Fano resonance

Fig. 8.23 Transmission spectra of a polystyrene microring resonator (a) without waveguide offsets and (b) sandwiched by two waveguide offsets. Asymmetric Fano resonant line shape is clearly observed. Reprinted from Ref. 49 with permission. 2008 American Institute of Physics...

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... 

Chiba, A. Fujiwara, H. Hotta, J. Takeuchi, S. Sasaki, K., Fano resonance in a multimode tapered fiber coupled with a microspherical cavity, Appl. Phys. Lett. 2005, 86, 261106... 

Familial amyotrophic lateral sclerosis, superoxide dismutase and, 45 148 Fano resonance, 35 349-350 Fast atom bombardment mass spectrometry, heteronuclear gold cluster compounds, 39 340-342... 

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... 

Feshbach-type resonances [51], also known as Fano resonances [52] and Floquet resonances [22] depending on the system studied, are formed in a different manner. We encounter this type of metastable states whenever a bound system is coupled to an external continuum. In the same spirit as before, one can define a reference Hamiltonian in which the closed channel containing the bound states is uncoupled from the open channel through which the asymptote can be reached. When the coupling is introduced, the previously bound state decays into the continuum of the open channel. The distinction from shape-type resonances, described above, is that the resonance state decays into a different channel of the reference Hamiltonian. 

J. Gores, D. Goldhaber-Gordon, S. Heemeyer, M.A. Kastner, H. Shtrikman, D. Mahalu, U. Meirav, Fano resonances in electronic transport through a single-electron transistor, Phys. Rev. B 62 (2000) 2188. 

Also, interesting STS results on individual non-size-selected Pt and Ag clusters produced by a PACIS source and deposited onto HOPG have been obtained recently [236]. The observed spectral structures for Pt have been interpreted in terms of a Fano resonance and those of Ag clusters in terms of 3D electron confinement. Effects of electron confinement have also been observed recently with STS for silver islands grown in nanopits on HOPG [237]. 

For metal eoverages at whieh the enhaneement of the Raman signal due to dipolar plasmon resonanees is observed, the bands at around 1606 em (in both PTCDA and DiMe-PTCDI) beeome asymmetrie towards the low Ife-queney side in all the investigated systems exeept for Mg/PTCDA. This line-shape asymmetry is likely to be related to a Fano resonant eoupling between the moleeular eleetronie levels and the plasmons in the metallie elusters modulated by the moleeular vibrations [21]. Interestingly, the mode at 1606 em stems from a breathing mode of the earbon rings. 

The Ch-related donor spectra differ on that point as several parity-forbidden transitions are observed. They start with symmetry-allowed transitions from the Is ground state to the valley-orbit split Is excited states, and are supplemented with 2s (T2) and 3s (T2) lines and Fano resonances within the photoionization spectrum. This is shown in Fig. 6.13 for Se°. Compared to group-V donors, this extends the energy span of the Ch°-related spectra to the ionization energy of the Is (T2) level (35-40 meV in isolated chalcogens) and it can even increase to 40-48 meV when singlet-triplet spin-forbidden transitions are observed. 

Fig. 6.13. Comparison between Se° spectra in silicon (a) absorption at a resolution of 1cm-1 or 0.12 meV ([Se] 3 x 1016 cm 3), and (b) PTIS at a resolution of 0.25cm-1 or 30peV ([Se] 3 x 1015cm-3) between 2100 and 2740cm-1. The Fano resonances above 330 meV are clearly observed in the PTI spectrum, (c) Enlarged view of (b) showing more details of the spectrum. C.B. corresponds to the ionization energy of Se° [118]. Copyright 1984 by the American Physical Society...

As for Mg°, no even-parity transition is detected in the Mg+ spectrum, but the Fano resonances involving the 2s (Ai) and 2s (T2) transitions allow determination of the position of these two levels [130]. This high-resolution... 

Fig. 6.20. Spectrum of Se2+ in silicon under TEC at LHeT. The sample contains a small concentration of Se°. Due to the experimental conditions, the only Se° line observed is the sharp ls(T2) line at 272.2 meV (2195 cm-1), barely visible, plus Fano resonances of the same transition...

Table 6.22. Comparison of the first energy levels measured for Se°, Te°, and Se+ in germanium with the calculated EM values [30] and those measured for P (meV units). The values for Se+ are divided by four except for ls(Ai). FR stands for Fano resonance...

Fig. 6.22. Absorption between 2055 and 2420 cm 1 of 77Se° in a qmi Ge sample with [77Se] = 3 x 101B cm 3. FR is the Fano resonance. The energy of the O (r) phonon is 37.7meV (304cm-1) (after [192]). Copyright 1998, with permission from Elsevier...

The electrical and optical activity of acceptors as a function of their charge state and of the electrical compensation of the semiconductor can be derived in the same way as what has been described for donors. Also, in all semiconductors and insulators, many of the spectroscopic properties of the hydrogen-like acceptors are determined by the energy structure of the VB maximum, located at k = 0. There is no strict equivalent of the Fano resonances observed for donors in crystals with several equivalent CB minima in k space, but discrete... 

Fig. 7.15. Absorption of Zn in germanium between 62 and 124 meV. The features denoted FG, FD, and Fc are Fano resonances associated with the zone-centre O(r) phonon of germanium and the corresponding lines. The features denoted by L are two-phonon lattice absorption bands of germanium. Reproduced from [138]. Copyright 1990, with permission from Elsevier...

Piezospectroscopic measurements show that the Be-I centre has tetrahedral symmetry which could be attributed to Be0 [77]. This attribution was expected from the observation of a red-shifted replica of the 1.7 K spectrum when the temperature is raised to 8K, attributed to a splitting of the ground state expected for a double acceptor, discussed above in the case of germanium. The replica is split by —4 cm-1 (—0.5meV) and is observed for all the lines of the Be0 spectrum. The direct transition between the Ti and T5 sublevels of the Be0 ground state has also been directly observed at 4 cm-1 (0.5 meV) in the very far IR at 1.2 K [137], A weak temperature-independent component of the Be0 spectrum shifted by +0.53 meV has been reported by [77] and attributed to a splitting of the final state. Fano resonances associated with lines of Be0 have been reported between 1925 and 2030 cm-1 ( 238 and 252 meV) by Kleverman and Grimmeiss [99]. 

Fig. 7.19. Spectra of Au (647.2-690.6 meV) and Pt (954.7-998.1 meV) in silicon at LHeT. Note the difference between the Fano resonance shapes of Pt in the transmission and photoconductive (PC) spectra. The splitting associated with the ls3/2 (rs) structure is attributed to the crystal field. The Fano resonances labelled Fi, F2, and F2 include the -Zi(o), 2(0) > and /2 (o) lines of Fig. 7.18. The T-lines are related to a Pt donor centre [101]. Copyright 1997 by the American Physical Society...

Figure 8.9 shows for F// [110], the anti-crossing of the h-e component of Is (T2) (Se°) with the h-e component of Is (E) as these components have the same symmetry (see Table 8.5). This interaction allows one to extrapolate the position of the Is (E) component at zero stress to 2.1 meV ( 25cm 1) above the Is (T2) line and to obtain a value of the position of this symmetry- and parity-forbidden line in good agreement with the one deduced from the Fano resonances [14]. 

The isolated Beutler-Fano resonance appears, at first sight, to be the simplest situation which can give rise to a resonance in the continuum. In principle, the resonance can appear at any energy above the threshold, since resonance and continuum belong to distinct channels. Thus, there... 

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