The quantum and classical Fano parameter q

Abstract

The Fano resonance has been a familiar and important feature in atomic and molecular physics for more than half a century. Typically, the combination of a discrete state with one or more continua results in an asymmetric peak in the ionization spectrum. The peak-shape, called the Fano profile, can be expressed by a simple formula derived by Fano in 1935. However, the interpretation of its characteristic parameter q, which represents the asymmetry of the peak in the formula, is not necessarily intuitively transparent. The Fano resonance is not necessarily a quantum effect, but it is a manifestation of a certain physical mechanism in various systems, both quantum and classical. Through the derivation of q from the known classical pictures with the classical coupled oscillator, we interpret the q value with a geometrical view. And further, we introduce a complex valued q parameter for the description of the resonance with a damped oscillator.

Reversible Active Switching of Fano and Fabry–Pérot Resonances by Electrochromic Operation

“…Note that after the thickness ( L m ) of the top metal Ag film was increased to 80 nm (that is, for an optically opaque top metal Ag film), Fano parameter q was close to zero ( q → 0) (Table S2, Supporting Information), which is the case for a vanishing discrete state excitation. [ 38 ] This suggested that the cavities (the Li x WO 3 /Ag and Ag/ITO/Ag cavities) became decoupled, and the Fano resonance disappeared (Figure 3e). The Fano resonance spectral line shapes diminished as the top metal Ag film's thickness increased, which was also shown in the reflection spectra (Figures S9 and S10, Supporting Information).…”

“…[ 37 ] The key Fano parameter, q , represents the ratio between the photoexcitation amplitudes to the discrete and continuum states. [ 38 ] To fit the Fano resonance for our structure at the lithiation of 142 mC (cm 2 µm) −1 , the main peaks in the reflection spectra at visible wavelengths (400–800 nm) were analyzed (Figure 3d). The fitting process was restricted to data points within half the maximum peak height to minimize the effects of the background absorption component.…”

Dual-channel scattering problem in the cavity-like potential

“…Another example is an atom-cavity coupled system; the dynamics can be described by a linearized set of quantum Langevin equations if appropriately approximated; thus, the system may have EIT and Fanotype spectra. Moreover, this characteristic behavior appears even in the classical system, such as a coupled oscillator consisting of a damped oscillator and a harmonic oscillator [16]. Therefore, our discussion provides important insights to beginners in understanding physics and engineering applications.…”

Nanostructure-derived anti-reflectivity in leafhopper brochosomes

“…In the weak-coupling regime, only one of the oscillators with larger damping is driven with frequency ω due to the external forces, and the spectral shape is determined by the geometry dependent Fano parameter q when the frequencies of the strongly and weakly damped oscillators become equal at resonance. The parameter q is a quantitative measure of the spectral shape of the Fano profile for a given photo absorption cross section (σ) defined [29] by equation ( 2) as:…”