The absorption of photons by quasiparticles in the Bloch bands of mult
ilayers, formed by alternating normal (N) and superconducting (S) regi
ons, is computed for the vector of the oscillating electric field bein
g perpendicular to the N-S interfaces. The absorption spectrum extends
down to frequencies below the gap of the S-layers, and its structure
results from the combined effects of Andreev scattering and convention
al scattering at the N-S interfaces. For not too different Fermi energ
ies epsilon(FS) and epsilon(FN) in the S and N layers there is one pro
minent resonance peak. With increasing temperature low frequency absor
ption goes up. For epsilon(FS) much greater than epsilon(FN), On the o
ther hand, a sharp multipeak structure at low frequencies is found.