Asymmetry to symmetry transition of Fano line-shape: Analytical derivation

An analytical derivation of Fano line-shape asymmetry ratio has been presented here for a general case. It is shown that Fano line-shape becomes less asymmetric as \q is increased and finally becomes completely symmetric in the limiting condition of q equal to infinity. Asymmetry ratios of Fano line-shapes have been calculated and are found to be in good consonance with the reported expressions for asymmetry ratio as a function of Fano parameter. Application of this derivation is also mentioned for explanation of asymmetry to symmetry transition of Fano line-shape in quantum confined silicon nanostructures.