Ultrashort ultra-intense laser pulses have delivered peak intensities of 1022–1023 W/cm2 that represents the strongest radiation in the laboratory and enables the experimental research of extreme high-field physics[1–3]. However, ultrashort pulses with broad bandwidths are prone to spatiotemporal couplings (STCs)[4–7]. That is, there exists an interdependence between the temporal (or spectral) and spatial (or angular) properties of electromagnetic fields. One of the simplest first-order STCs in space and time has a mathematical description of E(x, t + ξx) where ξ is the linear coupling coefficient. Since first-order STCs can be produced and compensated through angular-dispersion devices, they have been widely used to construct a pulse stretcher and compressor for chirped-pulse amplification (CPA)[9–16]. For example, in a pulse stretcher consisting of four prisms, the angular dispersion induced by the first prism is completely compensated in the second prism, which is anti-parallel to the first one, resulting in laser pulses with a pure temporal chirp at the output. However, it is non-trivial to compensate all the STCs introduced during the pulse propagation and amplification. For example, the misalignment of the gratings in either the stretcher or compressor results in residual couplings (also termed spatiotemporal distortions), including both first-order STCs and complicated high-order STCs. It has been experimentally demonstrated that the high-order STCs in imperfect compression are very difficult to be compensated and contribute to most of the spatiotemporal distortions of the compressed and focused signal[12,17–21].
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