpfer, R. Lötzsch, O. Wehrhan, W. Wagner, C. Detlefs, T. Roth, J. Härtwig, E. Förster, Th. Stöhlker, and G. G. Paulus
High-Precision X-Ray Polarimetry
Physical Review Letters 110, 254801 (2013)

Abstract: The polarization purity of 6.457- and 12.914-keV x rays has been improved to the level of 2.4×10-10 and 5.7×10-10. The polarizers are channel-cut silicon crystals using six 90° reflections. Their performance and possible applications are demonstrated in the measurement of the optical activity of a sucrose solution.

B. Aurand, S. Kuschel, O. Jäckel, C. Rödel, H. Y. Zhao, S. Herzer, A. E. Paz, J. Bierbach, J. Polz, B. Elkin, G. G. Paulus, A. Karmakar, P. Gibbon, T. Kühl, and M. C. Kaluza
Radiation pressure-assisted acceleration of ions using multi-component foils in high-intensity laser-matter interactions
New Journal of Physics 15, 033031 (2013)

Abstract: Experimental results on the acceleration of protons and carbon ions from ultra-thin polymer foils at intensities of up to 6 × 10^(19) W cm^(−2) are presented revealing quasi-monoenergetic spectral characteristics for different ion species at the same time. For carbon ions and protons, a linear correlation between the cutoff energy and the peak energy is observed when the laser intensity is increased. Particle-in-cell simulations supporting the experimental results imply an ion acceleration mechanism driven by the radiation pressure as predicted for multi-component foils at these intensities.

M. Yeung, B. Dromey, C. Rödel, J. Bierbach, M. Wünsche, G. Paulus, T. Hahn, D. Hemmers, C. Stelzmann, G. Pretzler, and M. Zepf
Near-monochromatic high-harmonic radiation from relativistic laser-plasma interactions with blazed grating surfaces
New Journal of Physics 15, 025042 (2013)

Abstract: Intense, femtosecond laser interactions with blazed grating targets are studied through experiment and particle-in-cell (PIC) simulations. The high harmonic spectrum produced by the laser is angularly dispersed by the grating leading to near-monochromatic spectra emitted at different angles, each dominated by a single harmonic and its integer-multiples. The spectrum emitted in the direction of the third-harmonic diffraction order is measured to contain distinct peaks at the 9th and 12th harmonics which agree well with two-dimensional PIC simulations using the same grating geometry. This confirms that surface smoothing effects do not dominate the far-field distributions for surface features with sizes on the order of the grating grooves whilst also showing this to be a viable method of producing near-monochromatic, short-pulsed extreme-ultraviolet radiation.

S. Fuchs, C. Rödel, M. Krebs, S. Hädrich, J. Bierbach, A. E. Paz, S. Kuschel, M. Wünsche, V. Hilbert, U. Zastrau, E. Förster, J. Limpert, and G. G. Paulus
Sensitivity calibration of an imaging extreme ultraviolet spectrometer-detector system for determining the efficiency of broadband extreme ultraviolet sources
Review of Scientific Instruments 84, 023101 (2013)

Abstract: We report on the absolute sensitivity calibration of an extreme ultraviolet (XUV) spectrometer system that is frequently employed to study emission from short-pulse laser experiments. The XUV spectrometer, consisting of a toroidal mirror and a transmission grating, was characterized at a synchrotron source in respect of the ratio of the detected to the incident photon flux at photon energies ranging from 15.5 eV to 99 eV. The absolute calibration allows the determination of the XUV photon number emitted by laser-based XUV sources, e.g., high-harmonic generation from plasma surfaces or in gaseous media. We have demonstrated high-harmonic generation in gases and plasma surfaces providing 2.3 μW and μJ per harmonic using the respective generation mechanisms.


