  Modulation of probe signal in pump-probe measurements of coherent phonons in
dielectrics, with and without spectral resolution, are investigated
theoretically taking diamond as an example. Analytical investigation as well as
first-principles calculations based on time-dependent density functional theory
is utilized to clarify the mechanism of the modulation of the probe signals.
Boundary and bulk effects are investigated systematically, putting emphasis on
the phase relation between the modulation and the atomic motion of the coherent
phonon. They are summarized as follows: Modulation by the boundary effect is in
phase with the coherent phonon amplitude, while that by the bulk effect shows
$\pi/2$ phase difference. Strong frequency dependence appears in the modulation
by the bulk effect, while no frequency dependence by the boundary effect.
First-principles calculations support the reliability of the analytical result.
