We present the experimental and theoretical details of our recent published letter [Phys. Rev. Lett. 115. 123002] on synchronized high-harmonic and terahertz-wave spectroscopy (HATS) from nonadiabatically aligned nitrogen molecules in dual-color laser fields. Associating the alignment-angle dependent terahertz wave generation with the synchronizing high-harmonic signal, the angular differential photoionization cross section (PICS) for molecules can be reconstructed, and the minima of the angle on PICS show great convergence between the theoretical predictions and the experimental deduced results. We also show the optimal relative phase between the dual-color laser fields for terahertz wave generation dose not change with the alignment angle at a precision of $50$ attoseconds. This all-optical method provides an alternative for investigating molecular structures and dynamics.
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