Photon absorption and scattering in Fano anti-resonances

The Green’s function method is utilized to obtain a modified treatment of Fano’s line-shape problem which takes into account the coupling between different states in the continuous (or quasi-continuous) non-radiative manifold due to their interaction with the same radiation field states. A new expression for the absorption line-shape is obtained in the form σ_a(ϵ)∞ [(ϵ + qY^L)² + (Y^Lq² + 1)(1 – Y^L)]/(ϵ² + 1), where e is the reduced energy parameter, ϵ is Fano’s line-shape index and Y^L is the non-radiative quantum yield obtained when the non-radiative manifold is optically forbidden. As Y^L is always smaller than unity, the absorption never strictly vanishes in contrast to the result obtained in Fano’s approximation. In addition, expressions are obtained for the emission line-shape and for the (energy dependent) emission quantum yield within a Fano resonance. The quantum yield so obtained is free from the singular behaviour which characterizes the same quantity obtained in Fano’s approximation.