Dipole moments oscillating

The Raman effect can be seen, from a classical point of view, as the result of the modulation due to vibrational motions in the electric field-induced oscillating dipole moment. Such a modulation has the frequency of molecular vibrations, whereas the dipole moment oscillations have the frequency of the external electric field. Thus, the dynamic aspects of Raman scattering are to be described in terms of two time scales. One is connected to the vibrational motions of the nuclei, the other to the oscillation of the radiation electric field (which gives rise to oscillations in the solute electronic density). In the presence of a solvent medium, both the mentioned time scales give rise to nonequilibrium effects in the solvent response, being much faster than the time scale of the solvent inertial response. 

Thus the dipole moment oscillates with three distinct frequencies Vq with amplitude ocqE Vo and Vo + v with much smaller amplitudes, doc/dq)qo E. Therefore we observe a relatively intense beam at one frequency and two very weak beams at frequencies slightly above and below that of the intense one. 

The dipole moment oscillates with the basic frequency of the incident light and in addition. with two other fi equencies the second (2co) and third (3 )) harmonics (SHG and THG, respectively). This is supported by experiments (mentioned in the example at the beginning of the chapter) applying incident light of fi-equency o), we obtain emitted light with frequencies 2o) and 3o). 

Three branches have zero frequency at the T point and are associated with the translation of the entire crystal along any direction in space. These branches are called acoustic modes as the corresponding vibrations behave as acoustic waves. All other branches show finite nonzero frequencies at T and are known as optical modes, because they correspond to unit-cell dipole moment oscillations that can interact with an electromagnetic radiation. Acoustic and optical modes can be identified clearly in Figure 32. 

Equation (36) is plotted in fig, 2 together with C2(<)P for the case (O12-O. It shows that the dipole moment oscillates at the transition frequency but its size increases and decreases at twice the nutation frequency. When the atom is in a well-defined state e) or g) the dipole does not oscillate, there is no emission or absorption at the corresponding times (t = 0 t = ji/Qq, t = 2j[/Qq . ..). 

Even without the external field, the expectation value of the atomic dipole moment oscillates with the eigenfrequency o)ba and the amplitude d -b if the wavefunction of the atomic system can be represented by the superposition (2.65). 

The (monochromatic) electric fields are characterized by Cartesian directions indicated by the Greek letters and by circular optical frequencies, ( i, ( 2, and 0)3. The induced dipole moment oscillates at (0 = 2i cOi. and are such that the p and y values associated with different NLO processes converge towards the same static value. The 0 superscript indicates that the properties are evaluated at zero electric fields. Eq. (2) is not the unique phenomenological expression defining the (hyper)polarizabilities. Another often-applied expression is the analogous power series expansion where the 1/2 and 1 /6 factors in front of the second- and third-order terms are absent. 

For a vibrating bond, the strength of the dipole moment oscillates as a function of time. 

The dipole moment is an electric field surrounding the bond. So as the dipole moment oscillates, the bond is essentially surrounded by an oscillating electric field, which serves as an antenna (so to speak) for absorbing IR radiation. Since electromagnetic radiation itself is comprised of an oscillating electric field, the bond can absorb a photon because the bond s oscillating electric field interacts with the oscillating electric field of the IR radiation. 

Fig. 1.21. A classical picture of the origin of parallel and perpendicular vibrational-rotational bands in the spectra of linear molecules. The band wings result when the rotation changes the orientation of the vibrationally caused dipole moment oscillation. The central peak results when rotation causes no orientation change in the oscillating dipole moment.

The expectation value of the atomic dipole moment oscillates under the influence of the EM field with the eigenfrequency... 

According to O Eqs. 11.88-11.91, in these processes we deal with a perturbation of frequency (o (and a static field in the Pockels effect) and we consider the resulting dipole moment oscillating with frequency 2u>, frequency or or static, respectively. 

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