Polar-field susceptibility

When (Na/3e ) = 1, both polarization and susceptibility go to infinity. At a critical temperature, T, the randomizing effect of temperature is balanced by the orienting effect of the internal field. Under such conditions, Xe is given by the Curie-lVeiss law... 

The medium effects are introduced in terms of s (the dielectric permittivity) or (the susceptibility). At space point f conventional electrostatic expressions relate the electric field strength E(r), the dielectric displacement D(r) and the polarization field P(r) as... 

Since detailed experimental data for ferrofluid susceptibilities in a strong oblique polarizing field (of intensity 10 T and higher) superimposed on which is a weak alternating-current field are not yet readily available, we shall in Section III.E confine ourselves to an illustration of how the weak alternating-current field susceptibilities [Eqs. (Ill), (113), and (116), which incorporate the effect of the fluid carrier] compare favorably with experiment. We shall also demonstrate the effect that a weak polarizing field Ho (0 100 kA/m) has on the susceptibility profiles (Figs. 7, 8, and 9) below. Furthermore, we shall show how... 

The interaction of laser radiation with the medium occurs through the third-order, non-linear, electric susceptibility denoted by and gives rise to an induced polarization field, which acts as a source term in Maxwell s wave equation. On solving the wave equation, one arrives at the following expression for the intensity of the CARS signal ... 

A number of exploitable effects exist, due to the non-linear response of certain dielectric materials to applied electric and optical fields. An applied field, E, gives rise to a polarization field, P, within any dielectric medium. In a linear material, the relationship between P and E may be characterized by a single (first-order, second-rank) susceptibility tensor... 

The main local variables of a spatially distributed pole in the energy of polarization are the polarization field ep,f and the vector of the surface density of polarization charge qp/ sometimes called polarization displacement, which is equal to P/Xe> that is, the polarization vector divided by the differential susceptibility. These vectors are linked by the polarization permittivity that is the combination of the electric permittivity and the reciprocal of the differential electric susceptibility... 

The proportionality constant Xe is called the electric susceptibility of the medium, and materials in which P and E are related linearly in this way are called linear optical materials. The field in the medium at any given time and position (E) can be viewed as the resultant of the polarization field and the electric displacement (D), which is the field that hypothetically would be present in the absence of the polarization. In a vacuum, P is zero and E = D. In cgs units, the field in a linear medium is given by... 

The macroscopic susceptibilities are the coefficients of a series expansion of the polarization field P with respect to the components of the Maxwell electric field E. Given the Maxwell field... 

Macroscopic polarization, 52 Macroscopic polarization field, 53, 54 Macroscopic susceptibility, 33, 35, 53-55 Magnetic dipole moment, 14 Maxwell electric field, 53, 54 Maxwell equation, 53 Maxwell field, 27, 33, 34 Mixed electric magnetic hyper-magnetizabili-ty, 28... 

The classic absorption, scattering, reflection, or refraction, the intensity of the light reaching the detector is proportional to the intensity of the incident radiation. When one or more laser beams propagating in materials are large enough, the induced polarization fields are proportional to the product of the incident fields. The polarization p. induced in an atom or a molecule by an external field E can be written as Eq. (1). Where the vectors of p- and E are related by the tensors a, 3, and 7, which are often referred to as the polarizability, hyperpolarizability, and second hyperpolarizability, respectively. Similarly, the polarization induced in a medium by an optical field, can be represented by a power series in the optical fields [Eiq. (2)] where X " is the nth-order susceptibility. 

Furthennore, the non-oscillating component of the integrand can best be sorted out by going to the complex representation of the total field, the polarization, and the susceptibility. The mathematically pure real quantities in equation (Bl.3.2) can be written in their complex representation as follows ... 

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. 

Another determination of the surface equilibrium entails the use of the coupling of the DC electric field present at charged interfaces with the electromagnetic field, as described in the theoretical section. Integration of the nonlinear polarization over the whole double layer leads to the following expression of the effective susceptibility tensor ... 

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