Dispersive element electric field

The author has calculated and will publish elsewhere the perturbations of a known system by a force of the form EoF t). As a special case we have the problem of dispersion— namely, an atomic system acted on by a plane wave. In this case we have an electric field o cos 2irv/. If general cylindrical coordinates are chosen with the z direction parallel to the electric field, the expression for an element of the first order perturbation of the 2/ dimensional matrix q is given by ... 

We showed in Section 2.3 that the real and imaginary parts of the electric susceptibility are connected by the dispersion relations (2.36) and (2.37). This followed as a consequence of the linear causal relation between the electric field and polarization together with the vanishing of x(<°) in the limit of infinite frequency to. We also stated that, in general, similar relations are expected to hold for any frequency-dependent function that connects an output with an input in a linear causal way. An example is the amplitude scattering matrix (4.75) the scattered field is linearly related to the incident field. Moreover, this relation must be causal the scattered field cannot precede in time the incident field that excited it. Therefore, the matrix elements should satisfy dispersion relations. In particular, this is true for the forward direction 6 = 0°. But 5(0°, to) does not have the required asymptotic behavior it is clear from the diffraction theory approximation (4.73) that for sufficiently large frequencies, 5(0°, to) is proportional to to2. Nevertheless, only minor fiddling with S makes it behave properly the function... 

For pure elemental semiconductors like silicon, the strong electronic absorption at energies above Eg produces a small non-linear dispersion of the refractive index below Eg in silicon, n = 3.57 near Eg at room temperature (RT) and it steadily decreases to 3.42 for wavelengths near 12 pm and stays close to this value down to radio frequency energies (see also [20]). For these elemental crystals, the dielectric constant at energies below Eg is real and equal to n2. The refractive index is isotropic for cubic crystals, but for crystals with one anisotropic axis, like those of the wurtzite type, the refractive index for the electric field component of the radiation parallel to this axis (n//) is slightly different from that for the component perpendicular to this axis (njJ. 

In polymer 1, the Kerr effect coincides in sign with the Maxwell effect, which means that the orientation of the side chains in an electric field correlates with the direction of the main chain. However, both the small values of K and [ig / Ql] and the absence of dispersion of the Kerr effect show that the chains of polymers 1 and 6 exhibit no high orientational axial and orientational polar orders characteristic of polymers with mesogenic side groups. In these polymers (1 and 6), the Kerr effect is due to small scale chain motion the kinetic elements are much smaller in size and their mobility is much higher than, for example, for polymer 7. 

One very important advantage of FLCPs over amorphous poled polymers is the possibility of phase matching, which is a precondition for efficient SHG. The mismatch of the refractive indices of the fundamental wave and the second harmonic due to the dispersion may be overcome using the birefringence of the FLC material in the geometry shown in Fig. 37 [15]. Due to the C2 symmetry of the unwound smectic C phase (achieved by surface stabilization or by application of a DC electric field along the y direction), the tensor has only four independent elements, which may be denoted in the contracted d tensor notation as... 

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