  The optical response of superconductors with odd-frequency Berezinskii
pairing is studied. By using a simple model with a parabolic dispersion law and
a non-magnetic disorder, the spectral function, the electron density of states,
and the optical conductivity are calculated for a few gap ansatzes. The
spectral function and the electron density of states clearly reveal the gap for
the Berezinskii pairing for the sufficiently strong frequency dependence of the
order parameters. It is found that, similarly to the conventional BCS pairing,
the odd-frequency gaps induce peaks in the real part of the conductivity,
which, however, are sharper than in the BCS case. The magnitude and position of
these peaks are determined by the frequency profile of the gap. The imaginary
part of the optical conductivity for the Berezinskii pairing demonstrates sharp
cusps that are absent in the case of the BCS superconductors. The corresponding
results suggest that the Berezinskii pairing might allow for the optical
transparency windows related to the onsets of the attenuation peaks in the real
part of the conductivity. Thus, the study of the optical response not only
provides an alternative way to probe the odd-frequency gaps but can reveal also
additional features of the dynamic superconducting pairing.
