Nonlinear permittivities

The nonlinear part of the susceptibility was introduced into the quasi-linear finite-difference scheme via iterations, so that at any longitudinal point, the magnitude of E calculated at the previous longitudinal point was used as a zero approximation. This approach is better than the split-step method since it allows one to jointly simulate both the mode field diffraction on irregular sections of the waveguide and the self-action effect by introducing the nonlinear permittivity into the implicit finite-difference scheme which describes the propagation of the total field. 

This means that the general rule is that capacitances are not constants, the exception being for a restricted domain and a limited class of materials. Such exceptions are met in electrodynamics where nonlinear permittivities are recognized for some materials (Jonscher 1996), but not yet in gravitation theories. Note that this last assertion must be tempered by the attempts of some astrophysicist to remove the constancy of the gravitational constant in order to decrease or suppress the recourse to dark matter for modeling the composition of the universe (Magueijo 2003 Moffat 2008). 

Hruska CK (1993) Conflicting values of the third-order nonlinear permittivity of a-quartz. J AppI... 

The nonlinear permittivities Bn can then be computed from a sum of Fourier coefficients however, Sn can also be obtained using the approximation... 

Ihble 2 stows a comparison of dielectric behavior in P(VDCN-VAc) with that in PAN and PVAc. P(VDCN-VAc) behaves as a typical noncrystallinc dielectric with a normal relaxation process except for the large linear and nonlinear permittivity. This indicates the existence of local order in the VDCN copolymer, which might be related to the structure shown by the X-ray diffraction results. Moreover, the observed dielectric behavior was discussed by assuming a freely rotating dipole system [42], whose polarization follows the Langevin function as given by... 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

Thin-film dielectrics (Ba0 92Ca108)(Ti0 92Zr0 08)O3 for the thin-film capacitors were prepared using Ba, Ca, and Zr ethoxides and Ti isopropoxide in refluxed methoxyethanol solutions as precursors. Films were deposited on a usual platinized Si substrate. Crystalline thin films after heat treatment at 800°C demonstrated dielectric permittivity of 1200, dielectric loss of0.5%, nonlinear coefficient a = 0.92, and break-down voltage of980 V [1595],... 

A linear dielectric medium is characterized by a linear relation between the polarization density and the electric field, P = e0xE, where eo is the permittivity of free space and x is the electric susceptibility of the medium. A nonlinear dielectric medium, on the other hand, is characterized by a nonlinear relation between P and E, as illustrated in Figure 4.19. 

Figure 5.7 (e) shows a so-called split post resonator, which allows for a highly precise determination permittivity and loss tangent of dielectric sheet materials [5], In addition, it is also considered to be useful for measurements of nonlinear dielectric films. 

This process is partially overlapped with the next process, the j3 relaxation. To analyze the loss permittivity in the subglass zone in a more detailed way, the fitting of the loss factor permittivity by means of usual equations is a good way to get confidence about this process [69], Following procedures described above Fig. 2.42 represent the lost factor data and deconvolution in two Fuoss Kirwood [69] as function of temperature at 10.3 Hz for P4THPMA. In Fig. 2.43 show the y and relaxations that result from the application of the multiple nonlinear regression analysis to the loss factor against temperature. The sum of the two calculated relaxations is very close to that in the experimental curve. 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

In most cases, the propagation equations discussed in this chapter do not require a specific form of material response. However, for the sake of concreteness, as well as for discussion of numerical methods, we want to describe a generic model of nonlinear material response. We consider a nonmagnetic, dispersive medium with relative permittivity e that is a function of the transverse coordinates x, y and of the angular frequency u>... 

Optical saturation in an optical field. Intense li t, whm traversing an isotropic medium, induces in it an optical non-linearity apparent as a dependence of the refractive index on the li t intensity I. The dynamical electric permittivity and magnetic permeability contributing to the nonlinear change in index are, with regard to equations (21) and (23) ... 

Mackay, T.G., Lakhtakia A.. Weiglhofer, W.S. Homogeneisation of isotropic, cubically nonlinear, composite mediums by the strong-permittivity-fluctuation theory third-order considerations. Opt. Commun. 204. 219-228 (2002)... 

Drozd-Rzoska, A., Rzoska, S. J., and Czupiyhski, K. (2000) Phase transitions from the isotropic liquid to liquid ciystalhne mesophases studied by linear and nonlinear static dielectric permittivity, Phys. Rev. E 61, 5355-5360 Rzoska, S. J., Paluch, M., Drozd-Rzoska, A., Paluch, M., Janik, P., Ziolo J., and Czupryhski, K. (2001) Glassy and fluidlike behavior of the isotropic phase of mesogens in broad-band dielectric, Europ. Phys. J. E 7, 387... 

H o permeability of vacuum, o permittivity of vacuum, A cross section of beam, d nonlinear optical constant Apparatus for harmonic generation measurements... 

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