  We study numerically the linear optical response of a quasiparticle moving on
a one-dimensional disordered lattice in the presence of a linear bias. The
random site potential is assumed to be long-range-correlated with a power-law
spectral density $S(k) \sim 1/k^{\alpha}$, $\alpha > 0$. This type of
correlations results in a phase of extended states at the band center, provided
$\alpha$ is larger than a critical value $\alpha_c$ [F. A. B. F. de Moura and
M. L. Lyra, Phys. Rev. Lett. \textbf{81}, 3735 (1998)]. The width of the
delocalized phase can be tested by applying an external electric field:
Bloch-like oscillations of a quasiparticle wave packet are governed by the two
mobility edges, playing now the role of band edges [F. Dom\'{\i}nguez-Adame
\emph{et al.}, Phys. Rev. Lett. \textbf{91}, 197402 (2003)]. We demonstrate
that the frequency-domain counterpart of these oscillations, the so-called
Wannier-Stark ladder, also arises in this system. When the phase of extended
states emerges in the system, this ladder turns out to be a comb of doublets,
for some range of disorder strength and bias. Linear optical absorption
provides a tool to detect this level structure.
