Polarization-dependent high-order two-color mixing

Generating circularly polarized radiation in the extreme ultraviolet spectral range at the free-electron laser FLASH

A new device for polarization control at the free electron laser facility FLASH1 at DESY has been commissioned for user operation. The polarizer is based on phase retardation upon reflection off metallic mirrors. Its performance is characterized in three independent measurements and confirms the theoretical predictions of efficient and broadband generation of circularly polarized radiation in the extreme ultraviolet spectral range from 35 eV to 90 eV. The degree of circular polarization reaches up to 90% while maintaining high total transmission values exceeding 30%. The simple design of the device allows straightforward alignment for user operation and rapid switching between left and right circularly polarized radiation.

Phase matching of noncollinear sum and difference frequency high harmonic generation above and below the critical ionization level

We investigate the macroscopic physics of noncollinear high harmonic generation (HHG) at high pressures. We make the first experimental demonstration of phase matching of noncollinear high-order-difference-frequency generation at ionization fractions above the critical ionization level, which normally sets an upper limit on the achievable cutoff photon energies. Additionally, we show that noncollinear high-order-sum-frequency generation requires much higher pressures for phase matching than single-beam HHG does, which mitigates the short interaction region in this geometry. We also dramatically increase the experimentally realized cutoff energy of noncollinear circularly polarized HHG, reaching photon energies of 90 eV. Finally, we achieve complete angular separation of high harmonic orders without the use of a spectrometer.

Selective suppression of high-order harmonics within phase-matched spectral regions

Phase matching in high-harmonic generation leads to enhancement of multiple harmonics. It is sometimes desired to control the spectral structure within the phase-matched spectral region. We propose a scheme for selective suppression of high-order harmonics within the phase-matched spectral region while weakly influencing the other harmonics. The method is based on addition of phase-mismatched segments within a phase-matched medium. We demonstrate the method numerically in two examples. First, we show that one phase-mismatched segment can significantly suppress harmonic orders 9, 15, and 21. Second, we show that two phase-mismatched segments can efficiently suppress circularly polarized harmonics with one helicity over the other when driven by a bi-circular field. The new method may be useful for various applications, including the generation of highly helical bright attosecond pulses.

Controlling Nonsequential Double Ionization in Two-Color Circularly Polarized Femtosecond Laser Fields

Atoms undergoing strong-field ionization in two-color circularly polarized femtosecond laser fields exhibit unique two-dimensional photoelectron trajectories and can emit bright circularly polarized extreme ultraviolet and soft-x-ray beams. In this Letter, we present the first experimental observation of nonsequential double ionization in these tailored laser fields. Moreover, we can enhance or suppress nonsequential double ionization by changing the intensity ratio and helicity of the two driving laser fields to maximize or minimize high-energy electron-ion rescattering. Our experimental results are explained through classical simulations, which also provide insight into how to optimize the generation of circularly polarized high harmonic beams.

Illuminating Molecular Symmetries with Bicircular High-Order-Harmonic Generation

We present a general theory of bicircular high-order-harmonic generation from N-fold rotationally symmetric molecules. Using a rotating frame of reference we predict the complete structure of the high-order-harmonic spectra for arbitrary driving frequency ratios and show how molecular symmetries can be directly identified from the harmonic signal. Our findings reveal that a characteristic fingerprint of rotational molecular symmetries can be universally observed in the ultrafast response of molecules to strong bicircular fields.

Two-color high-harmonic generation in plasmas: efficiency dependence on the generating particle properties

The high-order harmonic generation (HHG) in silver, gold, and zinc plasma plumes irradiated by orthogonally polarized two-color field is studied theoretically and experimentally. We find an increase of the HHG efficiency in comparison with the single-color case, which essentially depends on the plasma species and harmonic order. An increase of more than an order of magnitude is observed for silver plasma, whereas for gold and zinc it is lower; these results are reproduced in our calculations that include both propagation and microscopic response studies. We show that the widely used theoretical approach assuming the 1s ground state of the generating particle fails to reproduce the experimental results; the agreement is achieved in our theory using the actual quantum numbers of the outer electron of the generating particles. Moreover, our theoretical studies highlight the redistribution of the electronic density in the continuum wave packet as an important aspect of the HHG enhancement in the two-color orthogonally polarized fields with comparable intensities: in the single-color field the electronic trajectories with almost zero return energy are the most populated ones; in the two-color case the total field maximum can be shifted in time so that the trajectories with high return energies (in particular, the cut-off trajectory) become the most populated ones.

