Abstract
We propose a method for amplification of complex localized ultrashort wave packets ($\mathsf{X}$ pulses or $\mathsf{X}$ waves). We present an analytical derivation and numerical simulations of broadband parametric amplification of chirped $\mathsf{X}$ pulses in a noncentrosymmetric medium with quadratic nonlinearity. Our results suggest that $\mathsf{X}$ pulses with particular spatial and temporal chirps can be efficiently amplified in an optical parametric amplifier and compressed down to a few tens of femtoseconds during free-space propagation.
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