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Ultrafast laser pulse beams are four-dimensional, space–time phenomena that can exhibit complicated, coupled spatial and temporal profiles. Tailoring the spatiotemporal profile of an ultrafast pulse beam is necessary to optimize the focused intensity and to engineer exotic spatiotemporally shaped pulse beams. Here we demonstrate a single-pulse, reference-free spatiotemporal characterization technique based on two colocated synchronized measurements: (1) broadband single-shot ptychography and (2) single-shot frequency resolved optical gating. We apply the technique to measure the nonlinear propagation of an ultrafast pulse beam through a fused silica window. Our spatiotemporal characterization method represents a major contribution to the growing field of spatiotemporally engineered ultrafast laser pulse beams. 

High-intensity pulse-beams are ubiquitous in scientific investigations and industrial applications ranging from the generation of secondary radiation sources (e.g., high harmonic generation, electrons) to material processing (e.g., micromachining, laser-eye surgery). Crucially, pulse-beams can only be controlled to the degree to which they are characterized, necessitating sophisticated measurement techniques. We present a reference-free, full-field, single-shot spatiospectral measurement technique called broadband single-shot ptychography (BBSSP). BBSSP provides the complex wavefront for each spectral and polarization component in an ultrafast pulse-beam and should be applicable across the electromagnetic spectrum. BBSSP will dramatically improve the application and mitigation of spatiospectral pulse-beam structure. 

We present a phase retrieval algorithm for dispersion scan (d-scan), inspired by ptychography, which is capable of characterizing multiple mutually-incoherent ultrafast pulses (or modes) in a pulse train simultaneously from a single d-scan trace. In addition, a form of Newton’s method is employed as a solution to the square root problem commonly encountered in second harmonic pulse measurement techniques. Simulated and experimental phase retrievals of both single-mode and multi-mode d-scan traces are shown to demonstrate the accuracy and robustness of the root preserving ptychographic algorithm (RPPA). 

Ultrafast pulse-beam characterization is critical for diverse scientific and industrial applications from micromachining to generating the highest intensity laser pulses. The four-dimensional structure of a pulse-beam, $\stackrel{~<\#comment/>}{E}(x,y,z,\mathrm{\omega <\#comment/>})$, can be fully characterized by coupling spatiospectral metrology with spectral phase measurement. When temporal pulse dynamics are not of primary interest, spatiospectral characterization of a pulse-beam provides crucial information even without spectral phase. Here we demonstrate spatiospectral characterization of pulse-beams via multiplexed broadband ptychography. The complex spatial profiles of multiple spectral components, $\stackrel{~<\#comment/>}{E}(x,y,\mathrm{\omega <\#comment/>})$, from modelocked Ti:sapphire and from extreme ultra-violet pulse-beams are reconstructed with minimum intervening optics and no refocusing. Critically, our technique does not require spectral filters, interferometers, or reference pulses. 

Vacuum-ultraviolet (VUV) light is critical for the study of molecules and materials, but the generation of femtosecond pulses in the VUV region at high repetition rates has proven difficult. Here we demonstrate the efficient generation of VUV light at megahertz repetition rates using highly cascaded four-wave mixing processes in a negative-curvature hollow-core fiber. Both even- and odd-order harmonics are generated up to the 15th harmonic (69 nm, 18.0 eV), with high energy resolution of $\sim <\#comment/>40\mathrm{m}\mathrm{e}\mathrm{V}$. In contrast to direct high harmonic generation, this highly cascaded harmonic generation process requires lower peak intensity and therefore can operate at higher repetition rates, driven by a robust $\sim <\#comment/>10\mathrm{W}$fiber-laser system in a compact setup. Additionally, we present numerical simulations that explore the fundamental capabilities and spatiotemporal dynamics of highly cascaded harmonic generation. This VUV source can enhance the capabilities of spectroscopies of molecular and quantum materials, such as photoionization mass spectrometry and time-, angle-, and spin-resolved photoemission.