We investigate the interaction of Xe with isolated attosecond XUV pulses. Specifically, we calculate the ion yields and determine the pathways leading to the formation of ionic charged states up to Xe$^{5+}$. To do so, in our formulation we account for single-photon absorption, sequential multi-photon absorption, direct two-photon absorption, single and double Auger decays, and shake-off. We compare our results for the ion yields and for ion yield ratios with recent experimental results obtained for 93 eV and 115 eV attosecond XUV pulses. In particular, we investigate the role that a sequence of two single-photon ionization processes plays in the formation of Xe$^{4+}$. We find that each one of these two processes ionizes a core electron and thus leads to the formation of a double core-hole state. Remarkably, we find that the formation of Xe$^{5+}$ involves a direct two-photon absorption process and the absorption of a total of three photons.
We study theoretically the photoabsorption spectra of an attosecond XUV pulse by a laserdressed atomic system. A weak XUV excites an autoionizing state which is strongly coupled to another autoionizing state by a laser. The theory was applied to explain two recent experiments [Loh, Greene, and Leone, Chem. Phys. 350, 7 (2008); Wang, Chini, Chen, Zhang, Cheng, He, Cheng, Wu, Thumm, and Chang, Phys. Rev. Lett. 105 143002 (2010)] where the absorption spectra of the XUV lights were measured against the time delay between the laser and the XUV. In another example, we study an attosecond pulse excit…
We report the generation and characterization of isolated attosecond XUV and VUV pulses generated simultaneously via HHG driven by few-cycle pulses using an in-line dual gas target system. One gas jet target was operated with Kr gas that optimized HHG in the 15-25 eV photon energy range (VUV), whilst the second gas jet target was operated in Ne gas to optimize the high harmonic generation around 90 eV (XUV). Appropriate filters were used to isolate the required spectral components to synthesize isolated pulses. Sn and In filters were used for the VUV region while a Zr filter was used for the X…
Attosecond noncollinear four wave mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48 eV XUV photon excites a 2s electron into the 2s2p6[np] Rydberg series, broadband NIR pulses couple the 2s2p6[3p] XUV-bright state to neighboring 2s2p6[3s] and 2s2p6[3d] XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or …
Two XUV-photon double ionization of Ne, induced by an intense few-pulse attosecond train with a ~ 4 fs envelope duration is investigated experimentally and theoretically. The experiment is performed at ELI-ALPS utilizing the recently constructed 10 Hz gas phase high-order harmonic generation SYLOS GHHG-COMPACT beamline. A total pulse energy up to ~1 μJ generated in Argon in conjunction with high reflectivity optics in the XUV region, allowed the observation of the doubly charged state of Ne induced by 40 eV central XUV photon energies. The interaction of the intense attosecond pulse train with…
We use a Wigner distribution-like function based on the strong field approximation theory to obtain the time-energy distributions and the ionization time distributions of electrons ionized by an XUV pulse alone and in the presence of an infrared (IR) pulse. In the case of a single XUV pulse, although the overall shape of the ionization time distribution resembles the XUV-envelope, its detail shows dependence on the emission direction of the electron and the carrier-envelope phase of the pulse, which mainly results from the low-energy interference structure. It is further found that the electro…
Recent experimental developments of high-intensity, short-pulse XUV light sources are enhancing our ability to study electron-electron correlations. We perform time-dependent calculations to investigate the so-called "sequential" regime (photon energy above 54.4 eV) in the two-photon double ionization of helium. We show that attosecond pulses allow to induce and probe angular and energy correlations of the emitted electrons. The final momentum distribution reveals regions dominated by the Wannier ridge break-up scenario and by post-collision interaction.
