54,1-order Raman signal

D. The Total Nonresonant Fifth-Order Raman Signal... 

Since the direct and cascaded responses satisfy the same phase matching condition, the total nonresonant fifth-order Raman signal will contain both contributions. Using Equations (11), (14), and (28), the ratio between the absolute values of the direct and cascaded contributions is... 

As already mentioned, the first-order Raman signals do not distinguish local strains, so only one signal for the whole wire or dot can be obtained, which consists of the signals of the strained center as well as the relaxed edges. However, even in the first-order spectra, the strain relaxation can be observed as a shift of the LO-phonon frequency toward the value of the unstrained material. The amount of this shift depends on the ratio of the relaxed edges to the strained wire center and, therefore, on the wire width and length [218-222]. 

Upon integration along the propagation direction z from sample pathlength 0 to L the fifth-order Raman signal becomes... 

The first term in this Taylor expansion around qo has no coordinate dependence and is time independent The second term is Unear in coordinate dependence and corresponds to the signal measured in third-order Raman experiments. To generate a fifth-order Raman signal the third term is necessary if a single harmonic mode, qj, is assumed, signal generation requires a two-quantum coherence to be created by one of the interactions. Subsequent to this realization it was proposed [28] that the spectroscopy also probes any anharmonicity in the vibrational potential, which corresponds to the inclusion of a cubic anharmonicity term ... 

A large amount of effort has been devoted to evaluating the fifth-order Raman signal for a variety of systems. The first method used in such simulations is the multi-mode Brownian oscillator (MMBO) model [16] which approached the problem as a system of oscillators coupled to a heat bath. The oscillators are obtained from a fit of the low-frequency spectrum of the liquid in question ... 

Once the anharmonicity of the potential as a possible source for the fifth-order Raman signal was taken into account, some modifications were made to the MMBO model. In the simplest case the anharmonicity was introduced as a perturbation to the harmonic vibrational modes (see (1.9)) [31]. This model proved to have the same convenience in interpretation of the limiting cases as the simple MMBO model but with the added possibility of distinction between signal generated by the nonlinearity in the polarizability as opposed to signal generated by the anharmonicity. 

Fig. 1.4 Fifth-order Raman signal intensity calculation for water based on the MMBO method [30], (a) homogeneous limit, (b) inhomogeneous limit, n is the pump delay ra is the probe delay. Reprinted with permission from [30], Copyright 1994, American Chemical Society...

Fig. 1.7 Fifth-order Raman signal intensity for liquid Xe calculated using INM. Note the distinct echo signal along the time diagonal (fi =t2) [42]. Reused with permission from [42], Copyright 2002, American Institute of Physics...

The failure of INM theory is a strong indication of the sensitivity of the fifth-order Raman signal to anharmonicities. Ma and Stratt modified INM theory to allow for dephasing of the modes which they termed adiabatic instantaneous normal mode theory [42]. This allowed them to incorporate the dynamical anharmonicity which was missing from their previous calculation (see (1.9)). In an approach similar to Okumura and Tanimura, the response was broken into its component parts to investigate their dependence on the various signal contributions (see Fig. 1.10). When treated individually the dynamical anharmonicity... 

Fig. 1.23 Homodyne-detected iJiiim fifth-order Raman signal of CS2 measured using one color at 800 nm and a 1 mm pathlength by Blank et al. [85]. Reused with permission from [85]. Copyright 2000, American Institute of Physics...

Fig. 1.26 Active feedback heterodyne-detected fifth-order Raman signal of CS2 measured by Kaufman et al. using the Dutch Cross polarization settings. The node is represented by a blade line. The delay conventions used are D = pump delay and t2 = probe delay. Sample pathlength used was 1 mm. Note the significant reduction in the signal along in comparison to Fig. 1.24 and the shift in the node along to less than 100 fs [87]. Figure courtesy of L.J. Kaufman and G.R. Fleming...

Golonzka, O., Demirdoven, N., Khalil, M., Tokmakoff, A. (2000). Separation of cascaded and direct fifth-order Raman signals using phase-sensitive intrinsic heterodyne detection. J. Chem. Phys. 113 9893-9896. 

MOLE, however, is more sensitive than ETIR (<1 samples compared to about 100 p.m ). With surface-enhanced Raman spectroscopy the Raman signal is enhanced by several orders of magnitude. This requires that the sample be absorbed on a metal surface (eg, Ag, Cu, or Au). It also yields sophisticated characterization data for the polytypes of siUcon carbide, graphite, etc. 

Vibrational spectroscopies such as Raman and infrared are useful methods for the identification of chemical species. Raman scattering [4] is a second-order process, and the intensities are comparatively low. A quick estimate shows that normal Raman signals generated by species at a surface or an interface are too low to be observable. Furthermore, in the electrochemical situation Raman signals from the interface may be obscured by signals from the bulk of the electrolyte, a problem that also occurs in electrochemical infrared spectroscopy (see Section 15.3)... 

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