K. J. Betsch, N. Johnson, B. Bergues, M. Kübel, O. Herrwerth, A. Senftleben, I. Ben-Itzhak, G. G. Paulus, R. Moshammer, J. Ullrich, M. F. Kling, and R. R. Jones
Controlled directional ion emission from several fragmentation channels of CO driven by a few-cycle laser field
Physical Review A 86, 063403 (2012)

Abstract: We explore the dissociative ionization of CO with carrier-envelope-phase (CEP) tagged few-cycle laser pulses. We observe the CEP dependence of the directional emission of C^(p+) and O^(q+) fragments from transient CO^([p+q]+) ions, where p + q ≤ 3 and q ≤ 1. At I_0 = 3.5 × 10^(14) W/cm^2, a 180°. phase difference between the C^(+) and O^(+) fragments from the (p=1, q=0) and (p=0, q=1) channels reflects the orientation dependence of the CO ionization. At I_0 = 1.2 × 10^(15) W/cm^2, we find a ~35° phase shift between the C^(2+) fragments from the (p = 2, q = 0) and (p = 2, q = 1) channels, in contrast to the 180∘ shift previously observed between the C2+ fragment channels at I_0 = 6 × 10^(14) W/cm^2 [ Phys. Rev. Lett. 106 073004 (2011)].

X. Xie, K. Doblhoff-Dier, S. Roither, M. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. Paulus, A. Baltuska, S. Gräfe, and M. Kitzler
Attosecond-Recollision-Controlled Selective Fragmentation of Polyatomic Molecules
Physical Review Letters 109, 243001 (2012)

Abstract: Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wave packets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of predetermining fragmentation and isomerization reactions in polyatomic molecules on subfemtosecond time scales.

M. Kübel, K. J. Betsch, N. Johnson, U. Kleineberg, R. Moshammer, J. Ullrich, G. G. Paulus, M. F. Kling, and B. Bergues
Carrier-envelope-phase tagging in measurements with long acquisition times
New Journal of Physics 14, 093027 (2012)

Abstract: We present a detailed analysis of the systematic errors that affect single-shot carrier envelope phase (CEP) measurements in experiments with long acquisition times, for which only limited long-term laser stability can be achieved. After introducing a scheme for eliminating these systematic errors to a large extent, we apply our approach to investigate the CEP dependence of the yield of doubly charged ions produced via non-sequential double ionization of argon in strong near-single-cycle laser pulses. The experimental results are compared to predictions of semiclassical calculations.

A. Paz, S. Kuschel, C. Rödel, M. Schnell, O. Jäckel, M. C. Kaluza, and G. G. Paulus
Thomson backscattering from laser-generated, relativistically moving high-density electron layers
New Journal of Physics 14, 093018 (2012)

Abstract: We show experimentally that extreme ultraviolet radiation is produced when a laser pulse is Thomson backscattered from sheets of relativistic electrons that are formed at the rear surface of a foil irradiated on its front side with a high-intensity laser. An all-optical setup is realized using the Jena titanium:sapphire ten-terawatt laser system with an enhanced amplified spontaneous emission background of 10^{−12}. The main pulse is split into two: one of them accelerates electrons from thin aluminium foil targets to energies of the order of some MeV and the other, counterpropagating probe pulse Thomson-backscatters off these electrons when they exit the target rear side. The process produced photons within a wide spectral range of some tens of eV as a result of the broad electron energy distribution. The highest scattering intensity is observed when the probe pulse arrives at the target rear surface 100 fs after irradiation of the target front side by the pump pulse, corresponding to the maximum flux of hot electrons at the interaction region. These results can provide time-resolved information about the evolution of the rear-surface electron sheath and hence about the dynamics of the electric fields responsible for the acceleration of ions from the rear surface of thin, laser-irradiated foils.

C. Rödel, D. an der Brügge, J. Bierbach, M. Yeung, T. Hahn, B. Dromey, S. Herzer, S. Fuchs, A. Pour, E. Eckner, M. Behmke, M. Cerchez, O. Jäckel, D. Hemmers, T. Toncian, M. C. Kaluza, A. Belyanin, G. Pretzler, O. Willi, A. Pukhov, M. Zepf, and G. G. Paulus
Harmonic Generation from Relativistic Plasma Surfaces in Ultrasteep Plasma Density Gradients
Physical Review Letters 109, 125002 (2012)

Abstract: Harmonic generation in the limit of ultrasteep density gradients is studied experimentally. Observations reveal that, while the efficient generation of high order harmonics from relativistic surfaces requires steep plasma density scale lengths (L_p/λ < 1), the absolute efficiency of the harmonics declines for the steepest plasma density scale length L_p → 0, thus demonstrating that near-steplike density gradients can be achieved for interactions using high-contrast high-intensity laser pulses. Absolute photon yields are obtained using a calibrated detection system. The efficiency of harmonics reflected from the laser driven plasma surface via the relativistic oscillating mirror was estimated to be in the range of 10^{-4} – 10^{-6} of the laser pulse energy for photon energies ranging from 20 – 40 eV, with the best results being obtained for an intermediate density scale length.