We investigate the possibility to monitor the dynamics of autoionizing states in real time and control the yields of different ionization channels in helium by simulating XUV-pump IR-probe experiments focused on the N=2 threshold. The XUV pulse creates a coherent superposition of doubly excited states which is found to decay by ejecting electrons in bursts. Prominent interference fringes in the photoelectron angular distribution of the $2s$ and $2p$ ionization channels are observed, along with sizable out-of-phase quantum beats in the yields of the corresponding parent ions.
The generation of coherent light pulses in the extreme ultraviolet (XUV) spectral region with attosecond pulse durations constitutes the foundation of the field of attosecond science. Twenty years after the first demonstration of isolated attosecond pulses, they continue to be a unique tool enabling the observation and control of electron dynamics in atoms, molecules and solids. It has long been identified that an increase in the repetition rate of attosecond light sources is necessary for many applications in atomic and molecular physics, surface science, and imaging. Although high harmonic g…
In the present work we report on the current progress of the recently constructed GW attosecond extreme ultraviolet (XUV) source developed at the Institute of Electronic Structure and Laser of the Foundation for Research and Technology-Hellas (I.E.S.L-FO.R.T.H.). By the implementation of a compact-collinear polarization gating arrangement, the generation of a broadband, coherent XUV quasi-continuum produced by the interaction of a many-cycle infrared field with a gas phase medium is achieved. The spectral width of the XUV emission generated in Xenon, is spanning in the range of 17-32 eV and ca…
We present the first demonstration of two-photon double ionization of neon using an intense extreme ultraviolet (XUV) attosecond pulse train (APT) in a photon energy regime where both direct and sequential mechanisms are allowed. For an APT generated through high-order harmonic generation (HHG) in argon we achieve a total pulse energy close to 1 $μ$J, a central energy of 35 eV and a total bandwidth of $\sim30$ eV. The APT is focused by broadband optics in a neon gas target to an intensity of $3\cdot10^{12} $W$\cdot$cm$^{-2}$. By tuning the photon energy across the threshold for the sequential …
Studies of ultrafast dynamics along with femtosecond-pulse metrology rely on non-linear processes, induced solely by the exciting/probing pulses or the pulses to be characterized. Extension of these approaches to the extreme-ultraviolet (XUV) spectral region opens up a new, direct route to attosecond scale dynamics. Limitations in available intensities of coherent XUV continua kept this prospect barren. The present work overcomes this barrier. Reaching condition at which simultaneous ejection of two bound electrons by two-XUV-photon absorption becomes more efficient than their one-by-one remov…
Laser assisted photoemission by a chirped subfemtosecond extreme ultraviolet (XUV) pulse is considered within an exactly solvable quantum-mechanical model. Special emphasis is given to the energy dependence of photoexcitation cross-section. The streaked spectra are analyzed within the classical picture of initial time-momentum distribution r_ini(p,t) of photoelectrons mapped to the final energy scale. The actual time-momentum distribution in the absence of the probe laser field is shown to be a poor choice for r_ini, and a more adequate ansatz is suggested. The semiclassical theory offers a si…
We propose a new scenario to apply IR-pump-XUV-probe schemes to resolving strong field ionization induced and attosecond pulse driven electron-hole dynamics and coherence in real time. The coherent driving of both the infrared laser and the attoscond pulse correlates the dynamics of the core-hole and the valence-hole which leads to the otherwise forbidden absorption and emission of XUV photon. An analytical model is developed based on the strong-field approximation by taking into account of the essential multielectron configurations. The emission spectra from the core-valence transition and th…
