  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.
