Fano absorption spectrum with the complex spectral analysis

An approach to understanding the 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 results in a self-energy function with strong energy dependence which enhances the nonlinearity of the eigenvalue problem of the effective Hamiltonian, yielding several resonance states with a nonanalytic dependence on the coupling constants. The overall spectral features are perfectly reproduced by the direct transitions to these discrete resonance states. Even with a single optical transition path the spectrum exhibits the asymmetric Fano profile, which is enhanced for the transition to the nonanalytic resonance states. The spectral change around the exceptional point can also be well understood when we extract the resonant state component.