The generation of ultrashort pulses is a key to exploring the dynamic behaviour of matter on ever-shorter timescales. Recent developments have pushed the duration of laser pulses close to its natural limit-the wave cycle, which lasts somewhat longer than one femtosecond (1 fs = 10-15 s) in the visible spectral range. Time-resolved measurements with these pulses are able to trace dynamics of molecular structure, but fail to capture electronic processes occurring on an attosecond (1 as = 10-18 s) timescale. Here we trace electronic dynamics with a time resolution of

Monolayer MoS2 is a direct-gap two-dimensional semiconductor that exhibits strong electron-hole interactions, leading to the formation of stable excitons and trions. Here we report the existence of efficient exciton-exciton annihilation, a four-body interaction, in this material. Exciton-exciton annihilation was identified experimentally in ultrafast transient absorption measurements through the emergence of a decay channel varying quadratically with exciton density. The rate of exciton-exciton annihilation was determined to be (4.3 ± 1.1) × 10(-2) cm(2)/s at room temperature.

Single soft-x-ray pulses of approximately 90-electron volt (eV) photon energy are produced by high-order harmonic generation with 7-femtosecond (fs), 770-nanometer (1.6 eV) laser pulses and are characterized by photoionizing krypton in the presence of the driver laser pulse. By detecting photoelectrons ejected perpendicularly to the laser polarization, broadening of the photoelectron spectrum due to absorption and emission of laser photons is suppressed, permitting the observation of a laser-induced downshift of the energy spectrum with sub-laser-cycle resolution in a cross correlation measurement. We measure isolated x-ray pulses of 1.8 (+0.7/-1.2) fs in duration, which are shorter than the oscillation cycle of the driving laser light (2.6 fs). Our techniques for generation and measurement offer sub-femtosecond resolution over a wide range of x-ray wavelengths, paving the way to experimental attosecond science. Tracing atomic processes evolving faster than the exciting light field is within reach.

The theoretical investigation of sum and difference frequency generation in thin surface layers with rotational symmetry leads to formulas which connect the generated light intensities to the surface second order nonlinear susceptibility tensor. A maximum of seven tensor components can be determined in the case of lowest symmetry. Measurements in transmission should be especially useful since they allow easy variation of both polarization and angle of incidence. On the other hand, large signal enhancements are expected for total internal reflection geometries. A consistent set of Z t2) tensor components for a thin layer of rhodamine-6G adsorbed on fused silica is found based on data from reflection and transmission measurements.

Second-harmonic generation ͑SHG͒ from individual nanoscopic metal tips has been investigated. Compared to both planar interfaces, as well as spherical or ellipsoidal nanoparticles, very different polarization selection rules and SH-emission directions result. As a partially asymmetric nanostructure the tip allows for the distinction of otherwise inseparable local surface and nonlocal bulk second-harmonic polarizations. This provides opportunities for second-harmonic investigations of nanoparticles and in scattering-type near field microscopy.The optics of media of dimensions small compared to the optical wavelength is characterized by distinctive phenomena such as optical field confinement and structural resonances. With a strong focus in research on the linear optical processes of surface nanostructures and colloids, the nonlinear optical properties have remained largely unexplored. The nonlinear response, however, is expected to differ fundamentally due to its high symmetry selectivity. Specifically, for media with inversion symmetry the second-order nonlinearity is dominated by the interface where the symmetry is broken. 1 Second-harmonic generation ͑SHG͒ has thus become a well-established technique for the investigation of planar surfaces and interfaces. 2 Many applications, however, would call for an expansion of SHG to also address molecular adsorption and surface electronic and geometric structure on the nanoscale. Here, the problem of SHG becomes particularly intriguing: Although at the surface of the nanostructure the inversion symmetry is broken locally, depending on its dimension and macroscopic symmetry, emission can be highly restricted due to the destructive interference of the induced local surface second-harmonic ͑SH͒ polarizations. 3,4 In this paper we address the different contributions to the nonlinear source polarization and provide general directional and polarization selection rules for second-harmonic generation from partially asymmetric ͑mm͒ nanostructures. Metal wire tips with a nanometer-sized apex represent a model geometry, with the mirror symmetry being broken along the tip axis but conserved in all other directions. This structure allows for the direct separation between local surface and nonlocal higher-order bulk contributions to the SH response-a long-standing problem in nonlinear surface spectroscopy. 1,5 Recently, an attempt to resolve this issue for nanoparticles has been made, 6 yet the separation of surface and bulk contributions remained open.In SHG strong symmetry selection rules apply that are valid independent of the microscopic origin of the nonlinear polarization. 5,7 For media with inversion symmetry the process of SHG ͑and any other even-order nonlinear process͒ is forbidden in the electric dipole approximation. In contrast, the broken mirror symmetry at the interface allows for a local, second-order source polarization P ͑2͒ ͑2͒ = ⑀ 0 s ͑2͒ L͑2͒L͑͒L͑͒ : E͑͒E͑͒ to be induced. 1 Here, s ͑2͒ denotes the surface nonlinear susceptibility tensor with the components s,ЌЌЌ ͑...