Coherent sources of attosecond extreme ultraviolet (XUV) radiation present many challenges if their full potential is to be realized. While many applications benefit from the broadband nature of these sources, it is also desirable to produce narrow band XUV pulses, or to study autoionizing resonances in a manner that is free of the broad ionization background that accompanies above-threshold XUV excitation. Here we demonstrate a method for controlling the coherent XUV free induction decay that results from using attosecond pulses to excite a gas, yielding a fully functional modulator for XUV w…
Multi-electron dynamics in atoms and molecules very often occur on sub- to few-femtosecond timescales. The available intensities of extreme-ultraviolet (XUV) attosecond pulses have previously only allowed the time-resolved investigation of two-photon, two-electron interactions. Here we demonstrate attosecond control over double and triple ionization of argon atoms involving the absorption of up to five XUV photons. In an XUV-pump XUV-probe measurement using a pair of attosecond pulse trains (APTs), the Ar$^{2+}$ ion yield exhibits a weak delay dependence, showing that its generation predominan…
King’s College London（伦敦国王学院）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Max-Born-Institut（马克斯·玻恩研究所）
Noncollinear wave-mixing spectroscopies with attosecond extreme ultraviolet (XUV) pulses provide unprecedented insight into electronic dynamics. In infrared and visible regimes, heterodyne detection techniques utilize a reference field to amplify wave-mixing signals while simultaneously allowing for phase-sensitive measurements. Here, we implement a self-heterodyned detection scheme in noncollinear wave-mixing measurements with a short attosecond XUV pulse train and two few-cycle near infrared (NIR) pulses. The initial spatiotemporally overlapped XUV and NIR pulses generate a coherence of both…
We present experimental results showing the appearance of a near-continuum in the high-order harmonic generation (HHG) spectra of atomic and molecular species as the driving laser intensity of an infrared pulse increases. Detailed macroscopic simulations reveal that these near-continuum spectra are capable of producing IAPs in the far field if a proper spatial filter is applied. Further, our simulations show that the near-continuum spectra and the IAPs are a product of strong temporal and spatial reshaping (blue shift and defocusing) of the driving field. This offers a possibility of producing…
We develop the two-electron attosecond streak camera under realistic conditions using a quasi-classical model. We assume extreme ultra-violet (XUV) attosecond pulses with a full width at half maximum (FWHM) of 24 attoseconds, centered at 120 eV and a streaking infrared laser field of 1600 nm, and intensity of $1.8 \times 10^{12}$ W/cm$^2$. The proposed method is shown to be capable to time resolve intra-atomic collisions in double ionization.
The strong coupling between two autoionizing states in helium is studied theoretically with the pump-probe scheme. An isolated 100-as XUV pulse is used to excite helium near the 2s2p(1P) resonance state in the presence of an intense infrared (IR) laser. The laser field introduces strong coupling between 2s2p(1P) and 2p^2(1S) states. The IR also can ionize helium from both autoionizing states. By changing the time delay between the XUV and the IR pulses, we investigated the photoelectron spectra near the two resonances. The results are used to explain the recent experiment by Gilbertson et al. …
The release of conduction-band electrons from a metal surface by a sub-femtosecond extreme ultraviolet (XUV) pulse, and their propagation through the solid, provokes a dielectric response in the solid that acts back on the photoelectron wave packet. We calculated the (wake) potential associated with this photoelectron self-interaction in terms of bulk and surface plasmon excitations and show that it induces a considerable, XUV-frequency-dependent temporal shift in laser-streaked XUV photoemission spectra, suggesting the observation of the ultrafast solid-state dielectric response in contempora…
The R-Matrix incorporating Time (RMT) method is a new method for solving the time-dependent Schroedinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We have employed the RMT method to investigate the time delay in the photoemission of an electron liberated from a 2p orbital in a neon atom with respect to one released from a 2s orbital following absorption of an attosecond XUV pulse. Time delays due to XUV pulses in the range 76-105 eV are presented. For an XUV pulse at the experimentally relevant 105.2 eV, we calculate the time delay to be 10.2 +/- 1.…
