Broadening anomalous

Fig. 3.10. Anomalous broadening of oxygen isotropic Raman spectrum in the vicinity of (but above) the critical point [137]. The notation is the same as in Fig. 3.5.

The character of variations in the spatiotemporal field distribution in the guiding region depending on the sign of the GVD is shown in Fig.32. The most noticeable effect of dispersion manifests itself in the waveguide core, where in the case of normal GVD, the pulse continuously broadens simultaneously with the compression of its transverse distribution (Fig.32a). In the case of anomalous GVD, a so-called light bullet is formed (Fig.32b), which looks like a sharp increase in the intensity at the peak of the spatiotemporal distribution. 

A third example can be taken from analytical chemistry. Absorption and resonance Raman spectra of phenol blue were measured in liquid and supercritical solvents to determine the solvent dependence of absorption bandwidth and spectral shifts. Good correlation between absorption peak shift and resonance Raman bands and between Raman bands and bandwidth of C-N stretching mode were observed while anomalous solvent effect on the absorption bandwidth occnrred in liquid solvents. Large band-widths of absorption and resonance Raman spectra were seen in supercritical solvents as compared to liquid solvents. This was dne to the small refractive indices of the supercritical solvents. The large refractive index of the liqnid solvents only make the absorption peak shifts withont broadening the absorption spectra (Yamaguchi et al., 1997). 

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

The theory of the Fe(III) heme spectra has been given in the previous article (52) and in particular the difference between the absorption spectra of high-spin and low-spin species has been stressed. The application of this theory to some proteins has also been described in that article but its purpose was mainly to draw attention to normal spectra. Here we shall point to a number of anomalous spectra especially concerning the movement of the Soret band to much shorter wavelengths than 400 nm. There is a simultaneous notable broadening of this band and a fall in its extinction coefficient. Such effects have frequently been seen in simple model systems and so we deal these first. 

Very few experiments have been performed on vibrational dynamics in supercritical fluids (47). A few spectral line experiments, both Raman and infrared, have been conducted (48-58). While some studies show nothing unique occurring near the critical point (48,51,53), other work finds anomalous behavior, such as significant line broadening in the vicinity of the critical point (52,54-60). Troe and coworkers examined the excited electronic state vibrational relaxation of azulene in supercritical ethane and propane (61-64). Relaxation rates of azulene in propane along a near-critical isotherm show the three-region dependence on density, as does the shift in the electronic absorption frequency. Their relaxation experiments in supercritical carbon dioxide, xenon, and ethane were done farther from the critical point, and the three-region behavior was not observed. The measured density dependence of vibrational relaxation in these fluids was... 

This behavior is sketched in Fig. 18. Note that the parameter co directly controls the anomalous broadening of interfacial widths in confined geometry, since Eq. (121) can be rewritten as using k=2/[w0(1+co/2)] in the general case [266]... 

Finally, we return to the case of antisymmetric surfaces, i.e. a situation where one surface of the thin film favors the A-rich phase and the other the B-rich phase (Fig. Id). Simulations were recently carried out [266] in order to test the predictions Eq. (127) on the anomalous interfacial broadening (Sect. 2.5). Figure 24 demonstrates that this phenomenon can indeed be readily observed. Using the interfacial tension a that has been independently measured [215], o= 0.015, and the correlation length 3.6 lattice spacings from a direct study of the bulk correlation function, one can evaluate Eq. (127) quantitatively, using... 

Fig. 1 Top Behavior of the electronic linear chiroptical response in the vicinity of an excitation frequency. Re = real part (e.g., molar rotation [< ]), Im = imaginary part (e.g., molar ellipticity [0]). Without absorption line broadening, the imaginary part is a line-spectrum (5-functions) with corresponding singularities in the real part at coex. A broadened imaginary part is accompanied by a nonsingular anomalous OR dispersion (real part). A Gaussian broadening was used for this figure [37]. Bottom Several excitations. Electronic absorptions shown as a circular dichroism spectrum with well separated bands. The molar rotation exhibits regions of anomalous dispersion in the vicinity of the excitations [34, 36, 37]. See text for further details...

The well known anomalous fluorescence from S2 has been interpreted in terms of a much slower radiationless transition out of S2 than Si, such that for Si the fluorescence lifetime is severely shortened relative to the radiative lifetime. The anomaly is related to the unusual energy disposition of the two lowest excited singlet states. Hochstrasser and Li wished to ascertain whether the spectral linewidths were consistent with this interpretation and also whether the Si linewidths of azulene-ds were narrowed in comparison, as theoretically predicted. Their results are listed in Table 1. The spectral resolution was claimed to be <0.15 cm-1 as linewidths in the S2 system corresponding to the observed fluorescence lifetime are of the order of 10-4 cm-1, the linewidths of 0.50 cm-1 measured must be considered crystal-imposed. It is assumed that the maximum crystal inhomogeneity contribution to the Si linewidth is similarly 0.50 cm-1. This leads to a line broadening due to rapid nonradiative electronic relaxation of 1.61 (-hs) and 1.27 (-da) cm-1 as compared to 0.64 cm-1 (-hs) determined by Rentzepis 50> from lifetime studies of azulene in benzene solution at 300 K. 

Photocurrent transients that show the absence of a plateau or the anomalous broadening of the tail are frequently described as dispersive, a term introduced by Mort and Lakatos (1970) and Pai (1970). In the literature, dispersive transport is frequently used in different contexts and with different meanings (Scott et al., 1994). The most commonly used definition is based on the absence of either a plateau or an inflection in transients in double linear representation. In the following discussion, we will use this definition. 

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