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.
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