  We theoretically investigate the two-photon absorption spectrum of
conventional s-wave superconductors. The calculation is carried out in the
local limit at absolute zero. The direct excitation of quasiparticles is
excluded under the condition that the frequency of the external field is lower
than twice the magnitude of the superconducting gap. We calculate vertex
corrections with the conserving approximation, and show that the amplitude mode
is independent of the impurity scattering in the local limit. Because of this
property, a diverging absorption edge appears in the dirty limit. We propose
this behavior as a probe of the amplitude mode.
