Electric field oscillating

The interaction of electromagnetic radiation with matter can be explained using either the electric field or the magnetic field. For this reason, only the electric field component is shown in Figure 10.2. The oscillating electric field is described by a sine wave of the form... 

Thus, for X = y, F = 0 which gives rise to planes of zero field strength (Figure 25.2b). At all other positions between the poles, the oscillating electric field (F) causes ions to be alternately attracted to and repelled by the pairs of rods (A, B Figure 25.2). 

As our discussion of scattering proceeds, we shall examine the coupling between the oscillating electrical field of light and the electrons of the scatterer in detail. First, it is useful to consider the interaction of an electric field with matter, as this manifests itself in the dielectric behavior of a substance. This will not only introduce us to the field-matter interaction, but will also provide some relationships which will be useful later. 

When monochromatic radiation falls on a molecular sample in the gas phase, and is not absorbed by it, the oscillating electric field E (see Equation 2.1) of the radiation induces in the molecule an electric dipole which is related to E by the polarizability... 

In the context of discussion of the Raman effect, Equation (5.43) relates the oscillating electric field E of the incident radiation, the induced electric dipole fi and the polarizability a by... 

Answer. The third term in equation (9.11) involves the cube of the oscillating electric field which (cf. Equation 9.13) is given by... 

We have seen above how to calculate polarizabilities and hyperpolarizabilities for statie electric fields. I will consider a simple oscillating electric field... 

We only consider static response properties in this chapter, which arise from fixed external field. Their dynamic counterparts describe the response to an oscillating electric field of electromagnetic radiation and are of great importance in the context of non-linear optics. As an entry point to the treatment of frequency-dependent electric response properties in the domain of time-dependent DFT we recommend the studies by van Gisbergen, Snijders, and Baerends, 1998a and 1998b. 

A beam of light consists of two mutually perpendicular oscillating fields an oscillating electric field and an oscillating magnetic field. 

X-ray diffraction. The mechanism by which atoms diffract or scatter electromagnetic radiation via the coupling of the electron cloud of the atom to the incident oscillating electric field was discussed in the section on SERS. The X-rays scattered by an atom are the resultant of the waves... 

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... 

A molecule must have a permanent dipole moment to be micro-wave active. As it rotates, the changing dipole moment interacts with the oscillating electric field of the electromagnetic radiation, resulting in absorption or emission of energy. This requirement means that homonuclear molecules such as H2 are microwave inactive, but heteronuclear molecules such as SO3, S02, NO and, of course, H20 are active. 

As illustrated in Figure 39a, the application of a symmetrically oscillating electric field E of frequency co makes the molecule respond with an asymmetric polarization (or the wave amplitude of the polarization response in the positive ordinate is different from that in the negative ordinate) in that the electron density can only flow in the direction donor — acceptor, and not vice versa. 

Most of the four above-mentioned properties for Raman spectra can be explained by using a simple classical model. When the crystal is subjected to the oscillating electric field = fioc " of the incident electromagnetic radiation, it becomes polarized. In the linear approximation, the induced electric polarization in any specific direction is given by Pj = XjkEk, where Xjk is the susceptibility tensor. As for other physical properties of the crystal, the susceptibility becomes altered because the atoms in the solid are vibrating periodically around equilibrium positions. Thus, for a particular... 

Let us now analyze the interaction of a light wave with our collection of oscillators at frequency two- In this case, the general motion of a valence electron bound to a nucleus is a damped oscillator, which is forced by the oscillating electric field of the light wave. This atomic oscillator is called a Lorentz oscillator. The motion of such a valence electron is then described by the following differential equation ... 

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