A. Gopal, T. May, S. Herzer, A. Reinhard, S. Minardi, M. Schubert, U. Dillner, B. Pradarutti, J. Polz, T. Gaumnitz, M. C. Kaluza, O. Jäckel, S. Riehemann, W. Ziegler, H.-P. Gemünd, H.-G. Meyer, and G. G. Paulus
Observation of energetic terahertz pulses from relativistic solid density plasmas
New Journal of Physics 14, 083012 (2012)

Abstract: We report the first experimental observation of terahertz (THz) radiation from the rear surface of a solid target while interacting with an intense laser pulse. Experimental and two-dimensional particle-in-cell simulations show that the observed THz radiation is mostly emitted at large angles to the target normal. Numerical results point out that a large part of the emission originates from a micron-scale plasma sheath at the rear surface of the target, which is also responsible for the ion acceleration. This opens a perspective for the application of THz radiation detection for on-site diagnostics of particle acceleration in laser-produced plasmas.

M. Vogel, W. Quint, G.G. Paulus, and Th. Stöhlker
A Penning trap for advanced studies with particles in extreme laser fields
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 285, 65 (2012)

Abstract: We present a Penning trap as a tool for advanced studies of particles in extreme laser fields. Particularly, trap-specific manipulation techniques allow control over the confined particles’ localization and spatial density by use of trap electrodes as ‘electrostatic tweezers’ and by application of a ‘rotating wall’, respectively. It is thereby possible to select and prepare well-defined ion ensembles and to optimize the laser–particle interaction. Non-destructive detection of reaction educts and products with up to single-ion sensitivity supports advanced studies by maintaining the products for further studies at extended confinement times of minutes and above. The trap features endcaps with conical openings for applications with strongly focused lasers. We show that such a modification of a cylindrical trap is possible while harmonicity and tunability are maintained.

S. Zherebtsov, F. Süßmann, C. Peltz, J. Plenge, K. J. Betsch, I. Znakovskaya, A. S. Alnaser, N. G. Johnson, M. Kübel, A. Horn, V. Mondes, C. Graf, S. A. Trushin, A. Azzeer, M. J. J. Vrakking, G. G. Paulus, F. Krausz, E. Rühl, T. Fennel, and M. F. Kling
Carrier-envelope phase-tagged imaging of the controlled electron acceleration from SiO2 nanospheres in intense few-cycle laser fields
New Journal of Physics 14, 075010 (2012)

Abstract: Waveform-controlled light fields offer the possibility of manipulating ultrafast electronic processes on sub-cycle timescales. The optical lightwave control of the collective electron motion in nanostructured materials is key to the design of electronic devices operating at up to petahertz frequencies. We have studied the directional control of the electron emission from 95 nm diameter SiO_2 nanoparticles in few-cycle laser fields with a well-defined waveform. Projections of the three-dimensional (3D) electron momentum distributions were obtained via single-shot velocity-map imaging (VMI), where phase tagging allowed retrieving the laser waveform for each laser shot. The application of this technique allowed us to efficiently suppress background contributions in the data and to obtain very accurate information on the amplitude and phase of the waveform-dependent electron emission. The experimental data that are obtained for 4 fs pulses centered at 720 nm at different intensities in the range (1 - 4) × 10^13 W cm^(−2) are compared to quasi-classical mean-field Monte-Carlo simulations. The model calculations identify electron backscattering from the nanoparticle surface in highly dynamical localized fields as the main process responsible for the energetic electron emission from the nanoparticles. The local field sensitivity of the electron emission observed in our studies can serve as a foundation for future research on propagation effects for larger particles and field-induced material changes at higher intensities.

G. Maleshkov, P. Hansinger, N. Dimitrov, A. Dreischuh, and G. Paulus
Branching optical signals by fractional vortex dipoles
Optics Communications 285, 3529 (2012)

Abstract: We study the evolution and interaction of semi-infinite dark beams carrying phase dislocations, where step- and screw-like phase profiles are combined. Similar to dark beams with a finite length, semi-infinite dark beams tend to move in transversal direction with respect to their background beam. In addition, they develop a snake-like instability and optical vortices detach from their bending ends. We are looking for appropriate conditions to control the process of concatenating and crossing the ends of several such semi-infinite dark beams in a way suitable for probe-beam branching and routing in self-defocusing Kerr nonlinear media. Colinear and perpendicular probe beam propagations in the optically-induced guiding structures are modeled and analyzed with respect to the branching efficiency to respective virtual output channels.

