Gaussian wave-packet reshaping into conical via parametric amplification of the far field

In this paper we propose a method for pulsed conical wave parametric amplification (PCWPA) with subsequent spatio-temporal compression during propagation in free space. It is numerically demonstrated that Gaussian wave-packet can be reshaped into pulsed conical wave (PCW) just by means of lens and nonlinear crystal. We point out that performing the far field amplification of the PCW is the key for generation of localized PCWs with ultrahigh intensities. It allows to form ultra-intense and propagation invariant wave-packets capable to propagate over many Rayleigh range in the desired material. The method exploits achromatic phase matching and empowers the parametric amplification of bandwidths corresponding to few-cycle light pulses with Gaussian temporal spectrum. In contrast to ordinary chirped-pulse amplification technique it does not require a pulse compressor, thus greatly facilitates the parametric amplification of few-cycle light pulses.