Radiation fields susceptibility

Up to this point, we have calculated the linear response of the medium, a polarization oscillating at the frequency m of the applied field. This polarization produces its own radiation field that interferes with the applied optical field. Two familiar effects result a change in tlie speed of the light wave and its attenuation as it propagates. These properties may be related directly to the linear susceptibility The index of... 

The polarization P is given in tenns of E by the constitutive relation of the material. For the present discussion, we assume that the polarization P r) depends only on the field E evaluated at the same position r. This is the so-called dipole approximation. In later discussions, however, we will consider, in some specific cases, the contribution of a polarization that has a non-local spatial dependence on the optical field. Once we have augmented the system of equation B 1.5.16. equation B 1.5.17. equation B 1.5.18. equation B 1.5.19 and equation B 1.5.20 with the constitutive relation for the dependence of Pon E, we may solve for the radiation fields. This relation is generally characterized tlirough the use of linear and nonlinear susceptibility tensors, the subject to which we now turn. 

Using this approach, corrosion potentials have been calculated for various components in the heat-transport circuit of a BWR, as shown in Fig. 19, as a function of the concentration of hydrogen added to the feedwater. The calculations predict that the lower plenums and recirculation systems of many BWRs can be protected by hydrogen water chemistry, but that those components that are exposed to high radiation fields and/or high concentration of radiolysis products cannot be protected, at least under full-power operating conditions. Similar calculations have been carried out [46] for in-vessel materials in PWRs, in order to explore the susceptibility of various components to intergranular fracture. 

Another scheme to calculate and interpret macroscopic nonlinear optical responses was formulated by Mukamel and co-workers [112 114] and incorporated intermolecular interactions as well as correlation between matter and the radiation field in a consistent way by using a multipolar Hamiltonian. Contrary to the local field approximation, the macroscopic susceptibilities cannot be expressed as simple functionals of the single-molecule polarizabilities, but retarded intermolecular interactions (polariton effects) can be included. 

The nonlinear interaction of light with matter is useful both as an optical method for generating new radiation fields and as a spectroscopic means for probing the quantum-mechanical structure of molecules [1-5]. Light-matter interactions can be formally classified [5,6] as either active or passive processes and for electric field based interactions with ordinary molecules (electric dipole approximation), both may be described in terms of the familiar nonlinear electrical susceptibilities. The nonlinear electrical susceptibility represents the material response to incident CW radiation and its microscopic quantum-mechanical formalism can be found directly by diagrammatic techniques based on the perturbative density matrix approach including dephasing effects in their fast-modulation limit [7]. Since time-independent (DC) fields can only induce a... 

Nitric acid can be formed by the radiolysis of moist air. This nitric acid will rapidly dissolve in water and cause a decrease in the pH. On the other hand, intermediate products in the air radiolysis process interact rapidly with surfaces and other chemical species in the atmosphere. Furthermore, nitric acid is susceptible to decomposition in a radiation field. It has been difficult, then, to assess the overall effect nitric acid formation by radiolysis will have on solution pH. 

The presence of chirality introduces an additional component in the y direction. This component will rotate the polarization of die second-harmonic field with respect to the polarization of the incident radiation. The amount of optical rotation will depend on the relative magnitude of the chiral and achiral susceptibility components. Furthermore, Py changes sign between the enantiomers... 

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... 

The real and imaginary parts of the refractive index n quantify the scattering and absorption (or amplification) properties of a material- The refractive index is besfl derived from the susceptibility tensor y of the material, defined below, whi j describes the response of a macroscopic "system to incident radiation [212], Spe fically, an incident electric field E(r, t), where r denotes the location in the medium, tends to displace charges, thereby polarizing the medium. The change in dmd(r, the induced dipole moment, from point r to point r + dr is given in terms of th polarization vector P(r, t), defined as... 

The basis of NLO-effects arising from susceptibilities of second order, is the interaction of three electric fields with a material. The practical implementation of optical devices requires strong, coherent and monochromatic radiation and hence, laser technology. Not all of the interacting fields need to be optical fields, however. In devices that make use of the Pockels effect, an externally applied electric field is used to alter reversibly the refractive index of a material. In a second harmonic generation (SHG) process two photons of circular frequency w can be transformed into one photon of frequency Iw. SHG is the NLO effect used most for the evaluation of /3-tensor elements in solution. 

A measurement of the optical conductivity of PAni samples over the range 2 meV to leV is illustrated in Fig. 9.38. The reflection spectra were obtained using a Fourier transform interferometer and a synchrotron radiation source. The Kramers-Kroiiig transformation, with appropriate extrapolation of the data to zero and high energy, was used to extract the complex frequency-dependent conductivity and its real part, the optical conductivity. The optical conductivity is related to the imaginary component of the electric susceptibility, since the power dissipated by an optical field of amplitude E is given by ... 

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