Dynamics of Strong-Field Double Ionization in Two-Color Counterrotating Fields

The double ionization of helium in bichromatic, circularly polarized intense laser fields is analyzed with a classical ensemble approach. It is found that counterrotating fields produce significant nonsequential double-ion yield and drive novel ionization dynamics. It is shown that distinct pathways to ionization can be modified by altering the relative intensities of the two colors, allowing for unique control of strong-field processes. Electrons are observed to return to the ion at different angles from the angle of ionization, opening new possibilities for probing electronic and molecular structure on the ultrafast time scale.

Bicircular High-Harmonic Spectroscopy Reveals Dynamical Symmetries of Atoms and Molecules

We introduce bicircular high-harmonic spectroscopy as a new method to probe dynamical symmetries of atoms and molecules and their evolution in time. Our approach is based on combining a circularly polarized femtosecond fundamental field of frequency ω with its counterrotating second harmonic 2ω. We demonstrate the ability of bicircular high-harmonic spectroscopy to characterize the orbital angular momentum symmetry of atomic orbitals. We further show that breaking the threefold rotational symmetry of the generating medium-at the level of either the ensemble or that of a single molecule-results in the emission of the otherwise parity-forbidden frequencies 3qω  (q∈N), which provide a background-free probe of dynamical molecular symmetries.

Electron rescattering in a bicircular laser field

Above-threshold ionization of rare-gas atoms by a bicircular field with its two components counterrotating is theoretically investigated by means of the improved strong-field approximation. Both direct and rescattered electrons are considered and the quantum orbits that lead into a specific final state are calculated and depicted. The angle-dependent spectrum reflects the discrete rotational symmetry of the bicircular field. The backward-scattering contributions are very similar to those generated by a linearly polarized field; several such contributions are rotated one versus the other by the symmetry angle of the discrete rotational symmetry. The forward-scattering contributions dramatically affect the velocity map at comparatively low momenta. The direct-electron spectrum observes reflection symmetry about several symmetry axes determined by the field symmetry. This is broken by rescattering.

Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology

Bright, circularly polarized, extreme ultraviolet (EUV) and soft x-ray high-harmonic beams can now be produced using counter-rotating circularly polarized driving laser fields. Although the resulting circularly polarized harmonics consist of relatively simple pairs of peaks in the spectral domain, in the time domain, the field is predicted to emerge as a complex series of rotating linearly polarized bursts, varying rapidly in amplitude, frequency, and polarization. We extend attosecond metrology techniques to circularly polarized light by simultaneously irradiating a copper surface with circularly polarized high-harmonic and linearly polarized infrared laser fields. The resulting temporal modulation of the photoelectron spectra carries essential phase information about the EUV field. Utilizing the polarization selectivity of the solid surface and by rotating the circularly polarized EUV field in space, we fully retrieve the amplitude and phase of the circularly polarized harmonics, allowing us to reconstruct one of the most complex coherent light fields produced to date.

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 µm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phase-matching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.

Generating Isolated Elliptically Polarized Attosecond Pulses Using Bichromatic Counterrotating Circularly Polarized Laser Fields

We theoretically demonstrate the possibility to generate both trains and isolated attosecond pulses with high ellipticity in a practical experimental setup. The scheme uses circularly polarized, counterrotating two-color driving pulses carried at the fundamental and its second harmonic. Using a model Ne atom, we numerically show that highly elliptic attosecond pulses are generated already at the single-atom level. Isolated pulses are produced by using few-cycle drivers with controlled time delay between them.

Circularly polarized carrier-envelope-phase stable attosecond pulse generation based on coherent undulator radiation

In this Letter, we present a new method for generation of circularly polarized attosecond pulses. According to our calculations, shape-controlled, carrier-envelope-phase stable pulses of several hundred nanojoule energy could be produced by exploitation of the coherent undulator radiation of an electron bunch. Our calculations are based on an existing particle accelerator system (FLASH II in DESY, Germany). We investigated the energy dependence of the attosecond pulses on the energy of electrons and the parameters of the radiator undulator, which generate the electromagnetic radiation.

Generation of elliptically polarized attosecond pulse trains

Stimulated by the recent demonstration of the first bright source of circularly polarized high harmonics, we examine the attosecond pulse trains generated by a group of such harmonics. For the s ground state of an atom, the polarization of generated pulses is close to linear, with three different orientations per cycle. However, for the p ground state of the inert gases used in the experiments, the polarization of the attosecond pulses is close to elliptical. We show that this is caused by the different intensities of the high harmonics of the opposite helicity.

Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources

Recent advances in high-harmonic generation gave rise to soft X-ray pulses with higher intensity, shorter duration and higher photon energy. One of the remaining shortages of this source is its restriction to linear polarization, since the yield of generation of elliptically polarized high harmonics has been low so far. We here show how this limitation is overcome by using a cross-polarized two-colour laser field. With this simple technique, we reach high degrees of ellipticity (up to 75%) with efficiencies similar to classically generated linearly polarized harmonics. To demonstrate these features and to prove the capacity of our source for applications, we measure the X-ray magnetic circular dichroism (XMCD) effect of nickel at the M2,3 absorption edge around 67 eV. There results open up the way towards femtosecond time-resolved experiments using high harmonics exploiting the powerful element-sensitive XMCD effect and resolving the ultrafast magnetization dynamics of individual components in complex materials.

Efficient high-order harmonic generation boosted by below-threshold harmonics

High-order harmonic generation (HHG) in gases has been established as an important technique for the generation of coherent extreme ultraviolet (XUV) pulses at ultrashort time scales. Its main drawback, however, is the low conversion efficiency, setting limits for many applications, such as ultrafast coherent imaging, nonlinear processes in the XUV range, or seeded free electron lasers. Here we introduce a novel scheme based on using below-threshold harmonics, generated in a “seeding cell”, to boost the HHG process in a “generation cell”, placed further downstream in the focused laser beam. By modifying the fundamental driving field, these low-order harmonics alter the ionization step of the nonlinear HHG process. Our dual-cell scheme enhances the conversion efficiency of HHG, opening the path for the realization of robust intense attosecond XUV sources.

High-harmonic homodyne detection of the ultrafast dissociation of Br2 molecules

We report the time-resolved observation of the photodissociation of Br2 using high-harmonic generation (HHG) as a probe. The simultaneous measurement of the high-harmonic and ion yields shows that high harmonics generated by the electronically excited state interfere with harmonics generated by the ground state. The resulting homodyne effect provides a high sensitivity to the excited state dynamics. We present a simple theoretical model that accounts for the main observations. Our experiment paves the way towards the dynamic imaging of molecules using HHG.

High harmonic emission from a superposition of multiple unrelated frequency fields

We report observations and analysis of high harmonic generation driven by a superposition of fields at 1290 nm and 780 nm. These fields are not commensurate in frequency and the superposition leads to an increase in the yield of the mid-plateau harmonics of more than two orders of magnitude compared to using the 1290 nm field alone. Significant extension of the cut-off photon energy is seen even by adding only a small amount of the 780 nm field. These observations are explained by calculations performed in the strong field approximation. Most importantly we find that enhancement is found to arise as a consequence of both increased ionization in the sum-field and modification of the electron trajectories leading to an earlier return time. The enhanced yield even when using modest intensity fields of 5 x 10(13) Wcm(-2) is extended to the 80 eV range and is a promising route to provide a greater photon number for applications in XUV imaging and time-resolved experiments at a high repetition rate.

Attosecond pulse trains generated using two color laser fields

We investigate the spectral and temporal structure of high harmonic emission from argon exposed to an infrared laser field and its second harmonic. For a wide range of generating conditions, trains of attosecond pulses with only one pulse per infrared cycle are generated. The synchronization necessary for producing such trains ensures that they have a stable pulse-to-pulse carrier envelope phase, unlike trains generated from one color fields, which have two pulses per cycle and a pi phase shift between consecutive pulses. Our experiment extends the generation of phase stabilized few cycle pulses to the extreme ultraviolet regime.

Extreme-ultraviolet harmonic generation near 13 nm with a two-color elliptically polarized laser field

Theoretical results for high-harmonic generation by a two-color elliptically polarized laser field are presented. Special emphasis is placed on coherent radiation near 13 nm in connection with the development of extreme-ultraviolet lithography. Linearly polarized radiation at this wavelength can be obtained with a linearly polarized bichromatic laser field, whereas circularly polarized radiation can be generated with a bichromatic circularly polarized field with counterrotating coplanar components. In both cases the harmonic emission efficiencies at the saturation intensity are more than 1 order of magnitude larger than for harmonic generation with a monochromatic linearly polarized field.