Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for example, parasitic nonlinear effects, damage problems and geometrical considerations. Here, we show that many nonlinear optics phenomena in gaseous media are scale-invariant if spatial coordinates, gas density and laser pulse energy are scaled appropriately. We develop a general scaling model for (3+1)-dimensional wave equations, demonstrating the invariant scaling of nonlinear pulse propagation in gases. Our model is numerically applied to high-order harmonic generation and filamentation as well as experimentally verified using the example of pulse post-compression via filamentation. Our results provide a simple recipe for up-or downscaling of nonlinear processes in gases with numerous applications in many areas of science.Nonlinear interactions of intense short laser pulses with gaseous media form the basis behind a wealth of interesting phenomena such as multiphoton ionization [1] and plasma formation [2], spectral broadening (which can be used for pulse compression [3][4][5]), harmonic generation and wave-mixing [6], as well as the creation of attosecond pulses [7] and the formation of electron or ion beams [8]. Advances in femtosecond laser technology constantly yield shorter pulses, higher pulse energies, and higher repetition rates [9][10][11]. However, to fully explore this newly available parameter regime, which gives access to e.g. faster time scales and higher intensities, is often challenging because of damage problems, additional (unwanted) nonlinear effects, or geometrical restrictions. We illustrate this challenge for two important applications of nonlinear optics, filamentation in gases used e.g. for laser pulse compression, and high-order harmonic generation (HHG) providing the basis for attosecond science.The propagation of an intense short laser pulse in a transparent medium induces nonlinear effects caused e.g. by the intensity dependence of the refractive index. When self-focusing due to the Kerr effect balances defocussing caused by diffraction and plasma generation, a filament can be created. In addition, self-phase modulation and self compression may take place in the filament, resulting, possibly after further compression, in ultrashort pulses close to the fundamental limit of a single cycle [12]. Forming a filament requires a certain power, known as the critical power for self-focusing [13,14]. At slightly higher power, limitations arise and multiple filaments are created [15]. Different attempts were suggested to increase the output energy [12,[16][17][18][19][20]. However, pulse compression using filaments (or similarly hollow fibers) is still limited to pulse energies of typically a few mJ [21,22], which is approximately two to three orders of magnitude below the maximum pulse energies available from today's femtosecond laser sources. To scale up pulse po...

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.

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 (≈170  eV) using a THz pulse of constant wavelength, and a further factor of 3 enhancement when a chirped THz pulse is used.