  A new aspect of understanding a Fano absorption spectrum is presented in
terms of the complex spectral analysis. The absorption spectrum of an impurity
embedded in semi-infinite superlattice is investigated. The boundary condition
on the continuum causes a large energy dependence of the self-energy, enhances
the nonlinearity of the eigenvalue problem of the effective Hamiltonian,
yielding several nonanalytic resonance states. The overall spectral features is
perfectly reproduced by the direct transitions to these discrete resonance
states. Even with a single optical transition path the spectrum exhibits an
asymmetric Fano profile, which is enhanced for the transition to the
nonanalytic resonance states. Since this is the genuine eigenstates of the
total Hamiltonian, there is no ambiguity in the interpretation of the
absorption spectrum, avoiding the arbitrary interpretation based on the quantum
interference. The spectral change around the exceptional point is well
understood when we extract the resonant state component.
