  We theoretically investigate a relation between the crystalline symmetry and
the transient modulation of optical properties of crystalline dielectrics in
pump-probe measurements using intense pump and attosecond probe fields. When
the photon energy of the pump field is much below the bandgap energy, the
modulation of the optical conductivity is caused by the intraband electronic
motion, that is, the dynamical Franz-Keldysh effect. We analytically
investigate symmetry properties of the modulated optical conductivity utilizing
the Houston function, and derive a formula that relates the temporal
oscillation in the absorption with the transformation properties of the
modulated optical conductivity. To verify the validity of the formula, we
perform real-time first-principles calculations based on the time-dependent
density functional theory for a pump-probe process taking 4H-SiC crystal as an
example.
