Raman amplitude

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

Guo, H. (1998) An efficient method to calculate resonance Raman amplitudes via polynomial propagation. Cham. Phys. Lett. 289, 396-402. 

The nonresonant term may be obtained from the resonant term by the replacement cj, - tus, and, henceforth, will be neglected. Equation (2.9) states that the scattering amplitude is the half-Fourier transform of the overlap of the time-evolving wavepacket with the final state of interest (multiplied by the transition moment). Equation (2.9) bears a close resemblance to Eq. (2.3) for the absorption cross section, but there are three differences to note (1) the cross-correlation function of the moving wavepacket with the final vibrational state of interest is required, rather than the autocorrelation function (2) an integral over the range [0, oo], not [-00,00], is required for the Raman amplitude (3) The cross-section / " (to) is proportional to the absolute value squared of a ... 

This is the correlation function which determines the Raman amplitude for the transition i - f as a function of frequency. 

Here, as in the case of the one-photon spectrum, 1 ) is the bright state on the upper electronic potential energy surface which corresponds to the final state / on the ground electronic state. Equation (49) is a half Fourier transform in that it is limited to positive values of the time. One can regard it as an ordinary Fourier transform by defining the cross-correlation function to equal zero for negative times. Such a function is called causal in the theory of Fourier transform (51) and this puts conditions on the analytic properties of the Raman amplitude. These will be further discussed in Sec. IV. 

Additional insight into the vibronic dynamics can be achieved by performing time-dependent calculations. The latter allow for a more direct visualization of the coupled electronic and nuclear motions. Moreover, given only the spectrum, Eq. (31), or a small number of resonance Raman amplitudes, the information obtained from the time-dependent wavefunction differs also in principle from that of stationary spectra. 

An improvement in this kind of studies could be obtained if the density of states g(cu) could be properly weighted by a dipole factor in the infrared or polarizability factor in the Raman, Amplitude weighted glv) from neutron scattering can be easily evaluated since vibrational amplitudes can be routinely calculated for crystal and polymers. 

Smith T J and Cina J A 1996 Toward preresonant impulsive Raman preparation of large amplitude J. 

It has been important to determine if the neoxanthin distortion signature could be detected during the nonphotochemical quenching in vivo. Resonance Raman measurements on leaves and chlo-roplasts of various Arabidopsis mutants have revealed a small increase in the 950 cm 1 region. The relationship between the amplitude of this transition and the amount of NPQ suggests that the LHCII aggregation may be the sole cause of the protective chlorophyll fluorescence quenching in vivo (Ruban et al., 2007). 

Raman spectroscopy is an inelastic light scattering experiment for which the intensity depends on the amplitude of the polarizability variation associated with the molecular vibration under consideration. The polarizability variation is represented by a second-rank tensor, oiXyZ, the Raman tensor. Information about orientation arises because the intensity of the scattered light depends on the orientation of the Raman tensor with respect to the polarization directions of the electric fields of the incident and scattered light. Like IR spectroscopy, Raman... 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Isotope superlattices of nonpolar semiconductors gave an insight on how the coherent optical phonon wavepackets are created [49]. High-order coherent confined optical phonons were observed in 70Ge/74Ge isotope superlattices. Comparison with the calculated spectrum based on a planar force-constant model and a bond polarizability approach indicated that the coherent phonon amplitudes are determined solely by the degree of the atomic displacement, and that only the Raman active odd-number-order modes are observable. 

Transient transmittance of single-walled carbon nanotubes (SWNTs) in suspension was modulated at two periods of T40 and 21 fs, corresponding to the RBM and G mode, respectively [54,55]. The amplitude and the frequency of the coherent RBMs exhibited a clear excitation-wavelength dependence (Fig. 2.15) [54]. The different frequencies were attributed to SWNTs with different diameters coming to the excitonic resonance. The FT spectra of the coherent RBMs in Fig. 2.15 had noticeable differences from the resonant Raman spectra, such as the different intensities and better frequency resolution. 

When metals have Raman active phonons, optical pump-probe techniques can be applied to study their coherent dynamics. Hase and coworkers observed a periodic oscillation in the reflectivity of Zn and Cd due to the coherent E2g phonons (Fig. 2.17) [56]. The amplitude of the coherent phonons of Zn decreased with raising temperature, in accordance with the photo-induced quasi-particle density n.p, which is proportional to the difference in the electronic temperature before and after the photoexcitation (Fig. 2.17). The result indicated the resonant nature of the ISRS generation of coherent phonons. Under intense (mJ/cm2) photoexcitation, the coherent Eg phonons of Zn exhibited a transient frequency shift similar to that of Bi (Fig. 2.9), which can be understood as the Fano interference [57], A transient frequency shift was aslo observed for the coherent transverse optical (TO) phonon in polycrystalline Zr film, in spite of much weaker photoexcitation [58],... 

---