Nonlinear optical methods have become ubiquitous in many scientific areas, from fundamental studies of time-resolved electron dynamics to microscopy and spectroscopy applications. They are, however, often limited to a certain range of parameters such as pulse energy and average power. Restrictions arise from, for example, the required field intensity as well as from parasitic nonlinear effects and saturation mechanisms. Here, we identify a fundamental principle of nonlinear light–matter interaction in gases and show that paraxial nonlinear wave equations are scale-invariant if spatial dimensions, gas density, and laser pulse energy are scaled appropriately. As an example, we apply this principle to high-order harmonic generation and provide a general method for increasing peak and average power of attosecond sources. In addition, we experimentally demonstrate the implications for the compression of short laser pulses. Our scaling principle extends well beyond those examples and includes many nonlinear processes with applications in different areas of science.

The current potential for the use of migration modelling for studying polyolefin packaging materials (low- and high-density polyethylene and polypropylene) is summarized and demonstrated with practical examples. For these polymers, an upper limit of migration into foodstuffs can be predicted with a high degree of statistical confidence. The only analytical information needed for modelling in such cases is the initial concentration of the migrant in the polymer matrix. For polyolefins of unknown origin or newly developed materials with new properties, a quick experimental method is described for obtaining the characteristic matrix parameter needed for migration modelling. For easy handling of both the experimental results and the diffusion model, user-friendly software has been developed. An additional aim of the described method is the determination of the migrant partition between polymer and food or food simulant and the specific contribution of the migrant molecular structure on the diffusion coefficient. For migration modelling of packaging materials with multilayer structures, a numerical solution of the diffusion equation is described. This procedure has been also applied for modelling the migration into solid or high viscous foodstuffs.

Ultrafast spectroscopy in the extreme ultraviolet demands for ever-higher pulse repetition rates and photon energies. Here, we drive cavity-enhanced high-order harmonic generation (HHG) at a repetition rate of 250 MHz, with 30 fs pulses and an average power of 10 kW. Employing an optimized cavity geometry and a high-pressure gas target, we couple out nanowatt-level harmonics at photon energies around 100 eV. This constitutes an improvement of more than two orders of magnitude over previous megahertz-repetition-rate HHG experiments and paves the way toward high-photon-energy frequency-comb spectroscopy and toward pump-probe photoelectron microscopy and spectroscopy at unprecedented repetition rates.

For the analysis of high-order harmonics generated in a long gas jet by intense chirped femtosecond laser pulses, calculations of the laser propagation and harmonic generation were performed in terms of a nonadiabatic three-dimensional model. The self-guided propagation, observed at the conditions of bright harmonic generation, was confirmed by the model calculations. When using negatively chirped pulses, the calculated distribution of the harmonic field is spatially and spectrally confined, being generated on axis with a narrow spectral profile. The positively chirped pulses generate broad spectral distribution on axis, and narrow off axis, but in the latter case with a large emission angle. The estimation of harmonic beam divergence agreed well with experimentally measured data, showing the lowest divergence at the conditions of the brightest harmonic generation. Spectral, temporal, and spatial modifications of the propagated laser pulse are found to influence decisively the single-atom response and ultimately the harmonic field, providing a coherent picture of harmonic generation.

Generation of high-order harmonics in Xe was studied in a static cell at high pump energies, 5 m focal length, and up to 14 cm interaction lengths. Self-guided propagation of the pulse was observed experimentally and confirmed by a three-dimensional model. Phase-matched generation was demonstrated in the self-guided beam, and the high energy and low divergence of the harmonic radiation were explained. Harmonic field calculations, in good agreement with experimental results, allow for the explanation of the higher-order harmonic generation dynamics in the self-guided region.