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Optical amplifiers in all ranges of the electromagnetic spectrum exhibit two essential characteristics: i) the input signal during the propagation in the medium is multiplied by the avalanche effect of the stimulated emission to produce exponential growth and ii) the amplification saturates at increasing input signal. We demonstrate that the strong-field theory in the frame of high harmonic generation fully supports the appearance of both the avalanche and saturation effects in the amplification of extreme ultraviolet attosecond pulse trains. We confirm that the amplification takes place only if the seed pulses are perfectly synchronized with the driving strong field in the amplifier. We performed an experimental study and subsequent model calculation on He gas driven by intense 30-fs-long laser pulses, which was seeded with an attosecond pulse train at 110 eV generated in a separated Ne gas jet. The comparison of the performed calculations with the measurements clearly demonstrates that the pumped He gas medium acted as an amplifier of the extreme ultraviolet pulse train.

We report a novel quasi-phase matching technique for high-order harmonic generation in low-density gases. Numerical simulations show that in few-optical cycle pulsed Bessel beams it is possible to control the pulse envelope and phase velocities which in turn allows to control the carrier-envelope phase during propagation. The resulting oscillations in the peak intensity allow to phase-match the high-order harmonic generation process with a nearly two decade enhancement in the XUV power spectrum., Comment: 4 pagesm 4 figures

The four-wave mixing produced with two ultrashort phase-locked w-3w laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5w anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques., Comment: 4 pages, 4 figures

A theoretical investigation on the quantum control of optical coherent four-wave mixing interactions in two-level systems driven by two intense synchronized femtosecond laser pulses of central angular frequencies $\omega$ and $3\omega$ is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly-varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency $5\omega$ is found to depend critically on the initial relative phase $\phi$ of the two propagating pulses; the coupling is enhanced when the pulses interfere constructively in the center ($\phi=0$), while it is nearly suppressed when they are out of phase ($\phi=\pi$). The tuning of the initial absolute phase of the different frequency components of synchronously propapagating $\omega$-$3\omega$ femtosecond pulses can serve as a means to control coherent anti-Stokes Raman scattering (CARS) processes., Comment: 4 pages, 6 figures