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Unlike the classical electro-magnetic wave with uniform polarization distribution along the flat wave-front, the light pulses in either laboratory or industry usually have non-vanishing components in the direction of propagation. Therefore, the full description of a generally complex laser pulse should be implemented in multi-dimensional way, for the light in the free space is the combination of a three-dimensional(3D) electric field and a 3D magnetic field in the 3D Euclidean space which is the subspace of the four-dimensional space-time. Here we report on a novel technique for the full-vectorial characterization which includes the spatiotemporal amplitude and phase information as well as the vectorial features of the complex laser pulses. This new measurement capability opens the way to in-depth characterizations and optimizations of the complex laser pulses and ultimately to the study of new phenomena of the interactions between materials and structured ultra-short laser beams.
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