  A theory of ultra-fast pump-probe experiments proposed by us earlier [F.H.M.
Faisal et al., Phys. Rev. Lett. 98, 143001 (2007) and F.H.M. Faisal and A.
Abdurrouf, Phys. Rev. Lett. 100, 123005 (2008)] is developed here fully and
applied to investigate the phenomena of dynamic alignment and high harmonic
generation (HHG) from coherently rotating linear molecules. The theory provides
essentially analytical results for the signals that allow us to investigate the
simultaneous dependence of the HHG signals on the two externally available
control parameters, namely, the relative angle between the polarizations, and
the delay-time between the two pulses. It is applied to investigate the
characteristics of high harmonic emission from nitrogen and oxygen molecules
that have been observed experimentally in a number of laboratories. The results
obtained both in the time-domain and in the frequency-domain are compared with
the observed characteristics as well as directly with the data and are found to
agree remarkably well. In addition we have predicted the existence of a "magic"
polarization angle at which all modulations of the harmonic emission from
nitrogen molecule changes to a steady emission at the harmonic frequency. Among
other things we have also shown a correlation between the existence of the
"magic" or critical polarization angles and the symmetry of the active
molecular orbitals, that is deemed to be useful in connection with the "inverse
problem" of molecular imaging from the HHG data.
