Electric longitudinal component

Starting from Maxwell s equations with the ansatz of monochromatic, z-propagating fields, E, H Qx i k- co t)), transversal and longitudinal components get decoupled if the refractive index distribution is z-independent. Two physically equivalently meaningful equations for the transversal electric and the transversal magnetic field. 

If A] is phase-free, as discussed in Section III, and in Ref. 15, there are no longitudinal electric field components. This also occurs if A,-3"1 is zero [17]. The B(3) field is then a Fourier sum over modes with operators a qaq and is perpendicular to the plane defined by A and /1<2>. The four-dimensional dual to this term is defined on a time-like surface, following Crowell [17], which can be interpreted as E under dyad vector duality in three dimensions. The ( field vanishes because of the nonexistence of the raising and lowering operators l3 , . The BM is nonzero because of the occurrence of raising and lowering... 

This is clearly a Beltrami equation, but what is more amazing is that the field result (88) describes a solution to the free-space Maxwell equations that, in contrast to standard PWS, the electric (E0) and magnetic (Bo) vectors are parallel [e.g., Eo x Bo = 0, where Eo x Bo = i(E0 A Bo)], the signal (group) velocity of the wave is subluminal (v < c), the field invariants are non-null, and as (91) clearly shows, this wave is not transverse but possesses longitudinal components. Moreover, Rodrigues and Vaz found similar solutions to the free-space Maxwell equations that describe a superluminal (v > c) situation [71]. 

Here and below, we denote Efi, the transverse radiative electric field, by E since the, longitudinal component of E will be associated exclusively with the material charge- density p according to the first Maxwell equation [Eq. (1.1)]. 

Thus, it can be concluded that the Raman peak at 1569cm is sensitive to both the transverse and longitudinal components of the electric field, while the mode al 2100 cni is sensitive only to the longitudinal component and therefore can be screened by the electrons in the conduction band of the carbon chain. This screening can influence both the intensity and the position of this peak. 

In contrast to the plane waves, the field strengths of the multipole radiation can have any direction. In fact, the electric multipole radiation obey the condition -r = 0, while it can have nonzero longitudinal component (S r 0) of the electric field strength [25], In other words, this is the transversal magnetic radiation. In turn, the magnetic multipole field is characterized by the relations... 

We have not taken into consideration electrophoretic motion of polyions [35,39], However, we have already obtained characteristic features of the electric properties of polyelectrolytes in aqueous solution. Electric polarizability components originating from the fluctuations of condensed counterions show smaller concentration and salt dependence, while those due to a diffuse ion atmosphere, by contrast, a larger dependence. Anisotropy of the electrical polarizability Aa is positive without invoking an enhancement of the longitudinal component by the solvent flow. Simulation on the frequency dependence of the electrical polarizability is in progress to study how the... 

The long-wavelength field can be easily found if we take into account that in a medium without external charges the longitudinal component of the induction vector T> vanishes, and the macroscopic electric field is longitudinal, if the retardation, as assumed in the theory of Coulomb excitons, is not taken into account. From this considerations we obtain... 

Since the jp-polarized radiation at cpi 0° has tangential and normal electric field components (1.4.4°), these components will interact with those dipoles within the film that are oriented parallel and perpendicnlar to the snrface, respectively, according to the selection mle (1.27). Fmthermore, under action of the external electric field normal to the surface, the dipoles experience an additional electric field induced by the polarized chemical bonds within the layer. It follows that in the jp-polarized spectra, the band near the longitudinal optical mode vlo will be observed, in addition to the band near vro resulting from the dipoles parallel to the film. In light of the discussion in Section 1.8.2, it is evident that because the dipole oscillations responsible for the vro band are directed along the surface, these oscillations will be quenched by a metal surface and, hence, be absent in p-polarized spectra of films on mefal substrates, as demonstrated in Fig. 3.2. 

To determine the dependence of the diffusion and conductive characteristics of CNTs on the external electric field using the procedure outlined in Ref. [15]. The longitudinal component of the current density j =j has the following form ... 

Waveguide modes are typically classed according to the nature of the electric and magnetic field components Ez and H. These components are called the longitudinal components of the fields. Several types of modes are possible in waveguides. 

Therefore, electrons under the acceleration field due to traveling microwaves are kept accelerating and other electrons under the decelerating electric field of the traveling microwaves are kept decelerating. The longitudinal electric field component of traveling microwaves on the slow-wave transmission hne is expressed by... 

The numerical approach to the calculation of electric polarizabilities requires much higher accuracy of the total SCF energy than in standard applications. The convergence threshold on the density matrix elements was set up as 10In this work we are only interested in the longitudinal component, a, of the polarizability tensor gi, the z-axis being directed along tSe chain. The value of is obtain from the first derivative of the field-dependent dipole moment y(E)jwith respect to E in the limit of zero-field. 

We can separate out the longitudinal and transverse parts of the current (J , J,) and the electric field (E/, E ), with the longitudinal component of the electric field given by... 

Suppose the waveguide is composed of an unbounded uniform medium of refractive index i.e. effectively free space . The modal fields are then found from Maxwell s equations to be the fields of transverse electromagnetic, or TEM, waves propagating in the z-direction parallel to the waveguide axis. Thus, the propagation constant )S = n k, the longitudinal components satisfy e = h = 0, and the transverse electric and magnetic fields are related by... 

Consider an unperturbed fiber with the step profile of Fig. 18-7. The perturbed profile includes the narrow hatched region. Relative to the cylindrical polar directions in Fig. 14-1, the tangential, i.e. azimuthal and longitudinal components and e of the perturbed electric field are continuous across the interfaces at r = r, and r = rj. Hence e = e and e, S e everywhere including the perturbation region. However, since n changes abruptly from n to Hq at the interfaces, the normal, or radial, component e must be discontinuous to ensure continuity of n e. Consequently e differs from e within the perturbation region, the difference... 

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