  Motivated by the growing importance of the fidelity and fidelity
susceptibility (FS) in quantum critical phenomena, we use these concepts to
describe the pulse propagation inside the dispersive media. It is found that
there is a dramatic change in the fidelity and the FS of the pulse at a
critical propagation distance inside a dispersive medium, and whether such a
dramatic change for a light pulse occurs or not strongly depends on both the
dispersive strength of the media and the pulse property. We study in detail
about the changes of the fidelity and the FS for both a smooth and a truncated
Gaussian pulse through the abnormal and normal dispersive media, where the
group velocities are well defined. Our results show that both the fidelity and
the FS could be very useful to determine whether the pulse is completely
distorted or not at the critical distance, therefore it would be very helpful
to find the maximal effective propagation region of the pulse's group velocity,
in terms of the changes of the pulse's fidelity and FS.
