Time-resolved frequency modulation spectroscopy

In the previous Maxwelhan description of X-ray diffraction, the electron number density n(r, t) was considered to be a known function of r,t. In reality, this density is modulated by the laser excitation and is not known a priori. However, it can be determined using methods of statistical mechanics of nonlinear optical processes, similar to those used in time-resolved optical spectroscopy [4]. The laser-generated electric field can be expressed as E(r, t) = Eoo(0 exp(/(qQr ot)), where flo is the optical frequency and q the corresponding wavevector. The calculation can be sketched as follows. 

In their chapter on time- and frequency-resolved studies of photoelectrochemical kinetics, Peter and Vanmaekelbergh give an extensive survey of how modulation techniques such as photoelectrochemical impedance spectroscopy or intensity-modulated photocurrent spectroscopy can yield valuable information on the time dependence of reactions at semiconducting surfaces over a broad range of time scales. Kinetic studies with single crystals as well as porous or nanocrystalline material reveal the important role that is played by the bulk structure of semiconductor electrodes. 

We have already discussed quantum-beat spectroscopy (QBS) in connection with beam-foil excitation (Fig.6.6). There the case of abrupt excitation upon passage through a foil was discussed. Here we will consider the much more well-defined case of a pulsed optical excitation. If two close-lying levels are populated simultaneously by a short laser pulse, the time-resolved fluorescence intensity will decay exponentially with a superimposed modulation, as illustrated in Fig. 6.6. The modulation, or the quantum beat phenomenon, is due to interference between the transition amplitudes from these coherently excited states. Consider the simultaneous excitation, by a laser pulse, of two eigenstates, 1 and 2, from a common initial state i. In order to achieve coherent excitation of both states by a pulse of duration At, the Fourier-limited spectral bandwidth Au 1/At must be larger than the frequency separation ( - 2)/ = the pulsed excitation occurs at... 

Electron spin echo modulation spectroscopy (Norris et al., 1980 Dikanov Tsvetkov, 1992) is sometimes called FT-ENDOR because the echo modulation time series yields a frequency spectrum that corresponds to transitions among nuclear sublevel (Rowan et al., 1965). The ESEEM technique is often said to be complementary to ENDOR (Tsvetkov Dikanov, 1987) beeause ESEEM tends to yield well-resolved spectra in the low-frequency range (<4 MHz) of the nuclear hyperfine spectrum, where cw-ENDOR is often problematie. The eonverse is likewise true ESEEM tends to be problematic at recording hyperfine frequencies above 10 MHz. 

Figure 3.1 The various time periods in a two-dimensional NMR experiment. Nuclei are allowed to approach a state of thermal equilibrium during the preparation period before the first pulse is applied. This pulse disturbs the equilibrium ptolariza-tion state established during the preparation period, and during the subsequent evolution period the nuclei may be subjected to the influence of other, neighboring spins. If the amplitudes of the nuclei are modulated by the chemical shifts of the nuclei to which they are coupled, 2D-shift-correlated spectra are obtained. On the other hand, if their amplitudes are modulated by the coupling frequencies, then 2D /-resolved spectra result. The evolution period may be followed by a mixing period A, as in Nuclear Overhauser Enhancement Spectroscopy (NOESY) or 2D exchange spectra. The mixing period is followed by the second evolution (detection) period) ij.

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