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

We stabilized the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. We confirmed control of the pulse-to-pulse carrier-envelope phase using temporal cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which we used to perform absolute optical frequency measurements that were directly referenced to a stable microwave clock.

/pdf/carrier-envelope-phase-control-of-femtosecond-mode-locked-4lkf4vexna.pdf

Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis

Researchers report sub-angstrom fundamental-wavelength lasing at the SPring-8 Angstrom Compact Free-Electron Laser in Japan. The output has a maximum power of more than 10 GW, a pulse duration of 10−14 s and a lasing wavelength of 0.634 A.

A compact X-ray free-electron laser emitting in the sub-ångström region

Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.

/pdf/time-dependent-density-functional-theory-280q52hn1n.pdf

Time-Dependent Density Functional Theory

Recently there has been a remarkable synergy between the technologies of precision laser stabilization and mode-locked ultrafast lasers. This has resulted in control of the frequency spectrum produced by mode-locked lasers, which consists of a regular comb of sharp lines. Thus such a controlled mode-locked laser is a ``femtosecond optical frequency comb generator.'' For a sufficiently broad comb, it is possible to determine the absolute frequencies of all of the comb lines. This ability has revolutionized optical frequency metrology and synthesis. It has also served as the basis for the recent demonstrations of atomic clocks that utilize an optical frequency transition. In addition, it is having an impact on time-domain applications, including synthesis of a single pulse from two independent lasers. In this Colloquium, we first review the frequency-domain description of a mode-locked laser and the connection between the pulse phase and the frequency spectrum in order to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical frequency metrology and synthesis and optical atomic clocks are discussed. This is followed by a brief overview of how the comb technology is affecting and will affect time-domain experiments.

https://www.reading.ac.uk/physicsnet/units/4/4phla/Papers/RMP03_FemtosecondCombs_Cundiff.pdf

Colloquium: Femtosecond optical frequency combs

Coherent extreme-ultraviolet radiation extending to wavelengths below the carbon K edge at 4.37 nanometers (nm) has been generated at a repetition rate of 1 kilohertz by focusing 5-femtosecond near-infrared (780 nm) laser pulses into a helium gas jet. The incident light field performs just a few oscillations, which results in the emission of an x-ray supercontinuum rather than discrete harmonics. Owing to the extremely short rise time of the driving pulses, neutral atoms can be exposed to high fields before they are depleted by ionization. As a result, the observed x-ray radiation extends well into the water window and is delivered in a well-collimated beam (divergence less than 1 milliradian). The high repetition rate and spatial coherence result in a brightness of about 5 × 108 photons per square millimeter per square milliradian per second in a 1-percent bandwidth at 4.37 nm, the carbon edge of the water window. The compact laboratory system holds promise as a source for biological holography and nonlinear optics in the x-ray regime.

https://science.sciencemag.org/content/sci/278/5338/661.full.pdf

M. Schnürer

Papers

Generation of Coherent X-rays in the Water Window Using 5-Femtosecond Laser Pulses