Spectral calculations frequency dependences

Fig. 12b). Since practically the same spectral shape is obtained at Q-band (35 GHz) (Fig. 12c), the commonly used criterion stating that the shape of an interaction spectrum is frequency-dependent fails to apply in this case. Actually, outer lines arising from the exchange interaction are visible on the spectrum calculated at Q-band (Fig. 12c), but these lines would be hardly detectable in an experimental spectrum, because of their weak intensity and to the small signal-to-noise ratio inherent in Q-band experiments. In these circumstances, spectra recorded at higher frequency would be needed to allow detection and study of the spin-spin interactions. 

In Fig. 14 the low-frequency loss spectrum %"(x) is shown. It is calculated by using Eq. (32), in which the frequency dependence of the spectral function is neglected ... 

Temperature information from CARS spectra derives from spectral shapes either of the 2-branches or of the pure rotational CARS spectra of the molecular constituents. In combustion research it is most common to perform thermometry from nitrogen since it is the dominant constituent and present everywhere in large concentration despite the extent of chemical reaction. The 2-branch of nitrogen changes its shape due to the increased contribution of higher rotational levels which become more populated when the temperature increases. Figure 6.1-21 displays a calculated temperature dependence of the N2 CARS spectrum for experimental parameters typically used in CARS thermometry (Hall and Eckbreth, 1984). Note that the wavenumber scale corresponds to the absolute wavenumber value for the 2320 cm 2-branch of N2 when excited with the frequency doubled Nd.YAG laser at 532 nm ( 18796 cm ), i. e. = 18796 -1- 2320 = 21116 cm. The bands lower than about 21100 cm are due to the rotational structure of the first vibrational hot band. 

In Figure 9 we depict the frequency dependences of the partial absorption coefficients aq(v) and a (v) pertinent to two harmonic-vibration modes. These frequency dependences are calculated from formulas (A6), (21) [24], (25), (28), and (29). When the above-mentioned coupling is accounted for (solid lines in Fig. 9), the spectral functions are taken from Eq. (Al). On the other hand, when the coupling is neglected (open circles in Fig. 9), then Lq and L are found from Eq. (19). We see from Fig. 9a that for both cases the calculated partial absorption a (v) practically coincide. The same assertion is valid also for the partial absorption ocq(v) depicted in Fig. 8b. Hence, there is no practical need to account for the coupling between the harmonic reorientation and vibration of HB molecules for calculation of spectra in liquid water. However, the effect of such coupling becomes noticeable (being, however, a rather small) in the case of ice, where the absorption lines are much narrower. 

If near-field is to be used as a measurement tool for intrinsic fluorescence properties, then one needs to know the operating conditions or samples that are appropriate for lifetime and/or spectroscopic measurements. To address this question, the FDTD method was used to compute the spectral shift and fluorescence lifetime as a function of the tip-sample gap with the molecule directly under the center of the aperture. Fig. 18 shows these results. For a yg of about 3 x 10 /s, the frequency can red shift by about 10 GHz for distances less than 50 nm. This frequency shift is not important at room temperature where the vibronic bands are approximately 10 GHz wide. At low temperatures, the linewidths are in the 0.01 to 10 GHz range, and probe-induced frequency shifts should be measurable. The frequency dependence on distance was not calculated at the larger distances, 200-400 nm, relevant to the experiment of Moerner et al. [11] (Section 2.4.2). On the other hand, the fluorescence lifetime of high quantum yield molecules was predicted to be affected in first order throughout the near-field region. Bian et al. [25] point out that for systems with fast non-radiative decay channels, the perturbations by the probe may not be significant. 

Carbotte et al. (1995) analyzed the complex conductivity in the presence of disorder in the weak Bom-scattering limit assuming different symmetries of the order parameter. Their main result is that the data presented in fig. 20 are not consistent with an s-wave gap but can be qualitatively accounted for within a d-wave model. In particular, disordered d-wave superconductors are expected to reveal an enhancement of the spectral weight of the normal component in the superconducting state response. The frequency dependence of the conductivity at T and its evolution with disorder are remarkably similar in the experimental data by Basov et al. (1994b) and in theoretical calculations by Jiang et al. (1996). 

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