Fano interference

When metals have Raman active phonons, optical pump-probe techniques can be applied to study their coherent dynamics. Hase and coworkers observed a periodic oscillation in the reflectivity of Zn and Cd due to the coherent E2g phonons (Fig. 2.17) [56]. The amplitude of the coherent phonons of Zn decreased with raising temperature, in accordance with the photo-induced quasi-particle density n.p, which is proportional to the difference in the electronic temperature before and after the photoexcitation (Fig. 2.17). The result indicated the resonant nature of the ISRS generation of coherent phonons. Under intense (mJ/cm2) photoexcitation, the coherent Eg phonons of Zn exhibited a transient frequency shift similar to that of Bi (Fig. 2.9), which can be understood as the Fano interference [57], A transient frequency shift was aslo observed for the coherent transverse optical (TO) phonon in polycrystalline Zr film, in spite of much weaker photoexcitation [58],... 

Fano interference, 32, 38 Fast electron distribution, 134 Fast electron generation, 123 Fast electron transport, 125 Fast electrons, 176 Fast-ignition, 124 Femtosecond supercontinuum, 94 Feynman s path integral, 73 Feynman s propagator, 76 Field parameter, 172 Filamentation, 82, 84, 112 Floquet ladder, 11 Fluorescence, 85, 125 FROG, 66 FROG-CRAB, 66... 

At first glance it seems evident that the observed spectrum of Fig. 21.11 is a sequence of Beutler-Fano interference profiles, which reverse in the Fano q parameter across the line. Although the solution may ultimately be expressed in the same mathematical form,1 a simple consideration of the excitation amplitudes... 

It was quantitatively interpreted (Rice et al., 1977) as originating from bond alternation phase oscillations (in contrast to the bond alternation amplitude oscillations mentioned in subsection 4.8.2D). The vibrational absorption lines labeled 2 to 10 are directly related to the Ag Raman lines of TCNQ. The broad peak above 1600 cm originates from the single electron transition across the gap, and the indented line shape of mode 2 is a consequence of Fano interference between the single electron continuum and the phonon mode. The line intensities are determined by the respective electron - vibration coupling constants. 

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu. Tunneling induced transparency Fano interference in intersubband transitions. Applied Physics Letters 1997 Jun 23 70(25) 3455 -3457. 

K. Aoki, H. Yamawaki, M. Sakashita, Observation of Fano interference in high-pressure ice Vn. Phys. Rev. Lett. 76(5), 784-786 (1996)... 

Interference effects between allowed and induced phenomena have received attention [246], Most of the work reported to date is for liquids and thus outside the scope of this monograph. We mention, though, that the Fano profiles observed in the HD-X spectra, Fig. 3.36, are interesting examples of such interference. 

M. Shapiro The method of incoherent interference control used in our experiment is completely general and allows us to use Fano type interferences to control final states even if such lines do not naturally exist. Of course if the molecule accommodates you (as FNO) you do not need this but this is a rare situation. 

Suppose we have two close intermediate states, 2 and 3. In a two-frequency (0)1, 0)2) laser field the atom has two nondistinguishable channels of photoionization. Depending on the phase relationship, the quantum interference of the two channels can be constructive or destructive. In the latter case, the yield of photoionization can be greatly reduced. This effect is related to the well-known Fano resonances in atomic photoionization spectra. Also the interference will generate... 

The Kf matrix is related to the conventional K matrix of MQDT by a frame transformation from parabolic to spherical co-ordinates the K matrix is then related by a further frame transformation to the quantum defects [43, 45], The first term in Eq. (4) gives a contribution to the photoionization intensity borrowed from the bound-state spectrum. The dlyom term represents direct photoionization, and the overall expression allows Fano-type interference between these terms. In Eq. (5) A is a phase shift in the parabolic rep-... 

For the purposes of this review it is convenient to focus attention on that class of molecules in which the valence electrons are easily distinguished from the core electrons (e.g., -n electron systems) and which have a large number of vibrational degrees of freedom. There have been several studies of the photoionization of aromatic molecules.206-209 In the earliest calculations either a free electron model, or a molecule-centered expansion in plane waves, or coulomb functions, has been used. Only the recent calculation by Johnson and Rice210 explicitly considered the interference effects which must accompany any process in a system with interatomic spacings and electron wavelength of comparable magnitude. The importance of atomic interference effects in the representation of molecular continuum states has been emphasized by Cohen and Fano,211 but, as far as we know, only the Johnson-Rice calculation incorporates this phenomenon in a detailed analysis. 

Here the product is reached either via a single resonance or directly via the continuum. Hence the sum over s in Eq, (6.55) reduces to a single term, but the direct optical transitions to the continuum are not suppressed. This gives the case of a Fano-type interference [222] to an isolated resonance, where the two pathways to r the continuum interfere with one another. In this case Eq. (6.55) becomes... 

Free carriers change Raman spectra, either by single particle contribution to the spectrum, or by phonon- plasmon interaction. In addition, interference of electronic transition continua with single phonon excitations may lead to Fano line shapes, as mentioned in the introduction. The Fano effect is encountered in p-doped Si crystals, as shown in Fig. 4.8-19. The shown lines correspond to the respective Raman active mode at 520 cm for crystals with 4 different carrier concentrations, excited with a red laser. The continuous line is calculated according to Eq. 4.8-6. Antiresonance on the low frequency side and line enhancement on the high frequency side are a consequence of the positive value of Q. A reverse type of behavior is possible in the case of a negative Q. 

The first term arises from the resonance scattering, the second term, /bg, is due to the off-resonance phase o, while /int describes the interference between the first two. If the background term is small, the cross section reduces to the familiar Lorentzian form and Eq. (7) can be directly used to extract resonance parameters from the experimental or calculated (t(E). On the other hand, if /bg cannot be neglected, one encounters a complicated energy dependence of the cross section known as Fano profiles [112]. 

Inside the band of two-particle states a channel opens up for polariton decay into two phonons. This process leads to a broadening of the polariton line (see, e.g. (59), (60)), and also a change in the polariton dispersion law. The two most important effects in the latter case are (a) interference of scattering by a polariton and two-particle states (this can lead to drops in intensity of the Fano antiresonance type see (22)), and (b) the presence of singularities in the density of two-particle states (those, in particular, that correspond to quasibiphonons). 

---