  We present both static and time-resolved second harmonic generation (SHG)
measurements on polar antiferromagnet Fe$_2$Mo$_3$O$_8$ to monitor the
evolution of the electric polarization change and its coupling to magnetic
order. We find that only one of the second order tensor elements,
$\chi_{ccc}^{(2)}$ ,shows a prominent change below the Neel temperature $T_N =
60$ K, indicating a magnetic order induced electric polarization change along
the c-axis. Time-resolved SHG measurement reveals an ultrafast recovery of the
second order tensor element upon the ultrashort laser excitation with fluence
above 0.3 $mJ/cm^2$, yielding evidence for a photoinduced ultrafast phase
transition from the AFM ordered state to the paramagnetic state. Our work will
help understand the spin induced polarization and the ultrafast optical tuning
effect in Fe$_{2}$Mo$_{3}$O$_{8}$.
