Optical parametric amplification of X-shaped localised wave-packets

The general concepts for generation and amplification of the X-pulses in optical parametric amplifiers under the plane-wave and localised (Bessel beam, or more generally, X-pulse) pump are reviewed. It is shown numerically and experimentally that X-pulse phase-matching gives rise to spontaneous emergence of the localised light structures in the regime of the parametric frequency down-conversion. The parametric amplification technique of localised waves is extended to the chirped X-pulse optical parametric amplification concept, which allows one to achieve few optical cycle, high-peak power localised wave packets for laser—matter interactions.