Second-order Raman effect

Inelastic scattering of radiation in solids is typified by the Raman effect, which involves the creation or annihilation of phonons or magnons. If a single phonon is involved, the scattering event is referred to as the first-order Raman effect in second-order Raman effect two phonons are involved. The polarizability associated with a phonon mode can be represented as a power series of the phonon amplitude, u, as follows ... 

Table 4.1-59 Phonon wavenumbers of gallium compounds. Gallium nitride (GaN), T = 300K, from Raman spectroscopy gallium phosphide (GaP), RT, from an analysis of Raman, neutron, luminescence, and absorption data gallium arsenide (GaAs), T = 296 K, from coherent inelastic neutron scattering gallium antimonide (GaSb), T = 300 K, from second-order Raman effect...

Raman spectra of the two structures (obtained with a laser of 632.817 nm wavelength) are very similar (Figure 2.13(b)). A more marked contribution at a wave number slightly lower than the peak Ai is nevertheless observed for the IF structure. The Ai peak appears broadened for the IF structure. A shoulder is also observed and its contribution can be attributed to a second-order Raman effect [34]. Analyses performed with a laser of 514.5 nm lead to a better differentiation of the two structures (Figure 2.13(a)). In the IF spectrum, two characteristic peaks (modes and Ai ) are significantly shifted. This shift can be attributed to residual strains in the fullerene structure. 

Sourisseau, C., Cruege, F., Fouassier, M. and Alba, M., Second-order Raman effects, inelastic neutron scattering and lattice dynamics in 2H-WS2, Chemical Physics, 150, 1991,281-293. 

We have analyzed the influence of the annealing temperature, structural disorder, and the frequency of a continuous excitation laser radiation Vl on the first- and the second-order Raman spectra of several nanostructured carbon materials including single-wall carbon nanotubes (SWCNT), SWCNT-polymer composites, and nanostructured single-crystalline graphites. Consideration of the high-order nonlinear effects in Raman spectra and anharmonicity of characteristic Raman bands (such as G, G, and D modes) provides important information on the vibration modes and collective (phonon-like) excitations in such ID or 2D confined systems... 

The Raman effect is due to the same vibrations that give rise to the infrared spectrum. Raman scattering describes the inelastic scattering of incident light by certain vibrational transitions (described as Raman active). Note that this is not a fluorescence effect. The molecule is not electronically excited and the incident photon interacts with the vibration of the molecule on a time-scale of the order of 10 seconds. The Raman effect is also weak—except for resonant transitions, no more than one photon in a million is inelastically scattered in this way. Hence the need for powerful sources of monochromatic radiation (lasers) and sensitive detectors (photo-multiplier tubes or charge-coupled devices). 

Cyvin, S. J., Rauch, J. E. and Decius, J. C. (1965) Theory of hyper-Raman effects (nonlinear inelastic light scattering) selection rules and depolarization ratios for the second-order polarizability. 

Not long after the discovery of the stimulated Raman effect in liquids 63> it was also detected in single crystals 64), namely diamond, calcite, and a-sulfur. Only much later could it be shown that the effect can also be observed in crystal powders 651. The stimulated Raman effect 99 > is excited by giant-pulse lasers with a power of several MW. The strongest Raman lines of a substance are amplified until their intensity is of the same order of magnitude as that of the exciting line furthermore second, third, etc. Stokes lines of the fundamentals in question are observed with twice, thrice, etc. the frequency shift. 

The structure of vibration bands of the first and the second order in SWCNT Raman spectra has also been studied for ordered and disordered forms of graphite. This was accomplished by decomposition of the complex spectral bands into constituting components. We found proximity of spectral positions in most of spectral components of the nanotubes and graphite and considerable variation of their intensities. This also demonstrates variation of the electronic polarizabilities and can explain anomalous shifts of the harmonic bands 2vq and 2vd for nanotubes in comparison to corresponding bands of a single crystalline graphite. Narrow width of the low frequency mode Vrbm 160 cm leads to reproduction of the G-band structure in the sum harmonic band Vg+Vrbm" 1750 cm while the complex stmcture of the broad Vp band is remarkably reproduced in the Vq+Vg sum tone. The narrow width of SWCNT s 2vd and 2vg harmonics in the Raman spectra may be related to group synchronism effects [72]. 

Studying the temperature evolution of UV Raman spectra was demonstrated to be an effective approach to determine the ferroelectric phase transition temperature in ferroelectric ultrathin films and superlattices, which is a critical but challenging step for understanding ferroelectricity in nanoscale systems. The T. determination from Raman data is based on the above mentioned fact that perovskite-type crystals have no first order Raman active modes in paraelectric phase. Therefore, Raman intensities of the ferroelectric superlattice or thin film phonons decrease as the temperature approaches Tc from below and disappear upon ti ansition into paraelectric phase. Above Tc, the spectra contain only the second-order features, as expected from the symmetry selection rules. This method was applied to study phase transitions in BaTiOs/SrTiOs superlattices. Figure 21.3 shows the temperature evolution of Raman spectra for two BaTiOs/SrTiOa superlattices. From the shapes and positions of the BaTiOs lines it follows that the BaTiOs layers remain in ferroelectric tetragonal... 

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