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.

High-order harmonic generation by few-cycle 800 nm laser pulses in neon gas in the presence of a strong terahertz (THz) field is investigated numerically with propagation effects taken into account. Our calculations show that the combination of THz fields with up to 12 fs laser pulses can be an effective gating technique to generate single attosecond pulses. We show that in the presence of the strong THz field only a single attosecond burst can be phase matched, whereas radiation emitted during other half cycles disappears during propagation. The cutoff is extended and a wide supercontinuum appears in the near-field spectra, extending the available spectral width for isolated attosecond pulse generation from 23 to 93 eV. We demonstrate that phase-matching effects are responsible for the generation of isolated attosecond pulses, even in conditions when single-atom response yields an attosecond pulse train.

Studies of the quasi-phase-matched harmonics generated in spatially modulated silver plasma are presented. We analyze the influence of the driving and heating pulse energies on the enhancement and spectral tuning of the quasi-phase-matched harmonics and show the tuning of those enhanced groups of harmonics by tilting the multislit mask placed in front of the ablated targets. Calculations performed in the laser-produced plasmas demonstrate the joint influence of the electrons that appeared during target ablation and tunnel ionization on the tuning of the quasi-phase-matching conditions in the plasmas.

High-intensity laser pulses covering the ultraviolet to terahertz spectral regions are nowadays routinely generated in a large number of laboratories. In contrast, intense extreme-ultraviolet (XUV) pulses have only been demonstrated using a small number of sources including free-electron laser facilities and long high-harmonic generation (HHG) beamlines. Here, we demonstrate a concept for a compact intense XUV source based on HHG that is focused to an intensity of 2 × 10 14 W / c m 2 , with a potential increase up to 10 17 W / c m 2 in the future. Our approach uses tight focusing of the near-infrared (NIR) driving laser and minimizes the XUV virtual source size by generating harmonics several Rayleigh lengths away from the NIR focus. Accordingly, the XUV pulses can be refocused to a small beam waist radius of 600 nm, enabling the absorption of up to four XUV photons by a single Ar atom in a setup that fits on a modest (2 m) laser table. Our concept represents a straightforward approach for the generation of intense XUV pulses in many laboratories, providing exciting opportunities for XUV strong-field and nonlinear optics experiments, for XUV-pump XUV-probe spectroscopy and for the coherent diffractive imaging of nanoscale structures.

High-order harmonic generation in the presence of a chirped THz pulse is investigated numerically with a complete 3D nonadiabatic model. The assisting THz pulse illuminates the high-order harmonic generation gas cell laterally inducing quasi-phase-matching. We demonstrate that it is possible to compensate the phase mismatch during propagation and extend the macroscopic cutoff of a propagated strong IR pulse to the single-dipole cutoff. We obtain 2 orders of magnitude increase in the harmonic efficiency of cutoff harmonics ($\approx${}170\,\,eV) using a THz pulse of constant wavelength, and a further factor of 3 enhancement when a chirped THz pulse is used.