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Spectral singularities are predicted to occur in a non-Hermitian extension ofthe Friedrichs-Fano-Anderson model describing the decay of a discrete state $|a>$ coupled to a continuum of modes. A physical realization of the model, basedon electronic or photonic transport in a semi-infinite tight-binding latticewith an imaginary impurity site at the lattice boundary, is proposed. Theoccurrence of the spectral singularities is shown to correspond either to adiverging reflection probability (for an amplifying impurity) or to a vanishingreflection probability (for an absorbing impurity) from the lattice boundary.In the former case, the spectral singularity of the resolvent is alsoresponsible for the non-decay of state $|a>$ into the continuum, in spite ofthe absence of bound states.

Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model