M. Möller, Y. Cheng, S. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang
Dependence of high-order-harmonic-generation yield on driving-laser ellipticity
Physical Review A 86, 011401 (2012)

Abstract: High-order-harmonic-generation yield is remarkably sensitive to driving laser ellipticity, which is interesting from a fundamental point of view as well as for applications. The most well-known example is the generation of isolated attosecond pulses via polarization gating. We develop an intuitive semiclassical model that makes use of the recently measured initial transverse momentum of tunneling ionization. The model is able to predict the dependence of the high-order-harmonic yield on driving laser ellipticity and is in good agreement with experimental results and predictions from a numerically solved time-dependent Schrödinger equation.

J. Bierbach, C. Rödel, M. Yeung, B. Dromey, T. Hahn, A. Pour, S. Fuchs, A. E. Paz, S. Herzer, S. Kuschel, O. Jäckel, M. C. Kaluza, G. Pretzler, M. Zepf, and G. G. Paulus
Generation of 10 µW relativistic surface high-harmonic radiation at a repetition rate of 10 Hz
New Journal of Physics 14, 065005 (2012)

Abstract: Experimental results on relativistic surface HHG at a repetition rate of 10 Hz are presented. Average powers in the 10 μW range are generated in the spectral range of 51 to 26 nm (24 - 48 eV). The surface harmonic radiation is produced by focusing the second-harmonic of a high-power laser onto a rotating glass surface to moderately relativistic intensities of 3 × 10^{19} W cm^{−2}. The harmonic emission exhibits a divergence of 26 mrad. Together with absolute photon numbers recorded by a calibrated spectrometer, this allows for the determination of the extreme ultraviolet (XUV) yield. The pulse energies of individual harmonics are reaching up to the μJ level, equivalent to an efficiency of 10^{−5}. The capability of producing stable and intense high-harmonic radiation from relativistic surface plasmas may facilitate experiments on nonlinear ionization or the seeding of free-electron lasers.

B. Bergues, M. Kübel, N. Johnson, B. Fischer, N. Camus, K. Betsch, O. Herrwerth, A. Senftleben, A. Sayler, T. Rathje, T. Pfeifer, I. Ben-Itzhak, R. Jones, G. Paulus, F. Krausz, R. Moshammer, J. Ullrich, and M. Kling
Attosecond tracing of correlated electron-emission in non-sequential double ionization
Nature Communications 3, 813 (2012)

Abstract: Despite their broad implications for phenomena such as molecular bonding or chemical reactions, our knowledge of multi-electron dynamics is limited and their theoretical modelling remains a most difficult task. From the experimental side, it is highly desirable to study the dynamical evolution and interaction of the electrons over the relevant timescales, which extend into the attosecond regime. Here we use near-single-cycle laser pulses with well-defined electric field evolution to confine the double ionization of argon atoms to a single laser cycle. The measured two-electron momentum spectra, which substantially differ from spectra recorded in all previous experiments using longer pulses, allow us to trace the correlated emission of the two electrons on sub-femtosecond timescales. The experimental results, which are discussed in terms of a semiclassical model, provide strong constraints for the development of theories and lead us to revise common assumptions about the mechanism that governs double ionization.

Ph. A. Korneev, S. V. Popruzhenko, S. P. Goreslavski, T.-M. Yan, D. Bauer, W. Becker, M. Kübel, M. F. Kling, C. Rödel, M. Wünsche, and G. G. Paulus
Interference Carpets in Above-Threshold Ionization: From the Coulomb-Free to the Coulomb-Dominated Regime
Physical Review Letters 108, 223601 (2012)

Abstract: The velocity map recorded in above-threshold ionization of xenon at 800 nm exhibits a distinct carpetlike pattern of maxima and minima for emission in the direction approximately perpendicular to the laser polarization. The pattern is well reproduced by a numerical solution of the time-dependent Schrödinger equation. In terms of the simple-man model and the strong-field approximation, it is explained by the constructive and destructive interference of the contribution of the long and the short orbit. Strictly perpendicular emission is caused by ionization at the two peaks of the laser field per cycle, which results in a 2ℏω separation of the above-threshold ionization rings.

