Fano Resonance

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This Demonstration shows the normalized Fano resonance profile, , as a function of reduced energy, . The phenomenological shape parameter, , alters the asymmetry of the resonance shape. In this Demonstration, values are limited to lie between 0 to 100.

Contributed by: Shahrul Kadri (March 2011)
(Hokkaido University)
Open content licensed under CC BY-NC-SA



A Fano resonance (based on the work of Ugo Fano in 1961) exhibits an asymmetric profile due to interference between the resonant and background scattering probabilities.

The scattering cross section of the so-called Fano profile can be expressed as


where is a phenomenological shape parameter and is a reduced energy, defined by ; is a resonant energy, and is the width of the resonance.

For comparison between various values of , the normalized value of the Fano profile is defined by dividing by :


There are three special cases of resonance profiles:

: Antiresonance characteristic where a dip trough appears at the center of the resonance.

: Asymmetric resonance with maximum peak and minimum trough.

: Lorentzian shape resonance, which is typically seen in oscillating systems.


[1] U. Fano,"Effects of Configuration Interaction on Intensities and Phase Shift," Physical Review, 124(6), 1961 pp. 1866–1878.

[2] Wikipedia, "Fano Resonance,"

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