Femtosecond filamentation in transparent media

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 would like to make corrections to three equations in the above article Please see the PDF file for full details

https://iopscience.iop.org/article/10.1088/0034-4885/67/6/R01/pdf

The physics of attosecond light pulses

The electromagnetic field of visible light performs approximately 10(15) oscillations per second. Although many instruments are sensitive to the amplitude and frequency (or wavelength) of these oscillations, they cannot access the light field itself. We directly observed how the field built up and disappeared in a short, few-cycle pulse of visible laser light by probing the variation of the field strength with a 250-attosecond electron burst. Our apparatus allows complete characterization of few-cycle waves of visible, ultraviolet, and/or infrared light, thereby providing the possibility for controlled and reproducible synthesis of ultrabroadband light waveforms.

https://science.sciencemag.org/content/sci/305/5688/1267.full.pdf

Direct Measurement of Light Waves

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.

https://iopscience.iop.org/article/10.1088/0953-4075/39/14/R01/pdf

Above-threshold ionization by few-cycle pulses

Attosecond control of ionization and high-order harmonic generation in molecules

A new technique for directly measuring the electric field of linearly polarized few-cycle laser pulses is proposed. Based on the solution of the time-dependent Schrodinger equation (TDSE) for an H atom in the combined field of infrared (IR) femtosecond (fs) and ultraviolet (UV) attosecond (as) laser pulses we show that, as a function of the time delay between two pulses, the difference (or equivalently, asymmetry) of photoelectron signals in opposite directions (along the polarization vector of laser pulses) reproduces very well the profile of the electric field (or vector potential) in the IR pulse. Such ionization asymmetry can be used for directly measuring the carrier-envelope phase difference (i.e., the relative phase of the carrier frequency with respect to the pulse envelope) of the IR fs laser pulse.

Measuring the electric field of few-cycle laser pulses by attosecond cross correlation

Generation and propagation of high-order harmonics by intense, ultrashort laser pulses in static gas cells and gas-filled hollow waveguides are numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schr\"odinger and wave equations. It is shown that, when the 30-fs laser pulse is focused into a gas cell the emission spectrum consists of discrete and well-resolved harmonics. These high-order harmonics can be used for generation of a train of subfemtosecond pulses. When the 5-fs laser pulse propagates along a gas-filled hollow waveguide the emission spectrum exhibits a quasicontinous structure that permits the generation of a single subfemtosecond pulse. The effects of laser intensity and position of the interacting medium relative to the laser focus on the emission spectrum and pulse profile are investigated. The differences between results obtained by our model and by the model that uses the strong-field approximation for single-atom calculations are discussed.

High-order harmonic and attosecond pulse generations: Bulk media versus hollow waveguides

Generation of subfemtosecond pulses by beating a femtosecond pulse with a Raman coherence adiabatically prepared in solid hydrogen

Generation and propagation of high-order harmonics in high-pressure (0.5--4 atm) gases by intense, ultrashort laser pulses is numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schr\"odinger and one-dimensional wave equations. The results obtained from the second-order and from the reduced first-order wave equations are compared. It is shown that at high pressure and for the high-order harmonics the use of the reduced first-order wave equation is not adequate. At very high pressure (\ensuremath{\sim}4 atm) a new regime of phase matching was observed. The applicability of the reduced first-order wave equation is also discussed.

Nguyen Hong Shon

Papers

Attosecond control of ionization and high-order harmonic generation in molecules

Measuring the electric field of few-cycle laser pulses by attosecond cross correlation

High-order harmonic and attosecond pulse generations: Bulk media versus hollow waveguides

Generation of subfemtosecond pulses by beating a femtosecond pulse with a Raman coherence adiabatically prepared in solid hydrogen

Generation and propagation of high-order harmonics in high-pressure gases