Instantaneous electromagnetic fields

The instantaneous direction of propagation is, of course, perpendicular to the plane defined by the instantaneous electromagnetic fields E and B. But this time-dependent direction need not be parallel to the z axis, physically defined as the direction for the average propagation of energy. Let us illustrate the point with variations of the same simple example of previous section, for additional details see Munera and Guzman [67]. 

Fig. 4.1. Interference of incoming and the reflected X-ray waves inthe triangular region above a flat and thick reflecting substrate. The strength ofthe electromagnetic field is represented on the gray scale by instantaneous crests (white) andtroughs (black). Inthe course of time, the pattern moves from the left to the right [4.21].

The van der Waals force is ubiquitous in colloidal dispersions and between like materials, always attractive and therefore the most common cause of dispersion destabilization. In its most common form, intermolecular van der Waals attraction originates from the correlation, which arises between the instantaneous dipole moment of any atom and the dipole moment induced in neighbouring atoms. On this macroscopic scale, the interaction becomes a many-body problem where allowed modes of the electromagnetic field are limited to specific frequencies by geometry and the dielectric properties of the system. 

For the spectroscopic applications, it would be again instructive to separate the noninertial and inertial components of the electrostatic polarization of the dielectric medium. The first of them corresponds to the electrostatic polarization of the electron charge distribution in the solvent that is supposedly instantaneous as compared to any electronic or conformational transition of the solute. The second component arises from the orientational polarization of the solvent molecules in the electrostatic field of the solute. The noninertial polarization can be described by the optical dielectric permittivity of the solvent that corresponds to the infinite frequency of external electromagnetic field (e Ud) whereas the inertial polarization represents the slow, orientational part of the total dielectric constant of the solvent, s. In order to separate the noninertial polarization, it is helpful to determine the solute charge density as the sum of the respective nuclear and electronic parts... 

The precise form of this correction depends upon the gauge condition used to describe the electromagnetic field. In the Coulomb gauge, which has been employed more often in relativistic atomic structure, the electron-electron interactions come from one-photon exchange process and is sum of instantaneous Coulomb interaction and the transverse photon interaction. 

In all of these cases, it should be emphasized that the photoexcitation process itself is instantaneous. Once the electromagnetic field of the incident radiation arrives at the photocathode or penetrates the semiconductor, electrons are immediately excited at an average rate proportional to energy density but with a random distribution in time. Thus, even a picosecond (10 seconds) pulse of light of energy, Nhv, would produce r]N electrons within the picosecond, but the observed number would have an rms fluctuation of r]N. This, of course, assumes that the active photoexcitation region is smaller in extent than the spatial extent of the optical pulse, in this case, of order 300 /xm. 

The previous nonlinear optical processes for frequency conversion are coherent and essentially instantaneous as they do not involve any dynamics of material excitations and all energy transfer and storage only occur within the electromagnetic field modes material resonances eventually serve to enhance the efficiency of the process. 

In the present OKE experiment, the electromagnetic fields are characterized by the same frequency and wave-vector with different polarization states. Firr-thermore, we can assume the B-0 separation as reported in (2.16). So, neglecting the instantaneous electronic response, considering the time separation between excitation and probe pulses, and verifying the phase matching conditions and the energy conservation, the induced polarization becomes [40]... 

Let us consider the propagation of electromagnetic waves with both fields nonzero E O and B 0. As usual, propagation is parallel to the Poynting vector G, defined in Eq. (17). Evidently, by definition, vector G is perpendicular to both fields E and B. Hence, there cannot exist components of the magnetic field B parallel to the instantaneous direction of propagation G. 

Thus a plot of polarization as a function of the applied field is a straight line whose slope is the linear polarizability, a, of the optical medium (Figure lc). If the field oscillates with some frequency, (i.e., electromagnetic radiation, light), then the induced polarization will have the same frequency if the response is instantaneous (Figure la). Polarization is a vector quantity with both direction and magnitude. 

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