G. G. Paulus

Absolute-phase phenomena in photoionization with few-cycle laser pulses.

Currently, the shortest laser pulses that can be generated in the visible spectrum consist of fewer than two optical cycles (measured at the full-width at half-maximum of the pulses envelope). The time variation of the electric field in such a pulse depends on the phase of the carrier frequency with respect to the envelope—the absolute phase. Because intense laser–matter interactions generally depend on the electric field of the pulse, the absolute phase is important for a number of nonlinear processes. But clear evidence of absolute-phase effects has yet to be detected experimentally, largely because of the difficulty of stabilizing the absolute phase in powerful laser pulses. Here we use a technique that does not require phase stabilization to demonstrate experimentally the influence of the absolute phase of a short laser pulse on the emission of photoelectrons. Atoms are ionized by a short laser pulse, and the photoelectrons are recorded with two opposing detectors in a plane perpendicular to the laser beam. We detect an anticorrelation in the shot-to-shot analysis of the electron yield.

Attosecond Double-Slit Experiment

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are measured. A situation in which one and the same electron encounters a single and a double slit at the same time is observed. The investigation of the fringes makes possible interferometry on the attosecond time scale. From the number of visible fringes, for example, one derives that the slits are extended over about 500 as.

Above-threshold ionization by few-cycle pulses

The theoretical description and the experimental methods and results for above-threshold ionization (ATI) by few-cycle pulses are reviewed. A pulse is referred to as a few-cycle pulse if its detailed shape, parametrized by its carrier-envelope phase, affects its interaction with matter. Angular-resolved ATI spectra are analysed with the customary strong-field approximation (SFA) as well as the numerical solution of the time-dependent Schrodinger equation (TDSE). After a general discussion of the characteristics and the description of few-cycle pulses, the behaviour of the ATI spectrum under spatial inversion is related to the shape of the laser field. The ATI spectrum both for the direct and for the rescattered electrons in the context of the SFA is evaluated by numerical integration and by the method of steepest descent (saddle-point integration), and the results are compared. The saddle-point method is modified to avoid the singularity of the dipole transition matrix element at the steepest-descent times. With the help of the saddle-point method and its classical limit, namely the simple-man model, the various features of the ATI spectrum, their behaviour under inversion, the cut-offs and the presence or absence of ATI peaks are analysed as a function of the carrier-envelope phase of the few-cycle laser field. All features observed in the spectra can be explained in terms of a few quantum orbits and their superposition. The validity of the SFA and the concept of quantum orbits are established by comparing the ATI spectra with those obtained numerically from the ab initio solution of the TDSE.

Rescattering effects in above-threshold ionization: a classical model

Recent experimental investigations of the high-order above-threshold ionization peaks near the onset of the plateau have exhibited anomalous angular distributions of the emitted photoelectrons with pronounced side lobes surrounding emission in the direction of the laser electric field. It is shown that the existence and angular position of these side lobes are consequences of the classical kinematics of electrons in laser fields.

A strong-field driver in the single-cycle regime based on self-compression in a kagome fibre

Over the past decade intense laser fields with a single-cycle duration and even shorter, subcycle multicolour field transients have been generated and applied to drive attosecond phenomena in strong-field physics. Because of their extensive bandwidth, single-cycle fields cannot be emitted or amplified by laser sources directly and, as a rule, are produced by external pulse compression—a combination of nonlinear optical spectral broadening followed up by dispersion compensation. Here we demonstrate a simple robust driver for high-field applications based on this Kagome fibre approach that ensures pulse self-compression down to the ultimate single-cycle limit and provides phase-controlled pulses with up to a 100 μJ energy level, depending on the filling gas, pressure and the waveguide length.

Attosecond tracing of correlated electron-emission in non-sequential double ionization

Despite their broad implications for phenomena such as molecular bonding or chemical reactions, our knowledge of multi-electron dynamics is limited and their theoretical modelling remains a most difficult task. From the experimental side, it is highly desirable to study the dynamical evolution and interaction of the electrons over the relevant timescales, which extend into the attosecond regime. Here we use near-single-cycle laser pulses with well-defined electric field evolution to confine the double ionization of argon atoms to a single laser cycle. The measured two-electron momentum spectra, which substantially differ from spectra recorded in all previous experiments using longer pulses, allow us to trace the correlated emission of the two electrons on sub-femtosecond timescales. The experimental results, which are discussed in terms of a semiclassical model, provide strong constraints for the development of theories and lead us to revise common assumptions about the mechanism that governs double ionization.

Attosecond-recollision-controlled selective fragmentation of polyatomic molecules.

Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wave packets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of predetermining fragmentation and isomerization reactions in polyatomic molecules on subfemtosecond time scales.

Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime

We demonstrate a solid-state device capable of providing direct information about the carrier-envelope (CE) phase of ultrashort (4 fs) laser pulses. The measurement is based on multi-photon-induced photoelectron emission from a gold surface. The amount of the charge emitted from the surface gives a clear indication of phase sensitivity, as predicted by our simulations and also by a simple intuitive model. This phenomenon was used to determine the CE phase value of each laser pulse in a mode-locked, unamplified, low-energy pulse train. The inability of the commonly used f -to-2f interferometric method to measure accurately extracavity drifts of the CE phase is discussed and contrasted with the direct phase measurement method proposed here. The evolution of the CE phase upon propagation of pulses comparable in duration to the optical cycle is analysed.

Precision control of carrier-envelope phase in grating based chirped pulse amplifiers.

It is demonstrated that the carrier-envelope (CE) phase of pulses from a high power ultrafast laser system with a grating-based stretcher and compressor can be stabilized to a root mean square (rms) value of 180 mrad over almost 2 hours, excluding a brief re-locking period. The stabilization was accomplished via feedback control of the grating separation in the stretcher. It shows that the long term CE phase stability of a grating based chirped pulse amplification system can be as good as that of lasers using a glass-block stretcher and a prism pair compressor. Moreover, by adjusting the grating separation to preset values, the relative CE phase could be locked to an arbitrary value in the range of 2pi. This method is better than using a pair of wedge plates to adjust the phase after the hollow-core fiber compressor. The CE phase stabilization after a hollow-core fiber compressor was confirmed by a CE-phase meter based on the measurement of the left-to-right asymmetry of electrons produced by above-threshold ionization.

Precise, real-time, every-single-shot, carrier-envelope phase measurement of ultrashort laser pulses

In this Letter we demonstrate a method for real-time determination of the carrier-envelope phase of each and every single ultrashort laser pulse at kilohertz repetition rates. The technique expands upon the recent work of Wittmann and incorporates a stereographic above-threshold laser-induced ionization measurement and electronics optimized to produce a signal corresponding to the carrier-envelope phase within microseconds of the laser interaction, thereby facilitating data-tagging and feedback applications. We achieve a precision of 113 mrad (6.5°) over the entire 2π range.