The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

In principle, the temporal beating of superposed high harmonics obtained by focusing a femtosecond laser pulse in a gas jet can produce a train of very short intensity spikes, depending on the relative phases of the harmonics. We present a method to measure such phases through two-photon, two-color photoionization. We found that the harmonics are locked in phase and form a train of 250-attosecond pulses in the time domain. Harmonic generation may be a promising source for attosecond time-resolved measurements.

https://science.sciencemag.org/content/sci/292/5522/1689.full.pdf

Observation of a Train of Attosecond Pulses from High Harmonic Generation

Ultrafast lasers, which generate optical pulses in the picosecond and femtosecond range, have progressed over the past decade from complicated and specialized laboratory systems to compact, reliable instruments. Semiconductor lasers for optical pumping and fast optical saturable absorbers, based on either semiconductor devices or the optical nonlinear Kerr effect, have dramatically improved these lasers and opened up new frontiers for applications with extremely short temporal resolution (much smaller than 10 fs), extremely high peak optical intensities (greater than 10 TW/cm2) and extremely fast pulse repetition rates (greater than 100 GHz).

Recent developments in compact ultrafast lasers

Single-electron wavefunctions, or orbitals, are the mathematical constructs used to describe the multi-electron wavefunction of molecules. Because the highest-lying orbitals are responsible for chemical properties, they are of particular interest. To observe these orbitals change as bonds are formed and broken is to observe the essence of chemistry. Yet single orbitals are difficult to observe experimentally, and until now, this has been impossible on the timescale of chemical reactions. Here we demonstrate that the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmonics generated from intense femtosecond laser pulses focused on aligned molecules. Applying this approach to a series of molecular alignments, we accomplish a tomographic reconstruction of the highest occupied molecular orbital of N2. The method also allows us to follow the attosecond dynamics of an electron wave packet.

Tomographic imaging of molecular orbitals

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law Ip+3.17Up, where Ip is the atomic ionization potential and Up is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.

Theory of high-harmonic generation by low-frequency laser fields.

We present experimental results of harmonic generation using a 1-ps ${10}^{15\mathrm{\ensuremath{-}}}$W/${\mathrm{cm}}^{2}$ Nd-glass laser. We see up to the 29th harmonic in Xe, 57th in Ar, and at least up to the 135th harmonic in Ne (160 eV), being then limited by our monochromator's resolution. The conversion efficiencies in Xe, Ar, Ne, and He are compared and different ways of optimizing the number of photons by defocusing the laser beam or increasing the density are discussed.

High-order harmonic generation in rare gases with a 1-ps 1053-nm laser.

We investigate experimentally the optical tunneling times associated with frustrated total internal reflection of a light beam. Using as physical clocks the lateral shifts and angular deviations suffered by the transmitted and reflected beams, we measure both components of a complex tunneling time: the phase time and a semiclassical time. The phase time is shown to imply superluminal velocities and to depend strongly on boundary conditions not linked to the tunneling process. By contrast, the semiclassical time yields subluminal velocities and is related solely to tunneling.

Dual optical tunneling times in frustrated total internal reflection

We investigate the relevance of the absorption limit concept in the optimization of high harmonic generation. Thanks to the first direct observation of the coherence length of the process from high-contrast Maker fringes, we unravel experimental conditions for which the harmonic dipole response is enhanced when phase matching is realized within the absorption limit, leading to record conversion efficiencies in argon. Moreover, we show that harmonic generation in guided or freely propagating geometries are equivalent in the loose focusing regime. This analysis is generalized to other advanced phase-matching schemes, thereby predicting the possibility to boost the conversion efficiencies using light noble gases.

Ph. Balcou

Papers

Theory of high-harmonic generation by low-frequency laser fields.

Observation of a Train of Attosecond Pulses from High Harmonic Generation

High-order harmonic generation in rare gases with a 1-ps 1053-nm laser.

Dual optical tunneling times in frustrated total internal reflection

Global optimization of high harmonic generation.