Beyond carbon K-edge harmonic emission using a spatial and temporal synthesized laser field

Effect of multiple rescatterings on continuum harmonics from asymmetric molecules in multicycle lasers

A wide range of harmonics especially continuum harmonics is a prerequisite for attosecond pulse generation. One can use longer-wavelength lasers to push the cutoff to a higher order. However, this does not translate to the same amount of continuum range extension because multiple rescattering phenomena are also enhanced in the process, potentially affecting the lower end of the continuum harmonics. It is then important to understand exactly how multiple rescatterings affect the harmonic structure and their response to various laser parameters, which is the main theme of this paper. Particularly, by applying the synchrosqueezed time-frequency transform and classical electron trajectory analysis to the asymmetric molecule carbon monoxide (CO), we justify that the multiple rescatterings indeed influence the periodicity of the harmonic spectra and the stable periodicity is, in fact, bounded by the first- and third-order returns. Moreover, for the first time, we find that the high-order rescatterings are asymmetric regarding the molecular rotation of 180°, but always correlate with the first-order returns. Our last result is that by breaking the laser symmetry in an appropriate way, the contribution of multiple rescatterings is removed so that the continuum region is entirely defined by the first-order return energies.

Attosecond photoemission delay in the inhomogeneous field

We investigate the photoemission process of the hydrogen atom in a spatial-dependent infrared (IR) field. The results show that the inhomogeneous field induces an additional contribution to the photoemission time delay, which results in the increase (decrease) of the photoemission time delay due to the enhancement (decay) of the IR field intensity in space when compared to the case in the homogeneous field. Based on the photoemission time delay in the inhomogeneous field, we demonstrate a method to extract the inhomogeneous parameter that is vital for characterizing the spatial distribution of IR field. The proposed method might pave an accessible route toward describing the plasmon-enhanced fields in the vicinity of a nanostructure.

Control of the polarization direction of isolated attosecond pulses using inhomogeneous two-color fields

We theoretically demonstrate the control of the polarization direction of isolated attosecond pulses (IAPs) with inhomogeneous two-color fields synthesized by an 800-nm fundamental pulse and a 2000-nm control pulse having crossed linear polarizations. The results show that by using the temporally and spatially shaped field, the high-order harmonic generation (HHG) process can be efficiently controlled. An ultra-broad supercontinuum ranging from 150th to 400th harmonics which covers the water window region is generated. Such a supercontinuum supports the generation of a 64-as linearly polarized IAP, whose polarization direction is at about 45° with respect to the x axis. Moreover, we analyze the influence of the inhomogeneity parameters and the relative angle of the fundamental and control pulses on the IAP generation. It is shown that the polarization direction of the IAP can rotate in a wide range approximately from 8° to 90° relative to the x axis when the inhomogeneity parameters and the relative angle vary.

Attosecond single-cycle undulator light: a review

Research at modern light sources continues to improve our knowledge of the natural world, from the subtle workings of life to matter under extreme conditions. Free-electron lasers, for instance, have enabled the characterization of biomolecular structures with sub-ångström spatial resolution, and paved the way to controlling the molecular functions. On the other hand, attosecond temporal resolution is necessary to broaden our scope of the ultrafast world. Here we discuss attosecond pulse generation beyond present capabilities. Furthermore, we review three recently proposed methods of generating attosecond x-ray pulses. These novel methods exploit the coherent radiation of microbunched electrons in undulators and the tailoring of the emitted wavefronts. The computed pulse energy outperforms pre-existing technologies by three orders of magnitude. Specifically, our simulations of the proposed Soft X-ray Laser at MAX IV (Lund, Sweden) show that a pulse duration of 50-100 as and a pulse energy up to 5 [Formula: see text]J is feasible with the novel methods. In addition, the methods feature pulse shape control, enable the incorporation of orbital angular momentum, and can be used in combination with modern compact free-electron laser setups.

Tomography of asymmetric molecular orbitals with a one-color inhomogeneous field

We demonstrate image asymmetric molecular orbitals via high-order harmonic generation in a one-color inhomogeneous field. Due to the broken inversion symmetry of the inhomogeneous field in space, the returning electrons with energy in a broad range can be forced to recollide from only one direction for all the orientation angles of molecules, which therefore can be used to reconstruct asymmetric molecular orbitals. Following the procedure of molecular orbital tomography, the highest occupied molecular orbital of carbon monoxide (CO) is satisfactorily reconstructed with high-order harmonic spectra driven by the inhomogeneous field. This scheme is helpful to relax the requirement of laser conditions and is also applicable to other asymmetric molecules.

Nano-plasmonic near field phase matching of attosecond pulses

Nano-structures excited by light can enhance locally the electric field when tuned to plasmonic resonances. This phenomenon can be used to boost non-linear processes such as harmonic generation in crystals or in gases, Raman excitation, and four wave mixing. Here we present a theoretical investigation of the near-field phase matching of attosecond pulses emitted by high-order harmonic generation (HHG) of an atom immersed in a multi-cycle femtosecond infrared laser field and a spatially inhomogeneous plasmonic field. We demonstrate that the spatial inhomogeneity factor of the plasmonic field strongly affects the electron trajectory and recombination time which can be used to control the attosecond emission. For further insight into the plasmonic field effect, we monitor the phase of each quantum path as a function of the inhomogeneity strength. Moreover, we investigate the attosecond emission as a function of near-field phase matching effects. This is achieved by calculating the coherent field superposition of attosecond pulses emitted from various intensities or field inhomogeneities. Finally, far-field and near-field phase matching effects are combined to modulate the harmonic spectral phase towards the emission of a single attosecond pulse.

