Fano plot

Fig. 22.3 Lu-Fano plot of the high lying Ba even parity 7=2 levels above the 6s22d 3E>2 level. The full curve is calculated with the QDT parameters of ref. 8 observed 6snd3E>2 states (+), observed 6snd1D2 states ( ) observed 5d7d perturber (V) (from ref. 8).

The relatively well localized interaction of the Ba 5d7d D2 state with the Ba 6snd uD2 states is shown by the section of the Lu-Fano plot of Fig. 22.3.8 The... 

In Fig. 22.6(a) we show the spectrum of the transition from the Ba 5d6p F3 state to the 5d5/216d3/2 5/2 states which lie just above the Ba+5d 3/2 limit, and in Fig. 22.6(b) we show the spectrum from the same initial state to the 5d5/214d3/2 5/2 states which lie just below the Ba+ 5d3/2 limit. It is apparent that the envelopes of the excitations are identical. We have been discussing these states as if they were bound states, and in fact for our present purpose they might as well be. First, below the 5d3/2 limit the observed linewidths equal the laser linewidth, and second, there is no visible excitation of the 6seH continua below the 5d3/2 limit. It is also useful to note that a three channel quantum defect treatment of the 5d nd / = 4 series reproduces both the Lu-Fano plot of Fig. 22.2, and the spectra shown in Fig. 22.6. The experimental spectra were reproduced by QDT models using both the a and i channel dipole moment parametrizations described in Chapter 21. 

Lu-Fano plot is contained in a unit cube, and more generally, it will give rise to a curve in an JV-dimensional cube, at which point the simplicity of visualisation is lost, although a mathematical representation is still completely feasible. 

To demonstrate Fano-resonant behavior, a polystyrene microring resonator is nanoimprinted and two waveguide offsets are introduced in the bus waveguide, which provide partial reflection as shown in Fig. 8.22. Its spectrum is plotted in Fig. 8.23 together with the one without waveguide offsets. The slope is enhanced... 

Figure 6.2 Auger decay width of (2p n) Mg+-H+ as a function of the Mg-proton distance, R.z is Mg-proton axis. Diamonds and solid line Fano-ADC(2)x calculation with atomic orbital basis centered both on Mg and on the proton circles and long-dashed line Fano-ADC(2)x calculation with atomic orbital basis centered only on Mg stars and short-dashed line Fano-ADC(2)x calculation for (2p 1) Mg+ alone, with atomic orbital basis centered both on Mg and at the distance R along the z-axis, showing the so-called basis set superposition error (BSSE) triangles and dashed-dotted line Fano-ADC(2)x calculation with atomic orbital basis centered on Mg only, with the 3s orbital of Mg being frozen at its shape at R = 6.5A. The inset shows the low-r part of the plot on logarithmic scale. See Ref. [35] for the details of the computation.

Fig. 1.16 The plots of decay lifetime tspp of (1,0) and (—1,0) SPP modes with resonant wavelength at different hole radii and depths = (a) 100 nm, (b) 120 nm, and (c) 280 nm. All the lifetimes are determined by Fano fitting of the reflectivity spectra. The solid lines are the linearly fittings of the lifetimes to extract the n factor, indicating Tspp oc ires" The legends are hole radius in the unit of nm...

Once all the modes have been identified, we then move on to study the effects of hole radius and depth on SPP lifetime Tspp. The lifetimes of (1,0) and (—1,0) SPP modes of aU samples are determined by Fano fitting and are plotted in Fig. 1.16 with /Ires- Only the modes that are not coupled with the localized mode are ccaisidered here for simplification. Apparently, aU the SPP modes at different hole sizes seem to follow a log-log quasi-Unear relationship indicating Tspp oc 2 [67,76,77]. To fuUy dlustrate... 

For better comparison of theoretical predictions for different-order processes, we have plotted the quantum Fano factors for both interacting modes in the no-energy-transfer regime with N = 2 — 5 and r = 5 in Fig. 7. One can see that all curves start from F w(0) = 1 for the input coherent fields and become quasistationary after some relaxations. The quantum and semiclassical Fano factors coincide for high-intensity fields and longer times, specifically for t > 50/(Og), where il will be defined later by Eq. (54). In Fig. 17, we observe that all fundamental modes remain super-Poissonian [F (t) >1], whereas the iVth harmonics become sub-Poissonian (F (t) < 1). The most suppressed noise is observed for the third harmonic with the Fano factor 0.81. In Fig. 7, we have included the predictions of the classical trajectory method (plotted by dotted lines) to show that they properly fit the exact quantum results (full curves) for the evolution times t > 50/(Og). The small residual differences result from the fact that the amplitude r was chosen to be relatively small (r = 5). This value does not precisely fulfill the condition r> 1. We have taken r = 5 as a compromise between the asymptotic value r oo and computational complexity to manipulate the matrices of dimensions 1000 x 1000. Unfortunately, we cannot increase amplitude r arbitrary due to computational limitations. 

We now plot the usual Lu-Fano graph, using, as before ... 

Fig. 6.5. A plot of the rotation angles in a Beutler-Fano profile as a function of detuning, for several values of the shape index in the special case defined in the text. For negative values of q, reverse the abscissa (after J.-P. Connerade [294]).

Fig. 8.7. The form of a single resonance in the Rydberg series defined by the Dubau-Seaton formula (a) plotted with different combinations of parameters so that the maximum and minimum in the absorption cross section remain at fixed energies and (b) comparing a Dubau-Seaton profile (curve A) with a Beutler-Fano profile of the same shape near the resonance energy (curve B) (after J.-P. Connerade [413, 414]).

Fig. 8.31. The remaining figures in this chapter show a sequence of spectra and Lu-Fano graphs in which the q parameters and coupling strengths are changed, but all other parameters are held constant. For this figure, the q = 1000 for both series, and the coupling strength = 2. A zero coupling strength, zero combined asymmetry plot is shown as a dashed curve for reference. X = 0.3, X

Such model calculations display a rich variety of effects even on a very simple model. They show that the essential structure of two-dimensional quantum defect plots is preserved, but that conclusions as to the strength of inter-series coupling cannot be reached merely by inspecting Lu-Fano graphs a simultaneous study of the spectra is also required. 

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