Susceptibilities electric

The electric susceptibility of a material, denoted x, is a dimensionless physical quantity defined as the ratio of the electric polarization over the electric flux density, according to the following equation  

Therefore, the relation existing between electric susceptibility and relative permittivity is given by  

In fact, when the electric field strength is greater than the value of the interatomic electric field (i.e., 100 to 10,000 MV/m), the relationship between the polarization and the electric field strength becomes nonlinear and the relation can be expanded in a Taylor series  

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As implied by the trace expression for the macroscopic optical polarization, the macroscopic electrical susceptibility tensor at any order can be written in temis of an ensemble average over the microscopic nonlmear polarizability tensors of the individual constituents. 

It can be shown that the electric susceptibility is related to the relative permittivity or dielectric constant e of the particle by the relationship [88]... 

The relative permittivity, the electric susceptibility and the refractive index n are related by... 

The SHG signal intensity, 1(2 ), arising at the liquid-liquid interface is known to be proportional to the square of the second-order nonlinear electric susceptibility, c , at the surface [18,28,29],... 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

We want to introduce the properties of the crystal and of the X-rays and solve f or the electric displacement or flux density, D. Hart gives a careful discussion of the polarisability of a crystal, showing that a sufficient model of the crystal for X-ray scattering is a Fourier sum of either the electron density or the electric susceptibility over all the reciprocal lattice vectors h. Thus the crystal is represented as... 

Note 3 A polymer that exhibits a nonlinear optical effect due to anisotropic electric susceptibilities when subjected to electric field together with light irradiation is called an electro-optical polymer. A polymer that exhibits electro-optical behavior combined with photoconductivity is called a photorefractive polymer. 

There has been considerable interest in theoretical and quantum chemical calculations applied to the bipyridines over the past 25 years. 7i-Electron distributions, electron densities, and molecular orbital calculations on all the bipyridines have been determined, and the results are generally in accord with the known chemical reactions of the molecules.Calculations applied to 2,2 -, 3,3 -, and 4,4 -bipyridines have been correlated with ionization potentials,and reduction potentials ° "and electrical susceptibilities of most of the bipyridines have been determined.The ability of 3,3 - and 4,4 -bipyridines to act as electron-transfer bridges has been calculated. ... 

The electric susceptibility and dielectric constant of ferroelectric substances obey a Curie law dependence on temperature (Equation (9.13) ... 

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... 

Dixon, J. R., 1969. Electric-susceptibility mass of free carriers in semiconductors, in Optical Properties of Solids, S. Nudelman and S. S. Mitra (Eds.), Plenum, New York, pp. 61-83. 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

We will ignore these inhomogenous terms. The polarization vector is going to have contributions from the linear electric susceptibility and the nonlinear electric susceptibility due to the nonlinear response of the atoms ... 

P. K. Anastasovski, Theory of Magnetic and Electric Susceptibilities for Optical Frequencies, Nova Science, New York (1990). 

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

The quantity s/s0 is called the dielectric constant when E is independent of the field, and [(s/s0)— 1] is called the electric susceptibility, whose usual symbol is... 

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