Resonance Raman scattering amplitude

The amplitude i j,(t t)) has been previously defined in the theory of resonant Raman scattering (37) and referred to as the Raman wave function. In the present approach,... 

The neutral ir-conjugated polymer chain is free of excess charges. The neutral chain has a set of Raman active Ag vibrations that are strongly couple to the electronic bands by the e—p coupling [64]. These vibrations have been termed as amplitude modes (AM) since they modulate the electronic gap, 2A in the notation of Peierls gap [65]. The AM vibrations have been the subject of numerous studies and reviews since they play a crucial role in resonant Raman scattering dispersion with the laser excitation, and therefore can show important properties of the coupled electronic levels [66,67]. The most successful description of the AM-type vibrations was advanced by Horowitz [65], and its application to RRS by Vardeny et al. [64] and Ehrenfreund et al. [67]. 

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. 

Accordingly, for a given Raman-active resonance r, the amplitudes of XijM can be expressed in terms of the isotropy and symmetric anisotropy invariants of the corresponding spontaneous Raman scattering tensor, a2 and 7S2, respectively. In the case of frequency-degenerate CRS considered here, the two relevant independent tensor components assume the following form [33, 34] ... 

The Mie scattering model also helps explain the strong polarization anisotropy or antenna effects [9, 12] in the Raman scattering of semiconductor NWs, so named because of the selective Raman scattering of TM-polarized light by way of this structural resonance modulation. This behavior is quantifled in the polarization anisotropy ratio, calculated by an averaging of the squared held amplitudes of the product of incident and scattered flelds [12], determined from a Mie-type solution ... 

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 ... 

Interface modes only appear when a smooth interface is formed between the two materials. They are localized with the maximum of their amplitude in the interface layer and an exponentially decay of the amplitude into the well and barrier layers. Because of their amplitude in both well and barrier layers, the interface modes show resonance enhancement when the excitation energy or the energy of the scattered photon matches either the barrier or the well bandgap energy [109,132,141,170,171]. Figure 14 shows the resonance Raman spectrum of a (111) CdTe/Cdo.76Mno.24Te superlattice with = 7.1 nm, d2 = 12.8 nm, and the number of periods n - 128. The spectrum clearly shows the interface modes IFi and IF2 as well as their overtones and combinations up to the fourth order [109]. 

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