Fano resonance
In physics, a Fano resonance is a type of resonant scattering phenomenon that gives rise to an asymmetric line-shape. Interference between a background and a resonant scattering process produces the asymmetric line-shape. It is named after Italian-American physicist Ugo Fano, who in 1961 gave a theoretical explanation for the scattering line-shape of inelastic scattering of electrons from helium;[1][2] however, Ettore Majorana was the first to discover this phenomenon.[3] Fano resonance is a weak coupling effect meaning that the decay rate is so high, that no hybridization occurs.[4] The coupling modifies the resonance properties such as spectral position and width and its line-shape takes on the distinctive asymmetric Fano profile. Because it is a general wave phenomenon, examples can be found across many areas of physics and engineering.
History
The explanation of the Fano line-shape first appeared in the context of inelastic electron scattering by helium and autoionization. The incident electron doubly excites the atom to the state, a sort of shape resonance. The doubly excited atom spontaneously decays by ejecting one of the excited electrons. Fano showed that interference between the amplitude to simply scatter the incident electron and the amplitude to scatter via autoionization creates an asymmetric scattering line-shape around the autoionization energy with a line-width very close to the inverse of the autoionization lifetime.
Explanation
The Fano resonance line-shape is due to
For energies far from the resonant energy the background scattering process dominates. Within of the resonant energy, the phase of the resonant scattering amplitude changes by . It is this rapid variation in phase that creates the asymmetric line-shape.
Fano showed that the total scattering cross-section assumes the following form,
where describes the line width of the resonant energy and q, the Fano parameter, measures the ratio of resonant scattering to the direct (background) scattering amplitude. This is consistent with the interpretation within the Feshbach–Fano partitioning theory. In the case the direct scattering amplitude vanishes, the q parameter becomes zero and the Fano formula becomes :
Looking at transmission shows that this last expression boils down to the expected Breit–Wigner (Lorentzian) formula, as , the three parameters
Examples
Examples of Fano resonances can be found in
Fano can be observed with
See also
References
- ^ " A. Bianconi Ugo Fano and shape resonances in X-ray and Inner Shell Processes" AIP Conference Proceedings (2002): (19th Int. Conference Roma June 24–28, 2002) A. Bianconi arXiv: cond-mat/0211452 21 November 2002
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- S2CID 118439516.
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- ^ PMID 20733610.
- S2CID 124830448.
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- PMID 31889112.