Pulse excitation, duration limitations

Time-independent picture. The opposite extreme from short-pulse excitation involves the use of nearly monochromatic radiation. Practically, this means that the interaction between molecule and radiation field is of longer duration than Tnr. In this limit, the quantity measured is the absorption lineshape. It will be shown below that the linewidth observed in an energy-resolved experiment is related in a very simple way to the predissociation lifetime in the time-resolved experiment. 

With a short laser pulse of duration At, which has a Fourier-limited spectral bandwidth Amore than one energy level can be excited simultaneously if their energy separation AE < HAco. For simplicity, we restrict the discussion here to two atomic/molecular levels Ei and E2 (see Figure 2.10). The wave function of the excited species is now a linear combination of the wave functions t/, and j/2, the atom/molecule is said to be in a coherent superposition of the two states 11) and 2). 

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... 

Assume that two closely spaced levels 1 and 2 of an atom or molecule are simultaneously populated by optical pumping with a short laser pulse from a common initial lower level i (Fig.11.23a). In order to achieve coherent excitation of both levels by a laser pulse with duration aT, the Fourier limited spectral bandwidth Av = a/AT [a is a constant of the order of unity which depends on the pulse profile Ip(t)] must be larger than the frequency separation (E - Ej)/h. 

Precisely controllable rf pulse generation is another essential component of the spectrometer. A short, high power radio frequency pulse, referred to as the B field, is used to simultaneously excite all nuclei at the T,arm or frequencies. The B field should ideally be uniform throughout the sample region and be on the order of 10 ]ls or less for the 90° pulse. The width, in Hertz, of the irradiated spectral window is equal to the reciprocal of the 360° pulse duration. This can be used to determine the limitations of the sweep width (SW) irradiated. For example, with a 90° hard pulse of 5 ]ls, one can observe a 50-kHz window a soft pulse of 50 ms irradiates a 5-Hz window. The primary requirements for rf transmitters are high power, fast switching, sharp pulses, variable power output, and accurate control of the phase. 

Figure 5.4, one can easily understand why the interfacial electron transfer should take place in the 10-100 fsec range because this ET process should be faster than the photo-luminescence of the dye molecules and energy transfer between the molecules. Recently Zimmermann et al. [58] have employed the 20 fsec laser pulses to study the ET dynamics in the DTB-Pe/TiC>2 system and for comparison, they have also studied the excited-state dynamics of free perylene in toluene solution. Limited by the 20 fsec pulse-duration, from the uncertainty principle, they can only observe the vibrational coherences (i.e., vibrational wave packets) of low-frequency modes (see Figure 5.5). Six significant modes, 275, 360, 420, 460, 500 and 625 cm-1, have been resolved from the Fourier transform spectra of ultrashort pulse measurements. The Fourier transform spectrum has also been compared with the Raman spectrum. A good agreement can be seen (Figure 5.5). For detail of the analysis of the quantum beat, refer to Figures 5.5-5.7 of Zimmermann et al. s paper [58], These modes should play an important role not only in ET dynamics or excited-state dynamics, but also in absorption spectra. Therefore, the steady state absorption spectra of DTB-Pe, both in...

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