T. Rathje, N. Johnson, M. Möller, F. Süssmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler
Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization
Journal of Physics B 45, 074003 (2012)

Abstract: A precise, real-time, single-shot carrier–envelope phase (CEP) tagging technique for few-cycle pulses was developed and combined with cold-target recoil-ion momentum spectroscopy and velocity-map imaging to investigate and control CEP-dependent processes with attosecond resolution. The stability and precision of these new techniques have allowed for the study of intense, few-cycle, laser-matter dynamics with unprecedented detail. Moreover, the same stereo above-threshold ionization (ATI) measurement was expanded to multi-cycle pulses and allows for CEP locking and pulse-length determination. Here we review these techniques and their first applications to waveform characterization and control, non-sequential double ionization of argon, ATI of xenon and electron emission from SiO_2 nanospheres.

S. Fuchs, A. Blinne, C. Rödel, U. Zastrau, V. Hilbert, M. Wünsche, J. Bierbach, E. Frumker, E. Förster, and G. G. Paulus
Optical coherence tomography using broad-bandwidth XUV and soft X-ray radiation
Applied Physics B 106, 789 (2012)

Abstract: We present a novel approach to extend optical coherence tomography (OCT) to the extreme ultraviolet (XUV) and soft X-ray (SXR) spectral range. With a simple setup based on Fourier-domain OCT and adapted for the application of XUV and SXR broadband radiation, cross-sectional images of semiconductors and organic samples becomes feasible with current synchrotron or laser-plasma sources. For this purpose, broadband XUV radiation is focused onto the sample surface, and the reflected spectrum is recorded by an XUV spectrometer. The proposed method has the particular advantage that the axial spatial resolution only depends on the spectral bandwidth. As a consequence, the theoretical resolution limit of XUV coherence tomography (XCT) is in the order of nanometers, e.g., 3 nm for wavelengths in the water window (280 - 530 eV). We proved the concept of XCT by calculating the reflectivity of one-dimensional silicon and boron carbide samples containing buried layers and found the expected properties with respect to resolution and penetration depth confirmed.

B. Aurand, C. Rödel, H. Zhao, S. Kuschel, M. Wünsche, O. Jäckel, M. Heyer, F. Wunderlich, M. C. Kaluza, G. G. Paulus, and T. Kühl
Note: A large aperture four-mirror reflective wave-plate for high-intensity short-pulse laser experiments
Review of Scientific Instruments 83, 036104 (2012)

Abstract: We report on a four-mirror reflective wave-plate system based on a phase-shifting mirror (PSM) for a continuous variation of elliptical polarization without changing the beam position and direction. The system presented and characterized here can replace a conventional retardation plate providing all advantages of a PSM, such as high damage-threshold, large scalability, and low dispersion. This makes reflective wave-plates an ideal tool for ultra-high power laser applications.


N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus
Carrier-envelope phase effect in the yield of sequential ionization by an intense few-cycle laser pulse
New Journal of Physics 13, 123015 (2011)

Abstract: The relative yield of highly charged atomic ions produced by a short (4–6 fs at FWHM) intense (10^14 – 5 × 10^18 W cm^(−2)) laser pulse was investigated by numerical solution of the rate equations. We predict oscillations of the ion yield as a function of the absolute phase. A distinctive property of this phase dependence is that it can only be observed when at least two ions have comparable yields. It is shown that with currently available laser systems the effect should be experimentally detectable for various rare gas atoms: Xe, Kr, Ar and Ne.

S. Khan, Y. Cheng, M. Möller, K. Zhao, B. Zhao, M. Chini, G. Paulus, and Z. Chang
Ellipticity dependence of 400 nm-driven high harmonic generation
Applied Physics Letters 99, 161106 (2011)

Abstract: We studied the dependence of high harmonic generation efficiency on the ellipticity of 400 nm driving laser pulses at 7.7 × 10^14 W/cm2 and compared it with the 800 nm driving laser under the same conditions. The measured decrease of high harmonic yield with the ellipticity of the 400 nm laser is ∼1.5 times slower that of the 800 nm, which agrees well with theoretical predictions based on a semi-classical model. The results indicate that it is feasible to use the generalized double optical gating with 400 nm lasers for extracting single attosecond pulses with high efficiency.