High harmonic spectroscopy can access structural and dynamical information on molecular systems encoded in amplitude and phase of high harmonic generation (HHG) signals4. However, measurement of the harmonic phase is a daunting task. Here we present a precise measurement of HHG phase difference between two isotopes of molecular hydrogen using the advanced extreme-ultraviolet (XUV) Gouy phase interferometer. The measured phase difference is about 200 mrad, corresponding to 3 attoseconds (1 as = 10^-18 s) time delay which is nearly independent of harmonic order. The measurements agree very well …
We present a study of high-order-harmonic generation (HHG) assisted by extreme ultraviolet (XUV) attosecond pulses, which can lead to the excitation of inner-shell electrons and the generation of a second HHG plateau. With the treatment of a one-dimensional model of krypton, based on time-dependent configuration interaction singles (TDCIS) of an effective two-electron system, we show that the XUV-assisted HHG spectrum reveals the duration of the semiclassical electron trajectories. The results are interpreted by the strong-field approximation (SFA) and the importance of the hole transfer durin…
We theoretically investigate the generation of higher harmonics and the construction of a single attosecond pulse by means of two oppositely polarized sinc-shaped driver pulses. In comparison to a few-cycle Gaussian pulse of the same energy, here we observe a significant broadening in the bandwidth of an XUV/soft-Xray supercontinuum spectrum in the synthesized pulse. Furthermore, we observe that the harmonic cutoff and its corresponding intensity follow a well-defined scaling with the {\it delay parameter} between the two pulses. In principle, this delay can easily be tuned in on an optical be…
In attosecond streaking, an electron is released by a short xuv pulse into a strong near infrared laser field. When the laser coupling between two states in the target is weak relative to the detuning, the streaking technique, which allows for a complete determination of the driving field, also gives an accurate measurement of the relative phase of the atomic or molecular ionization matrix elements from the two states through the interference from the two channels. The interference may change the phase of the photoelectron streaking signal within the envelope of the ir field, an effect to be a…
The recent development of ultrafast extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter. Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution. However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within a XUV p…
We show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization (TPDI) of helium by an attosecond XUV pulse. The Eisenbud-Wigner-Smith time delay for the emission of a two-electron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular dis…
Parametric amplification of attosecond coherent pulses around 100 eV at the single-atom level is demonstrated for the first time by using the 3D time-dependent Schr{ö}dinger equation in high-harmonic generation processes from excited states of He$^+$. We present the attosecond dynamics of the amplification process far from the ionization threshold and resolve the physics behind it. The amplification of a particular central photon energy requires the seed XUV pulses to be perfectly synchronized in time with the driving laser field for stimulated recombination to the He$^+$ ground state and is o…
We report on the first streaking measurement of water-window attosecond pulses generated via high harmonic generation, driven by sub-2-cycle, CEP-stable, 1850 nm laser pulses. Both the central photon energy and the energy bandwidth far exceed what has been demonstrated thus far, warranting the investigation of the attosecond streaking technique for the soft X-ray regime and the limits of the FROGCRAB retrieval algorithm under such conditions. We also discuss the problem of attochirp compensation and issues regarding much lower photo-ionization cross sections compared with the XUV in addition t…
We propose a method for programmable shaping of the amplitude and phase of the XUV and x-ray attosecond pulses produced by high-order harmonic generation. It overcomes the bandwidth limitations of existing spectral filters and enables removal of the intrinsic attosecond chirp as well as the synthesis of pulse sequences. It is based on partial phase matching, such as quasi-phase matching, using a longitudinally addressable modulation.
