  It has been shown that an inhomogeneously broadened optical transition shaped
into an atomic frequency comb can store a large number of temporal modes of the
electromagnetic field at the single photon level without the need to increase
the optical depth of the storage material. The readout of light modes is made
efficient thanks to the rephasing of the optical-wavelength coherence similarly
to photon echo-type techniques and the re-emission time is given by the comb
structure. For on-demand readout and long storage times, two control fields are
used to transfer back and forth the optical coherence into a spin wave. Here,
we present a detailed analysis of the spin wave storage based on chirped
adiabatic control fields. In particular, we verify that chirped fields require
significantly weaker intensities than $\pi$-pulses. The price to pay is a
reduction of the multimode storage capacity that we quantify for realistic
material parameters associated with solids doped with rare-earth-metal ions.
