In 1964 Keldysh1 helped lay the foundations of strong-field physics by introducing a theoretical framework that characterized atomic ionization as a process that evolves with the intensity and wavelength of the fundamental field. Within this context, experiments 2 have examined the intensity-dependent ionization but, except for a few cases, technological limitations have confined the majority to wavelengths below 1 µm. The development of intense, ultrafast laser sources in the midinfrared (1 µm < l < 5 µm) region enables exploration of the wavelength scaling of the Keldysh picture while enabling new opportunities in strong-field physics, control of electronic motion and attosecond science. Here we report a systematic experimental investigation of the wavelength scaling in this region by concurrently analysing the production of energetic electrons and photons emitted by argon atoms interacting with few-cycle, mid-infrared fields. The results support the implicit predictions contained in Keldysh's work, and pave the way to the realization of brighter and shorter attosecond pulsed light sources using longer-wavelength driving fields. Keldysh 1 described the two main effects an intense lowfrequency laser field has on an atom as (1) a bending of the Coulomb potential by the field, forming a sufficiently narrow barrier for the electron to tunnel into the continuum, and (2) an oscillating motion of the free electron induced by the field of strength E and frequency ω. The cycle-averaged kinetic energy of the oscillating electron (ponderomotive energy) is given in atomic units as U p = E 2 /4ω 2 . The limit of validity of the Keldysh approach is defined by the condition that the adiabaticity parameter γ = √

The group delay dispersion, also known as the attochirp, of high-order harmonics generated in gases has been identified as the main intrinsic limitation to the duration of Fourier-synthesized attosecond pulses. Theory implies that the attochirp, which is inversely proportional to the laser wavelength, can be decreased at longer wavelength. Here we report the first measurement of the wavelength dependence of the attochirp using an all-optical, in situ method [N. Dudovich et al., Nature Phys. 2, 781 (2006)]. We show that a 2 m driving wavelength reduces the attochirp with respect to 0:8 m at comparable intensities. DOI: 10.1103/PhysRevLett.102.093002 PACS numbers: 32.80.Fb Attosecond science, or attophysics, is the study of electron dynamics at time-scales approaching the atomic unit of time (1 a:u: % 24 as) [1]. Currently, the production of attosecond pulses and the development of attophysics are based on high harmonic generation in gases, a nonperturbative, highly nonlinear process. Using this method, light pulses close to 100 as have been demonstrated either as an attosecond pulse train (APT) with a repetition period of half the fundamental cycle [2] or as a single pulse [3,4]. So far the carrier frequency of attosecond pulses has been limited to the extreme ultraviolet (XUV) to soft-x-ray domain (30-80 eV) but significantly more applications will be enabled if shorter bursts of more energetic x rays can be created, particularly time resolved studies of corelevel and multielectron dynamics [5]. In order to evaluate the physical limitations it is important to understand the role of the driving field characteristics. The recent development of intense midinfrared femtosecond pulses with wavelength 5 times that of the commonly used titanium: sapphire laser system has opened new routes to extreme harmonic generation and attophysics [6,7]. In this report, a measurement of the driving wavelength dependence of the group delay dispersion or attochirp, a property crucial for attosecond pulse synthesis, is described.High harmonic generation is a quantum mechanical process involving the absorption of a large number of photons, for which the usual nonlinear optics treatment breaks down. In a more effective description based on classical trajectories, a field-driven electron freed by intense field ionization is accelerated for approximately half an optical cycle, and then can recombine to emit an attosecond burst of light [8,9]. This process occurs twice every optical cycle, which in the frequency domain corresponds to a comb of odd-order harmonics of the fundamental driving field. The corresponding quantum mechanical treatment is based on the strong field approximation [10] in which the time-dependent one-electron dipole is calculated by solving the Schrödinger equation neglecting the influence of the Coulomb potential on the motion of the free electron wave packet. In this approximation the main contribution to the dipole comes from the quantum paths whose quasiclassical action is stationary and therefore follow the af...

International audienceThe nonlinear interaction of an intense femtosecond laser pulse with matter can lead to the emission of a train of sub-laser-cycle--attosecond--bursts of short-wavelength radiation1, 2. Much effort has been devoted to producing isolated attosecond pulses, as these are better suited to real-time imaging of fundamental electronic processes3, 4, 5, 6. Successful methods developed so far rely on confining the nonlinear interaction to a single sub-cycle event7, 8, 9. Here, we demonstrate for the first time a simpler and more universal approach to this problem10, applied to nonlinear laser-plasma interactions. By rotating the instantaneous wavefront direction of an intense few-cycle laser field11, 12 as it interacts with a solid-density plasma, we separate the nonlinearly generated attosecond pulse train into multiple beams of isolated attosecond pulses propagating in different and controlled directions away from the plasma surface. This unique method produces a manifold of isolated attosecond pulses, ideally synchronized for initiating and probing ultrafast electron motion in matter

