Dipole moment, induced oscillating

Another inherent property of polyacetylene chains, associated with the highly de-locahzed rc-system, is the polarizability in an electromagnetic field. The dipole moment induced by the oscillating electric field of electromagnetic radiation may be expressed as the sum of the hnear polarizabihty and nonlinear higher terms (hy-... 

The simplest approach to the theory of light scattering in general and Raman scattering in particular is to introduce an oscillating electric dipole moment induced in the molecule by the electric field vector JE of the light wave. In cartesian tensor notation, the -component is written... 

The resulting dipole moment induced by the oscillating E-field is just p = —ex co) and the polarizability, a, is defined as... 

The induced dipole moment that oscillates at a particular frequency component is thus given by... 

Finite values of the off-diagonal elements p would imply that the phases of the oscillating electric dipole moments induced in different atoms were coherently related to one another. Such a situation can only be achieved if the atoms are stationary and are interacting with a beam of radiation of high spatial and temporal coherence, as for instance obtained from a laser. 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

When the oscillating electric held of an incident light ray interacts with a molecule, a small oscillating dipole moment is induced in the molecule as a consequence of its polarisability, a. Polarisability itself is a measure of the change in the dipole moment of a molecule induced by an electric held, and in the simplest case, where the electric held E and induced dipole moment p are in the same direction ... 

The exciting radiation, usually laser light, may be of any wavelength. Interaction is not by absorption and only requires the presence of polarizable molecules. The oscillating electric field of the incident radiation E = E0 cos 27xut induces a dipole moment... 

Given the response of a single oscillator to a time-harmonic electric field, the optical constants appropriate to a collection of such oscillators readily follow. The induced dipole moment p of an oscillator is ex. If 91 is the number of oscillators per unit volume, the polarization P (dipole moment per unit... 

In order to relate the dressed state population dynamics to the more intuitive semiclassical picture of a laser-driven charge oscillation, we analyze the induced dipole moment n) t) and the interaction energy V)(0 of the dipole in the external field. To this end, we insert the solution of the TDSE (6.27) into the expansion of the wavefunction Eq. (6.24) and determine the time evolution of the charge density distribution p r, t) = -e r, f)P in space. Erom the density we calculate the expectation value of the dipole operator... 

Figure 6.19 Quantum dynamics simulations for the two distinct situations of selective population of the (a) upper and (b) the lower target state. The frame (iv) shows the population dynamics induced by the shaped laser field pictured in (iii). The remaining panels depict (ii) the oscillations of the laser field together with the induced dipole moment and (1) the induced energetic splitting in the X-A-subsystem along with the accessibility of the target states. Gray backgrounds highlight the relevant time windows that are discussed in the text.

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

Objects having a dipole can be set into rotational motion by applying a torque by means of an electric field [95], Electrorotation is the rotation of particles as a consequence of the induction of dipole moments and torque exertion by a rotating electric field. Coupled electrorotation (CER) uses static external fields which are spatially fixed to induce dipoles in two or more adjacent particles. This creates oscillating components of the electric field, finally resulting in a rotating electric field (for more details, refer to the original literature [95]). 

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. 

---