## 2 Overview on the Optical Parametric Amplification Process
When ultrashort pulses are used as an input for amplification, wave packet effects have to be mentioned. First, for energy transfer to occur from the pump to the signal/idler, spatial and temporal superposition of the three pulses is required. However, this superposition gets gradually lost along the propagation direction because of the group velocity mismatch. Thus, OPA systems are designed for providing multiple amplification stages, to compensate for this temporal walk-off dynamics. Moreover, for a fixed pump and signal propagation direction, the idler propagation direction is deduced by the wavevector equations. In a broad bandwidth amplification configuration, a number of spectral components of the signal beams must be phase-matched. The corresponding idler components arise so as to match both energy and wavevector equations. As a result, the idler beam is affected by spatial chirp. It is worth mentioning here that OPA originally arises as an alternative to amplification systems based on population inversion in laser active media. With respect to the active media systems, OPA provides a number of advantages, which are here briefly discussed [7; 8]. Unlike stimulated emission in active media, parametric amplification is not a resonant process, and it does not involve any real energy levels, the non-linear materials acting exclusively as an intermediate during the three-wave interaction. As a consequence, OPA systems can potentially work at any wavelength, even in those spectral regions that are not supported by lasing media. Moreover, by properly varying the phase-matching conditions, different spectral components can be selected for amplification. OPAs thus provide highly tunable sources, the region of tunability being subjected to the above-mentioned energy conservation rule. The main restriction limiting this amplification band is set by the transparency range of the non-linear crystal. Indeed, the energy exchange process among the pump, signal and idler waves is boosted by their mutual interaction; consequently, for the non-linear interaction to occur efficiently, transparency is required at the three frequencies involved. Transparency at the working wavelengths prevents thermal effects, which are instead particularly critical in amplification systems based on stimulated emission, strongly limiting power scalability. As a major advantage, in OPAs, the gain bandwidth is dictated by the possibility to satisfy the phase-matching condition over a broad spectral range. First of all, restrictions due to the line width of electronic or vibrational lasing transitions are avoided. Moreover geometrical degrees of freedom are available in birefringent media for optimizing the parametric amplification gain bandwidth, involving the propagation direction and the polarization of the interacting waves. A number of OPA architectures have been introduced for achieving broadband phase-matching. In this sense, ultra-broadband OPAs have been experimentally demonstrated, delivering pulses with durations down to the single-cycle limit from the visible to the mid-IR spectral region [9]. Actually, parametric amplification systems are approaching the intensity levels provided by the most advanced amplified laser sources [10]. Moreover, they were established over the years as a powerful technology for applications related to ultrafast spectroscopy and for strong field applications [11].