P. Hansinger, A. Dreischuh, and G. G. Paulus
Vortices in ultrashort laser pulses
Applied Physics B 104, 561 (2011)

Abstract: The propagation of optical vortices nested in broadband femtosecond laser beams was studied both numerically and experimentally. Based on the nonlinear Schrödinger equation, the dynamics of different multiple-vortex configurations with varying topological charge were modelled in self-focussing and self-defocussing Kerr media. We find a similar behavior in both cases regarding the vortex–vortex interaction. However, the collapsing background beam alters the propagation for a positive nonlinearity. Regimes of regular and possibly stable multiple filamentation were identified this way. Experiments include measurements on pairs of filaments generated in a vortex beam on an astigmatic Gaussian background with argon gas as the nonlinear medium. Spectral broadening of these filaments leads to a supercontinuum which spans from the visible range into the infrared. Recompression yields < 19 fs pulses. Further optimization may lead to much better recompression.

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus
Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime
Applied Physics Letters 99, 121108 (2011)

Abstract: Polarization gating is used to extend a real-time, single-shot, carrier-envelope phase (CEP) measurement, based on high-energy above-threshold ionization in xenon, to the multi-cycle regime. The single-shot CEP precisions achieved are better than 175 and 350 mrad for pulse durations up to 10 fs and 12.5 fs, respectively, while only 130 μJ of pulse energy are required. This opens the door to study and control of CEP-dependent phenomena in ultra-intense laser-matter interaction using optical parametric chirped pulse amplifier based tera- and petawatt class lasers.

D. Adolph, A. M. Sayler, T. Rathje, K. Rühle, and G. G. Paulus
Improved carrier-envelope phase locking of intense few-cycle laser pulses using above-threshold ionization
Optics Letters 36, 3639 (2011)

Abstract: A robust nonoptical carrier-envelope phase (CEP) locking feedback loop, which utilizes a measurement of the left–right asymmetry in the above-threshold ionization (ATI) of Xe, is implemented, resulting in a significant improvement over the standard slow-loop f-to-2f technique. This technique utilizes the floating average of a real-time, every-single-shot CEP measurement to stabilize the CEP of few-cycle laser pulses generated by a standard Ti:sapphire chirped-pulse amplified laser system using a hollow-core fiber and chirped mirror compression scheme. With this typical commercially available laser system and the stereographic ATI method, we are able to improve short-term (minutes) CEP stability after a hollow-core fiber from 450 to 290 mrad rms and long-term (hours) stability from 480 to 370 mrad rms.

F. Süssmann, S. Zherebtsov, J. Plenge, N. Johnson, M. Kübel, A. M. Sayler, V. Mondes, C. Graf, E. Rühl, G. G. Paulus, D. Schmischke, P. Swrschek, and M. F. Kling
Single-shot velocity-map imaging of attosecond light-field control at kilohertz rate
Review of Scientific Instruments 82, 093109 (2011)

Abstract: High-speed, single-shot velocity-map imaging (VMI) is combined with carrier-envelope phase (CEP) tagging by a single-shot stereographic above-threshold ionization (ATI) phase-meter. The experimental setup provides a versatile tool for angle-resolved studies of the attosecond control of electrons in atoms, molecules, and nanostructures. Single-shot VMI at kHz repetition rate is realized with a highly sensitive megapixel complementary metal-oxide semiconductor camera omitting the need for additional image intensifiers. The developed camera software allows for efficient background suppression and the storage of up to 10^24 events for each image in real time. The approach is demonstrated by measuring the CEP-dependence of the electron emission from ATI of Xe in strong (≈ 10^13 W/cm2) near single-cycle (4 fs) laser fields. Efficient background signal suppression with the system is illustrated for the electron emission from SiO_2 nanospheres.

B. Aurand, S. Kuschel, C. Rödel, M. Heyer, F. Wunderlich, O. Jäckel, M. C. Kaluza, G. G. Paulus, and T. Kühl
Creating circularly polarized light with a phase-shifting mirror
Optics Express 19, 17151 (2011)

Abstract: We report on the performance of a system employing a multi-layer coated mirror creating circularly polarized light in a fully reflective setup. With one specially designed mirror we are able to create laser pulses with an ellipticity of more than ε = 98% over the entire spectral bandwidth from initially linearly polarized Titanium:Sapphire femtosecond laser pulses. We tested the homogeneity of the polarization with beam sizes of the order of approximately 10 cm. The damage threshold was determined to be nearly 400 times higher than for a transmissive quartz-wave plate which suggests applications in high intensity laser experiments. Another advantage of the reflective scheme is the absence of nonlinear effects changing the spectrum or the pulse-form and the scalability of coating fabrication to large aperture mirrors.