Attosecond physics at the nanoscale

Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond  =  1 as  =  10^-18 s), which is comparable with the optical field. For comparison, the revolution of an electron on a 1s orbital of a hydrogen atom is  ∼152 as. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with nanometric precision. Although nano-engineering is a vast and well-established research field on its own, the merger with intense laser physics is relatively recent. In this report on progress we present a comprehensive experimental and theoretical overview of physics that takes place when short and intense laser pulses interact with nanosystems, such as metallic and dielectric nanostructures. In particular we elucidate how the spatially inhomogeneous laser induced fields at a nanometer scale modify the laser-driven electron dynamics. Consequently, this has important impact on pivotal processes such as above-threshold ionization and high-order harmonic generation. The deep understanding of the coupled dynamics between these spatially inhomogeneous fields and matter configures a promising way to new avenues of research and applications. Thanks to the maturity that attosecond physics has reached, together with the tremendous advance in material engineering and manipulation techniques, the age of atto-nanophysics has begun, but it is in the initial stage. We present thus some of the open questions, challenges and prospects for experimental confirmation of theoretical predictions, as well as experiments aimed at characterizing the induced fields and the unique electron dynamics initiated by them with high temporal and spatial resolution.

Interference effects on harmonic generation from H2 + in nonhomogeneous laser field

By solving the time-dependent Schrödinger equation both in simplified one-dimensional coordinate and three-dimensional cylindrical coordinate systems, the high-order harmonic generation from H₂ ⁺ in spatially symmetric and asymmetric nonhomogeneous laser fields was studied. At large internuclear distances, minima were clearly observed in high energy part of harmonic spectra, which can be attributed to two-center interference in diatomic molecule. Compared with previous studies, the minima in nonhomogeneous laser field are more distinct. Remarkably, the positions of the minima are different in these two types of fields, which demonstrate that interference effects are greatly influenced by laser parameters. Besides, the asymmetric nonhomogeneous field leads to an asymmetric recollision of the ionized electron, and both odd and even order harmonics could be emitted, which is explained in detail based on quantum dynamics calculations.

High-order harmonics in a quantum dot and metallic nanorod complex

We investigate the high-order harmonic generation (HHG) in a semiconductor quantum dot (SQD) and metallic nanorod (MNR) complex driven by a moderate intensity (<10(12)  W/cm(2)) frequency-chirped Gaussian few-cycle pulse. Our numerical results indicate that the cutoff energy of the HHG can be controlled by optimizing the shape of the MNR and surface-to-surface distance between the SQD and the MNR. We also show that the extreme ultraviolet supercontinuum harmonics (25 eV maximal photon energy) and isolated ultrashort pulses (2.67-4.36 fs FWHM) are achievable.

Quantum control of electron wave packet during high harmonic process of H2(+) in a combination of a circularly polarized laser field and a Terahertz field

By solving a two-dimensional time-dependent Schrödinger equation we investigate high harmonic generation (HHG) and isolated attosecond pulse generation for the H2+ molecular ion in a circularly polarized laser pulse combined with a Terahertz (THz) field. The harmonic intensity can be greatly enhanced and a continuum spectrum can be obtained when a THz field is added. The HHG process is studied by the semi-classical three-step model and the time-frequency analysis. Our studies show that only short trajectories contribute to HHG. Furthermore, we present the temporal evolution of the probability density of electron wave packet, which perfectly shows a clear picture of the electron's two-time recombination when a THz field is added, and it is the main mechanism of HHG. By superposing the harmonics in the range of 216-249 eV, an isolated attosecond pulse with a duration of about 69 attoseconds can be generated.

Coherent kiloelectronvolt x-rays generated by subcycle optical drivers: a feasibility study

We theoretically explored the feasibility of high-harmonic generation in the kiloelectronvolt spectral range by optical waveforms of durations progressively shortened from multicycle to subcycle. Our study revealed that subcycle optical pulses offer a clear advantage in generating isolated x-ray attosecond pulses. In combination with their sub-fs optical drivers these pulses will open the route for x-ray attosecond pump-optical attosecond probe experiments, advancing attosecond streaking and attosecond absorption techniques to new realms of investigation of electronic processes.

Generation of isolated sub-10-attosecond pulses in spatially inhomogenous two-color fields

We present a theoretical investigation of high-order harmonic generation in spatially inhomogeneous two-color laser fields by solving three dimensional time dependent Schrödinger equation. The cutoff in the harmonic spectra can be significantly extended by means of our proposed method (i.e., from helium interacting with the plasmon-enhanced two-color laser fields), and an ultrabroad supercontinuum up to 1.5 keV is generated by selecting proper carrier-envelope phase of the controlling field. Moreover, classical trajectory extraction, time-dependent ionization and recombination rates, and time-frequency analyses are used to explain the generation of this ultrabroadband supercontinuum. As a result, an isolated 8.8 attosecond pulse can be generated directly by the superposition of the supercontinuum harmonics.

High-order harmonic generation from Rydberg atoms in inhomogeneous fields

We theoretically investigate the high-order harmonic generation (HHG) from Rydberg atoms considering the spatial inhomogeneity of the driving field. It is found that in the inhomogeneous field, the effect of the cutoff extension in the harmonic spectrum from Rydberg atoms can be extended to multi-cycle regime, while in the homogeneous field case, the extension of the harmonic cutoff is limited to the few-cycle regime (less than two optical cycles). The underlying physics of the cutoff extension from Rydberg atoms in the inhomogeneous field is analyzed based on the classical and quantum-mechanical models. Furthermore, by optimizing the field inhomogeneity, the electron dynamics can be well controlled to generate a smooth supercontinuum in the extended spectral region. This can support the efficient generation of isolated attosecond pulses in Rydberg atoms from multi-cycle laser fields.