We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{ö}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease i…
Intense extreme-ultraviolet (XUV) pulses enable the investigation of XUV-induced nonlinear processes and are a prerequisite for the development of attosecond pump - attosecond probe experiments. While highly nonlinear processes in the XUV range have been studied at free-electron lasers (FELs), high-harmonic generation (HHG) has allowed the investigation of low-order nonlinear processes. Here we suggest a concept to optimize the HHG intensity, which surprisingly requires a scaling of the experimental parameters that differs substantially from optimizing the HHG pulse energy. As a result, we are…
We study the higher-harmonic generation (HHG) using elliptically polarized two-color driving fields. The HHG via bi-chromatic counter-rotating laser fields is a promising source of circularly polarized ultrashort XUV radiation at the attosecond time scale. The ellipticity or the polarization of the attosecond pulses can be tweaked by modifying the emitted harmonics' ellipticity, which can be controlled by varying the driver fields. We propose a simple setup to control the polarization of the driving fields, which eventually changes the ellipticity of the attosecond pulses. A well-defined scali…
We investigate the absorption line shapes of laser-dressed atoms beyond the single-atom response, by using extreme ultraviolet (XUV) attosecond pulse trains to probe an optically thick helium target under the influence of a strong infrared (IR) field. We study the interplay between the IR-induced phase shift of the microscopic time-dependent dipole moment and the resonant-propagation-induced reshaping of the macroscopic XUV pulse. Our experimental and theoretical results show that as the optical depth increases, this interplay leads initially to a broadening of the IR-modified line shape, and …
Multiphoton-ionized electrons are born into a strong light field that will determine their short-term future. By controlling the infrared beam, we enable atoms or molecules to generate extreme ultraviolet (XUV) pulses and synthesize attosecond pulses - the shortest controlled events ever produced. Here we show that a weak obliquely incident beam imposes an optical grating on the fundamental beam, resulting in a spatially modulated attosecond pulse. We observe the modulation on a spectrally resolved near-field XUV image, encoding all information of the spectral phase of the recollision electron…
We study the temporal aspects of laser-assisted extreme ultraviolet (XUV) photoionization using attosecond pulses of harmonic radiation. The aim of this paper is to establish the general form of the phase of the relevant transition amplitudes and to make the connection with the time-delays that have been recently measured in experiments. We find that the overall phase contains two distinct types of contributions: one is expressed in terms of the phase-shifts of the photoelectron continuum wavefunction while the other is linked to continuum--continuum transitions induced by the infrared (IR) la…
Natively, atomic and molecular processes develop in a sub-femtosecond time scale. In order to, for instance, track and capture the electron motion in that scale we need suitable `probes'. Attosecond pulses configure the most appropriate tools for such a purpose. These ultrashort bursts of light are generated when a strong laser field interacts with matter and high-order harmonics of the driving source are produced. In this work, we propose a way to twist attosecond pulse trains. In our scheme, each of the attosecond pulses in the train has a well-defined linear polarization, but with a differe…
We investigate the evolution of extreme ultraviolet (XUV) spectral lineshapes in an optically-thick helium gas under near-infrared (IR) perturbation. In our experimental and theoretical work, we systematically vary the IR intensity, time-delay, gas density and IR polarization parameters to study lineshape modifications induced by collective interactions, in a regime beyond the single atom response of a thin, dilute gas. In both experiment and theory, we find that specific features in the frequency-domain absorption profile, and their evolution with propagation distance, can be attributed to th…
We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab-initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows to discriminate between sequential …
This tutorial presents an introduction to the interaction of light and matter on the attosecond timescale. Our aim is to detail the theoretical description of ultra-short time-delays, and to relate these to the phase of extreme ultraviolet (XUV) light pulses and to the asymptotic phase-shifts of photoelectron wave packets. Special emphasis is laid on time-delay experiments, where attosecond XUV pulses are used to photoionize target atoms at well-defined times, followed by a probing process in real time by a phase-locked, infrared laser field. In this way, the laser field serves as a "clock" to…