N. I. Shvetsov-Shilovski, A. M. Sayler, T. Rathje, and G. G. Paulus
Momentum distributions of sequential ionization generated by an intense laser pulse
Physical Review A 83, 033401 (2011)

Abstract: The relative yield and momentum distributions of all multiply charged atomic ions generated by a short (30 fs) intense (10^14 - 5 × 10^18 W/cm2) laser pulse are investigated using a Monte Carlo simulation. We predict a substantial shift in the maximum (centroid) of the ion-momentum distribution along the laser polarization as a function of the absolute phase. This effect should be experimentally detectable with currently available laser systems even for relatively long pulses, such as 25 - 30 fs. In addition to the numerical results, we present semianalytical scaling for the position of the maximum.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. C. Kaluza, and G. G. Paulus
High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude
Applied Physics B 103, 295 (2011)

Abstract: We present a plasma mirror configuration that improves the temporal pulse contrast of femtosecond terawatt laser pulses by a factor of thousand using a single antireflection coated glass target. The device provides ultra-high contrast for experiments with a maximum repetition rate of 10 Hz. A third-order cross-correlator has been used to measure the temporal pulse contrast for several different plasma mirror targets. It is shown that the ASE can be suppressed to a level of 10^(−11.) A comparison between a triggered and an untriggered plasma mirror reveals differences in the intensity distribution of the focused beam. The triggered plasma mirror produces a slightly larger focus due to the expansion of the triggered plasma mirror at -3 ps before the main pulse. We propose a cost-effective AR-coated and a blank glass target to reduce the costs of the consumable target material. High-harmonic radiation on solid surfaces has been generated with different plasma mirror targets to demonstrate the high laser contrast.

M. Behmke, D. an der Bruegge, C. Rödel, M. Cerchez, D. Hemmers, M. Heyer, O. Jäckel, M. Kübel, G. G. Paulus, G. Pretzler, A. Pukhov, M. Toncian, T. Toncian, and O. Willi
Controlling the Spacing of Attosecond Pulse Trains from Relativistic Surface Plasmas
Physical Review Letters 106, 185002 (2011)

Abstract: When a laser pulse hits a solid surface with relativistic intensities, XUV attosecond pulses are generated in the reflected light. We present an experimental and theoretical study of the temporal properties of attosecond pulse trains in this regime. The recorded harmonic spectra show distinct fine structures which can be explained by a varying temporal pulse spacing that can be controlled by the laser contrast. The pulse spacing is directly related to the cycle-averaged motion of the reflecting surface. Thus the harmonic spectrum contains information on the relativistic plasma dynamics.

B. Marx, I. Uschmann, S. Höfer, R. Lötzsch, O. Wehrhan, E. Förster, M. C. Kaluza, T. Stöhlker, H. Gies, C. Detlefs, T. Roth, J. Hartwig, and G. G. Paulus
Determination of high-purity polarization state of X-rays
Optics Communications 284, 915 (2011)

Abstract: We report on the measurement of the highest purity of polarization of X-rays to date. The measurements are performed by combining a brilliant undulator source with an X-ray polarimeter. The polarimeter is composed of a polarizer and an analyzer, each based on four reflections at channel-cut crystals with a Bragg angle very close to 45°. Experiments were performed at three different X-ray energies, using different Bragg reflections: Si(400) at 6457.0 eV, Si(444) at 11,183.8 eV, and Si(800) at 12,914.0 eV. At 6 keV a polarization purity of 1.5 × 10^{-9} is achieved. This is an improvement by more than two orders of magnitude as compared to previously reported values. The polarization purity decreases slightly for shorter X-ray wavelengths. The sensitivity of the polarimeter is discussed with respect to a proposed experiment that aims at the detection of the birefringence of vacuum induced by super-strong laser fields.