We report the compression of intense, carrier-envelope phase stable mid-IR pulses down to few-cycle duration using an optical filament. A filament in xenon gas is formed by using self-phase stabilized 330 J 55 fs pulses at 2 m produced via difference-frequency generation in a Ti:sapphire-pumped optical parametric amplifier. The ultrabroadband 2 m carrier-wavelength output is self-compressed below 3 optical cycles and has a 270 J pulse energy. The self-locked phase offset of the 2 m difference-frequency field is preserved after filamentation. This is to our knowledge the first experimental realization of pulse compression in optical filaments at mid-IR wavelengths ͑Ͼ0.8 m͒. © 2007 Optical Society of America OCIS codes: 190.5530, 320.5520. Progress in strong-field physics has been accelerated by the development of lasers operating near the 0.8 m wavelength that feature high peak power, few-cycle duration, and reliable control over the carrier-envelope phase 1 (CEP). Furthermore, the fundamental scaling laws 2,3 governing the intense laseratom interaction suggest that the advancement of longer-wavelength mid-IR laser sources capable of similar optical quality will have a major impact in strong-field physics. The most compelling examples include the generation of shorter attosecond x-ray bursts and the rescattering of electrons at kilovolt energies. [3][4][5] A recently demonstrated 80 J, 2 m prototype system 6 based on optical parametric chirped-pulse amplification via difference-frequency generation defines a standard for future development of longwavelength drivers. However, the optical parametric chirped-pulse amplification architecture is faced with important technical challenges, 7 such as the need for specific pump laser design and unwanted generation of parasitic fluorescence underlying the primary pulse for high parametric gain configurations. 6 Currently, femtosecond optical parametric amplifiers (OPAs) pumped by multimillijoule Ti:sapphire chirped-pulse amplification systems can deliver multicycle pulses in the mid-IR with sufficient peak power to investigate the efficacy of the nonlinear pulse compression techniques developed at shorter wavelengths. In particular, optical filaments formed in a noble gas by intense 0.8 m pulses have demonstrated pulse compression down to the few-cycle regime with excellent beam stability and spatial mode quality. 8This Letter demonstrates, for the first time to our knowledge, the self-compression in an optical filament of high-peak-power mid-IR pulses derived by difference-frequency generation in a Ti:sapphire pumped OPA. This efficient scheme produces fluorescence-free, sub-3 optical cycle pulses near the 2 m wavelength with 270 J energy at a 1 kHz repetition rate. The intense 2 m field carries a constant CEP offset, thus making it an attractive longwavelength driver for benchmark strong-field experiments.A schematic of the experimental setup is shown in Fig. 1. High-peak-power multicycle mid-IR pulses are produced in a slightly modified traveling-wave OPA (TOPAS, L...

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High harmonic generation (HHG) is used to measure the spectral phase of the recombination dipole matrix element (RDM) in argon over a broad frequency range that includes the 3p Cooper minimum (CM). The measured RDM phase agrees well with predictions based on the scattering phases and amplitudes of the interfering s- and d-channel contributions to the complementary photoionization process. The reconstructed attosecond bursts that underlie the HHG process show that the derivative of the RDM spectral phase, the group delay, does not have a straightforward interpretation as an emission time, in contrast to the usual attochirp group delay. Instead, the rapid RDM phase variation caused by the CM reshapes the attosecond bursts.

This paper provides an overview of ultrafast wavefront rotation of femtosecond laser pulses and its various applications in highly nonlinear optics, focusing on processes that lead to the generation of high-order harmonics and attosecond pulses. In this context, wavefront rotation can be exploited in different ways, to obtain new light sources for time-resolved studies, called 'attosecond lighthouses', to perform time-resolved measurements of nonlinear optical processes, using 'photonic streaking', or to track changes in the carrier-envelope relative phase of femtosecond laser pulses. The basic principles are explained qualitatively from different points of view, the experimental evidence obtained so far is summarized, and the perspectives opened by these effects are discussed.

TeV center-of-mass energy electron-positron linear colliders comprising seamlessly staged capillary laser-plasma accelerators are presented. A moderate intensity laser pulse coupled with the single electromagnetic hybrid mode in a gas-filled capillary can generate plasma waves in the linear regime, where laser wakefields can accelerate equally focused electron and positron beams. In multiple stage capillary accelerators, a particle beam with respect to the laser wakefield can undergo consecutive acceleration up to TeV energies, associated with continuous transverse focusing in a beam size down to a nanometer level, being capable of a promising electron-positron linear collider with very high luminosities of the order of 10[Formula: see text] cm[Formula: see text]s[Formula: see text]. The transverse and longitudinal beam dynamics of beam particles in plasma wakefields with the effects of radiation reaction and multiple Coulomb scattering are investigated numerically to estimate the luminosities in beam-beam collisions with the effects of beamstrahlung radiation and bunch disruption.