High-order Harmonic Propagation Research Articles

Generation and propagation of high-order harmonics in crystals

The observation of nonperturbative high-order-harmonic generation in periodic solids has been interpreted in terms of a two step process comprising tunnel ionization and radiation from electrons undergoing frequency modulated Bloch oscillations in a strong laser field [Ghimire et al., Nat. Phys. 7, 138 (2011)]. Here we extend the model to include propagation effects. We show that the predicted efficiency is limited by phase velocity mismatch for emission below the band gap and by absorption above the band gap. The efficiency of harmonics scales with the square of the carrier density, suggesting that direct seeding could lead to higher yield. The emitted harmonics should have a temporal profile consisting of a train of subcycle pulses with duration on the order of 650 as depending on the crystal thickness.

Propagation characteristics of the broadband supercontinuum with an attosecond ionization gate

The propagation of high-order harmonics with attosecond ionization gate is simulated with three-dimensional propagation equation. After 0.5 mm propagation distance， the short trajectories in the harmonics， which are generated by two 5 fs laser pulses centered at 800 and 400 nm， are selected and a highly efficient smooth supercontinuum with the bandwidth of about 80 eV is obtained in the plateau， because of the phase matching. Simulation results of different propagation distances show the broadband supercontinuum can last steadily. A highly efficient pure isolated attosecond pulse with the duration of about 135 as can be generated by directly filtering out of the harmonics from 60—90 eV in the supercontinuum， and a single 50 as pulse can be generated， which facilitates the experimental implementation for the isolated attosecond pulse generation.

Macroscopic effects in attosecond pulse generation

We examine how the generation and propagation of high-order harmonics in a partly ionized gas medium affect their strength and synchronization. The temporal properties of the resulting attosecond pulses generated in long gas targets can be significantly influenced by macroscopic effects, in particular by the intensity in the medium and the degree of ionization which control the dispersion. Under some conditions, the use of gas targets longer than the absorption length can lead to the generation of compressed attosecond pulses. We show these macroscopic effects experimentally, using a 6 mm-long argon-filled gas cell as the generating medium.

High-order harmonic and attosecond pulse generations: Bulk media versus hollow waveguides

Generation and propagation of high-order harmonics by intense, ultrashort laser pulses in static gas cells and gas-filled hollow waveguides are numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schr\odinger and wave equations. It is shown that, when the 30-fs laser pulse is focused into a gas cell the emission spectrum consists of discrete and well-resolved harmonics. These high-order harmonics can be used for generation of a train of subfemtosecond pulses. When the 5-fs laser pulse propagates along a gas-filled hollow waveguide the emission spectrum exhibits a quasicontinous structure that permits the generation of a single subfemtosecond pulse. The effects of laser intensity and position of the interacting medium relative to the laser focus on the emission spectrum and pulse profile are investigated. The differences between results obtained by our model and by the model that uses the strong-field approximation for single-atom calculations are discussed.

Generation and propagation of high-order harmonics in high-pressure gases

Generation and propagation of high-order harmonics in high-pressure (0.5--4 atm) gases by intense, ultrashort laser pulses is numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schr\"odinger and one-dimensional wave equations. The results obtained from the second-order and from the reduced first-order wave equations are compared. It is shown that at high pressure and for the high-order harmonics the use of the reduced first-order wave equation is not adequate. At very high pressure (\ensuremath{\sim}4 atm) a new regime of phase matching was observed. The applicability of the reduced first-order wave equation is also discussed.

Generation and propagation of high-order harmonics in a rapidly ionizing medium.

We present the results from simulations of harmonic generation using intense ultrashort laser pulses, both for single atoms and in an extended gaseous medium. Using a windowing technique on the single-atom spectrum, we show that the highest-order harmonics are generated simultaneously with rapid ionization, and that these harmonics have a phase dependence which is consistent with a quasiclassical tunneling model. By solving the atomic dynamics simultaneously with the propagation equations, we have obtained spectra that directly show the effects of phase mismatching and blueshifting produced by an ionizing medium. At experimental pressures, the plasma-induced phase mismatch is only important for the highest-order harmonics near the plateau cutoff. All harmonic orders, however, are seen to be blueshifted, by an amount consistent with a blueshifting of the fundamental as it propagates through the ionizing medium.