A. M. Sayler, T. Rathje, W. Müller, C. Kürbis, K. Rühle, G. Stibenz, and G. G. Paulus
Real-time pulse length measurement of few-cycle laser pulses using above-threshold ionization
Optics Express 19, 4464 (2011)

Abstract: The pulse lengths of intense few-cycle (4 - 10 fs) laser pulses at 790 nm are determined in real-time using a stereographic above-threshold ionization (ATI) measurement of Xe, i.e. the same apparatus recently shown to provide a precise, real-time, every-single-shot, carrier-envelope phase measurement of ultrashort laser pulses. The pulse length is calibrated using spectral-phase interferometry for direct electric-field reconstruction (SPIDER) and roughly agrees with calculations done using quantitative rescattering theory (QRS). This stereo-ATI technique provides the information necessary to characterize the waveform of every pulse in a kHz pulse train, within the Gaussian pulse approximation, and relies upon no theoretical assumptions. Moreover, the real-time display is a highly effective tool for tuning and monitoring ultrashort pulse characteristics.

A. M. Sayler, T. Rathje, W. Müller, K. Rühle, R. Kienberger, and G. G. Paulus
Precise, real-time, every-single-shot, carrier-envelope phase measurement of ultrashort laser pulses
Optics Letters 36, 1 (2011)

Abstract: In this Letter we demonstrate a method for real-time determination of the carrier-envelope phase of each and every single ultrashort laser pulse at kilohertz repetition rates. The technique expands upon the recent work of Wittmann and incorporates a stereographic above-threshold laser-induced ionization measurement and electronics optimized to produce a signal corresponding to the carrier-envelope phase within microseconds of the laser interaction, thereby facilitating data-tagging and feedback applications. We achieve a precision of 113 mrad (6.5°) over the entire 2π range.

N. Johnson, O. Herrwerth, A. Wirth, S. De, I. Ben-Itzhak, M. Lezius, B. Bergues, M. F. Kling, A. Senftleben, C. D. Schröter, R. Moshammer, J. Ullrich, K. J. Betsch, R. R. Jones, A. M. Sayler, T. Rathje, K. Rühle, W. Müller, and G. G. Paulus
Single-shot carrier-envelope-phase-tagged ion-momentum imaging of nonsequential double ionization of argon in intense 4-fs laser fields
Physical Review A 83, 013412 (2011)

Abstract: Single-shot carrier-envelope-phase (CEP) tagging is combined with a reaction mircoscope (REMI) to investigate CEP-dependent processes in atoms. Excellent experimental stability and data acquisition longevity are achieved. Using this approach, we study the CEP effects for nonsequential double ionization of argon in 4-fs laser fields at 750 nm and an intensity of 1.6 × 10^14 W/cm2. The Ar^(2+) ionization yield shows a pronounced CEP dependence which compares well with recent theoretical predictions employing quantitative rescattering theory [S. Micheau et al. Phys. Rev. A 79 013417 (2009)]. Furthermore, we find strong CEP influences on the Ar^(2+) momentum spectra along the laser polarization axis.


V. Bagnoud, J. Fils, J. Hein, M. C. Kaluza, G. G. Paulus, Th. Stöhlker, and M. Wolf
High‐Contrast Ultrafast OPA Module For The PHELIX Facility
AIP Conference Proceedings 1228, 217 (2010)

Abstract: In this paper, a new system for improvement of the pulse contrast in CPA laser systems by use of an ultrafast OPA is reviewed together with a scheme to create sub‐picosecond synchronized OPA pump pulses. The scheme is being implemented at the PHELIX facility at GSI‐Darmstadt, Germany.

J. Hein, M. Hornung, R. Bödefeld, S. Podleska, A. Sävert, R. Wachs, A. Kessler, S. Keppler, M. Wolf, J. Polz, O. Jäckel, M. Nicolai, M. Schnepp, J. Körner, M. C. Kaluza, and G. G. Paulus
Multiterawatt peak power generated by the all diode pumped laser—POLARIS
AIP Conference Proceedings 1228, 159 (2010)

Abstract: At the Institute of Optics and Quantum Electronics, University of Jena, a fully diode pumped ultrahigh peak power laser system—POLARIS—has been realized. Presently, this laser system reaches a peak power of some ten terawatt. The last amplifier, which will boost the output energy to the 100 J level, is nearly completed and will be soon commissioned. The applied technologies and the basic design are reviewed here.