Two-frequency excitation

For two-frequency excitation, the averaged resi.lt for a rotating pair is given by... 

Because of the two frequencies, Wj and Wg, that enter into the Raman spectrum, Raman spectroscopy may be thought of as a two-dimensional fomi of spectroscopy. Nomially, one fixes oij and looks at the intensity as a frmction of tOj, however, one may vary tOj and probe the intensity as a frmction of tOj - tOg. This is called a Raman excitation profile. 

This behavior is consistent with experimental data. For high-frequency excitation, no fluorescence rise-time and a biexponential decay is seen. The lack of rise-time corresponds to a very fast internal conversion, which is seen in the trajectory calculation. The biexponential decay indicates two mechanisms, a fast component due to direct crossing (not seen in the trajectory calculation but would be the result for other starting conditions) and a slow component that samples the excited-state minima (as seen in the tiajectory). Long wavelength excitation, in contrast, leads to an observable rise time and monoexponential decay. This corresponds to the dominance of the slow component, and more time spent on the upper surface. 

Since Raman scattered light intensity is very weak, of the order of 10-7 of the excitation line intensity, more powerful laser sources than the He-Ne laser are often needed. The Ar+ laser emits various lines in the region from 457.9 nm to 514.5 nm, of which the most powerful lines (typically — 700 mW) at 488.0 nm (blue) and 514.5 nm (green) are preferred. Furthermore, two other factors which favor the use of the high frequency excitation lines are the peak sensitivity of the photomultipliers in this blue-green region (Fig. 8) and the fourth power Raman intensity law... 

Figure 16. The effective frequency 0(x) for two transversal excitations in HO2. Solid line shows the results of numerical solution of Eqs. (79) and (80). Dotted line represents the frequency in the adiabatic approximation, y = 1[3] corresponds to the mode (0,0,1) [(1,0,0)] (see Fig. 14). Taken from Ref. [32].

Two-dimensional excitation experiments (two wavelengths excitation in fluorescence spectroscopy or two frequency experiments in 2D-NMR) also generate three-dimensional signal functions. 

A number of other up-conversion processes are known. The blue emission from a Yb3+/Tm3+ couple in which the active emitters are defect Tm3+ centers is mainly due to the efficient excitation ET process from Yb3+ centers. Two-frequency up-conversion has been investigated using Pr3+ defects in a fluoride glass matrix. Illumination with one pump wavelength results in GSA, while simultaneous irradiation with a second pump wavelength further excites the GSA centers via ESA. The doubly excited defects emit red light. Up-conversion and visible output only takes place at the intersection of the two beams. 

There exists an extensive literature on theoretical calculations of the vibrational damping of an excited molecule on a metal surface. The two fundamental excitations that can be made in the metal are creation of phonons and electron-hole pairs. The damping of a high frequency mode via the creation of phonons is a process with small probability, because from pure energy conservation, it requires about 6-8 phonons to be created almost simultaneously. 

Because of the low energy of a ruby-laser photon (X = 6940 A A 1.8 eV), most of the photolysis experiments with ruby laser sources either use frequency doubling or proceed by two-step excitation or two-photon processes. 

Sorokin and Lankard illuminated cesium and rubidium vapors with light pulses from a dye laser pumped by a ruby giant-pulse laser, and obtained two-step excitation of Csj and Rbj molecules (which are always present in about 1 % concentration at atomic vapor pressures of 10" - 1 torr) jhe upper excited state is a repulsive one and dissociates into one excited atom and one ground-state atom. The resulting population inversion in the Ip level of Cs and the 6p level of Rb enables laser imission at 3.095 jum in helium-buffered cesium vapor and at 2.254 pm and 2.293 /zm in rubidium vapor. Measurements of line shape and frequency shift of the atomic... 

Fig. 4. Numerical simulations showing the effect of 20% miscalibration of the rf amplitudes of two selective excitation pulses (Top) A 270° Gaussian of 30 ms duration (peak amplitudes from left to right 43 Hz, 54 Hz, and 65 Hz) and (Bottom) a Quaternion cascade of 30 ms duration (peak amplitudes from left to right 121 Hz, 151 Hz, and 181 Hz). The multiplets were obtained by simulating a three-spin system with couplings Jam = 7 Hz, Jax = 12 Hz, and Jmx = 0 Hz. The vertical axes show a constant arbitrary amplitude, whereas the horizontal axis gives the frequencies 1 a 50 Hz.

The term that depends on the third power of the frequency shift is known as third-order dispersion (TOD). When a TL pulse acquires a significant amount of TOD, the pulse envelope is distorted and a series of sub-pulses is produced, as shown in Figure 8.1. Unlike a pulse with SOD, a pulse with TOD leads to two-photon excitation with the same efficiency as a TL pulse but only for a particular two-photon frequency. At other frequencies, the amount of excitation is suppressed. The control over TOD would allow for preferential excitation in different spectral regions, while its correction would lead to efficient two-photon excitation over the whole accessed spectral range. Unfortunately, measuring and correcting TOD is not a simple task. 

The instanton method takes into account only the dynamics of the lowest energy doublet. This is a valid description at low temperature or for high barriers. What happens when excitations to higher states in the double well are possible And more importantly, the equivalent of this question in the condensed phase case, what is the effect of a symmetrically coupled vibration on the quantum Kramers problem The new physical feature introduced in the quantum Kramers problem is that in addition to the two frequencies shown in Eq. (28) there is a new time scale the decay time of the flux-flux correlation function, as discussed in the previous Section after Eq. (14). We expect that this new time scale makes the distinction between the comer cutting and the adiabatic limit in Eq. (29) to be of less relevance to the dynamics of reactions in condensed phases compared to the gas phase case. 

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