The evolution of electron wavepackets determines the course of many physical and chemical phenomena and attosecond spectroscopy aims to measure and control such dynamics in real-time. Here, we investigate radial electron wavepacket motion in Helium by using an XUV attosecond pulse train to prepare a coherent superposition of excited states and a delayed femtosecond IR pulse to ionize them. Quantum beat signals observed in the high resolution photoelectron spectrogram allow us to follow the field-free evolution of the bound electron wavepacket and determine the time-dependent ionization dynamic…
Quasi-free field-driven electron trajectories are a key element of strong-field dynamics. Upon recollision with the parent ion, the energy transferred from the field to the electron may be released as attosecond duration XUV emission in the process of high harmonic generation (HHG). The conventional sinusoidal driver fields set limitations on the maximum value of this energy transfer, and it has been predicted that this limit can be significantly exceeded by an appropriately ramped-up cycleshape. Here, we present an experimental realization of such cycle-shaped waveforms and demonstrate contro…
In this work we demonstrate the generation of two intense, ultrafast laser pulses that allow a controlled interferometric measurement of higher harmonic generation pulses with 12.8 attoseconds in resolution (half the atomic unit of time) and a precision as low as 680 zeptoseconds ($10^{-21}$ seconds). We create two replicas of a driving femtosecond pulse which share the same optical path except at the focus where they converge to two foci. An attosecond pulse train emerges from each focus through the process of HHG. The two attosecond pulse trains from each focus interfere in the far field pro…
We present theoretical studies on real-time probing the electron density evolution of an atom in a strong infrared (IR) laser field with few-cycle near-infrared (NIR) and attosecond extreme-ultraviolet (XUV) pulses. Our results indicate that the electron density near the tunneling barrier is reflected in the additional tunneling ionization yield with a delayed NIR pulse and the electron density near the nucleus can be probed by the single photoionization yield with a delayed XUV pulse. It turns out the NIR-probing scheme can be used to study the polarization of the system in an external IR fie…
The development of ultra-short intense laser sources in the visible and extreme ultraviolet (XUV) spectral range led to fascinating studies in laser-matter interactions and attosecond science. In the majority of these studies the system under investigation interacts with a focused laser beam, which ionizes the system. The ionization products are usually measured by devices, which spatiotemporally integrate the ionization signal originating from the entire focal area, discarding in this way valuable information about the ionization dynamics that take place in the interaction volume. Here, we re…
We generalize the one electron attosecond streaking camera to time-resolve the correlated two-electron escape dynamics during a collision process involving a deep core electron. The collision process is triggered by an XUV attosecond pulse and probed by a weak infrared field. The principle of our two-electron streak camera is that by placing the maximum of the vector potential of the probing field at the time of collision we get the maximum splitting of the inter-electronic angle of escape. We thus identify the time of collision.
Probing autoionization decay lifetimes of the $\mathbf{4d^{-1}6\boldsymbol{\ell}}$ core-excited states in xenon using attosecond noncollinear four-wave-mixing spectroscopy
Extreme-ultraviolet (XUV) sources including high-harmonic generation, free-electron lasers, soft x-ray lasers and laser-driven plasmas are widely used for applications ranging from femtochemistry and attosecond science to coherent diffractive imaging and EUV lithography. The bandwidth of the XUV light emitted by these sources reflects the XUV generation process used. While light from soft-x-ray lasers and XUV FELs typically has a relatively narrow bandwidth, plasma sources and HHG sources driven by few-cycle laser pulses emit broadband XUV pulses. Since these characteristic properties of a giv…
The basic properties of atoms, molecules and solids are governed by electron dynamics which take place on extremely short time scales. To measure and control these dynamics therefore requires ultrafast sources of radiation combined with efficient detection techniques. The generation of extreme ultraviolet (XUV) attosecond (1 as = 10-18 s) pulses has, for the first time, made direct measurements of electron dynamics possible. Nevertheless, while various applications of attosecond pulses have been demonstrated experimentally, no one has yet captured or controlled the full three dimensional motio…
We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wavepacket resulting from the integration of the time-dependent Schroedinger equation in a finite-element discrete variable representation basis. These techniques are: projection on products of hydrogenic bound and continuum states, projection onto multi-channel scattering states computed in a B-spline clos…
A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomson-backscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using the received formulae, the collective spectrum and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch can be easily computed. For certain suitable and realisti…
